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Google published a groundbreaking research paper about identifying page quality with AI. The details of the algorithm seem remarkably similar to what the helpful content algorithm is known to do.

Google Doesn’t Identify Algorithm Technologies

Nobody outside of Google can say with certainty that this research paper is the basis of the helpful content signal.

Google generally does not identify the underlying technology of its various algorithms such as the Penguin, Panda or SpamBrain algorithms.

So one can’t say with certainty that this algorithm is the helpful content algorithm, one can only speculate and offer an opinion about it.

But it’s worth a look because the similarities are eye opening.

The Helpful Content Signal 1. It Improves a Classifier

Google has provided a number of clues about the helpful content signal but there is still a lot of speculation about what it really is.

The first clues were in a December 6, 2023 tweet announcing the first helpful content update.

The tweet said:

“It improves our classifier & works across content globally in all languages.”

A classifier, in machine learning, is something that categorizes data (is it this or is it that?).

2. It’s Not a Manual or Spam Action

The Helpful Content algorithm, according to Google’s explainer (What creators should know about Google’s August 2023 helpful content update), is not a spam action or a manual action.

“This classifier process is entirely automated, using a machine-learning model.

It is not a manual action nor a spam action.”

3. It’s a Ranking Related Signal

The helpful content update explainer says that the helpful content algorithm is a signal used to rank content.

“…it’s just a new signal and one of many signals Google evaluates to rank content.”

4. It Checks if Content is By People

The interesting thing is that the helpful content signal (apparently) checks if the content was created by people.

Google’s blog post on the Helpful Content Update (More content by people, for people in Search) stated that it’s a signal to identify content created by people and for people.

Danny Sullivan of Google wrote:

“…we’re rolling out a series of improvements to Search to make it easier for people to find helpful content made by, and for, people.

…We look forward to building on this work to make it even easier to find original content by and for real people in the months ahead.”

The concept of content being “by people” is repeated three times in the announcement, apparently indicating that it’s a quality of the helpful content signal.

And if it’s not written “by people” then it’s machine-generated, which is an important consideration because the algorithm discussed here is related to the detection of machine-generated content.

5. Is the Helpful Content Signal Multiple Things?

Lastly, Google’s blog announcement seems to indicate that the Helpful Content Update isn’t just one thing, like a single algorithm.

Danny Sullivan writes that it’s a “series of improvements” which, if I’m not reading too much into it, means that it’s not just one algorithm or system but several that together accomplish the task of weeding out unhelpful content.

This is what he wrote:

“…we’re rolling out a series of improvements to Search to make it easier for people to find helpful content made by, and for, people.”

Text Generation Models Can Predict Page Quality

What this research paper discovers is that large language models (LLM) like GPT-2 can accurately identify low quality content.

They used classifiers that were trained to identify machine-generated text and discovered that those same classifiers were able to identify low quality text, even though they were not trained to do that.

Large language models can learn how to do new things that they were not trained to do.

A Stanford University article about GPT-3 discusses how it independently learned the ability to translate text from English to French, simply because it was given more data to learn from, something that didn’t occur with GPT-2, which was trained on less data.

The article notes how adding more data causes new behaviors to emerge, a result of what’s called unsupervised training.

Unsupervised training is when a machine learns how to do something that it was not trained to do.

That word “emerge” is important because it refers to when the machine learns to do something that it wasn’t trained to do.

The Stanford University article on GPT-3 explains:

“Workshop participants said they were surprised that such behavior emerges from simple scaling of data and computational resources and expressed curiosity about what further capabilities would emerge from further scale.”

A new ability emerging is exactly what the research paper describes.  They discovered that a machine-generated text detector could also predict low quality content.

The researchers write:

“Our work is twofold: firstly we demonstrate via human evaluation that classifiers trained to discriminate between human and machine-generated text emerge as unsupervised predictors of ‘page quality’, able to detect low quality content without any training.

This enables fast bootstrapping of quality indicators in a low-resource setting.

Secondly, curious to understand the prevalence and nature of low quality pages in the wild, we conduct extensive qualitative and quantitative analysis over 500 million web articles, making this the largest-scale study ever conducted on the topic.”

The takeaway here is that they used a text generation model trained to spot machine-generated content and discovered that a new behavior emerged, the ability to identify low quality pages.

OpenAI GPT-2 Detector

The researchers tested two systems to see how well they worked for detecting low quality content.

One of the systems used RoBERTa, which is a pretraining method that is an improved version of BERT.

These are the two systems tested:

OpenAI’s RoBERTa-based GPT-2 detector

Looks for the “statistical signature” of machine-generated content. Uses BERT and GPT-2.

They discovered that OpenAI’s GPT-2 detector was superior at detecting low quality content.

The description of the test results closely mirror what we know about the helpful content signal.

AI Detects All Forms of Language Spam

The research paper states that there are many signals of quality but that this approach only focuses on linguistic or language quality.

For the purposes of this algorithm research paper, the phrases “page quality” and “language quality” mean the same thing.

The breakthrough in this research is that they successfully used the OpenAI GPT-2 detector’s prediction of whether something is machine-generated or not as a score for language quality.

They write:

“…documents with high P(machine-written) score tend to have low language quality.

…Machine authorship detection can thus be a powerful proxy for quality assessment.

It requires no labeled examples – only a corpus of text to train on in a self-discriminating fashion.

This is particularly valuable in applications where labeled data is scarce or where the distribution is too complex to sample well.

For example, it is challenging to curate a labeled dataset representative of all forms of low quality web content.”

What that means is that this system does not have to be trained to detect specific kinds of low quality content.

It learns to find all of the variations of low quality by itself.

This is a powerful approach to identifying pages that are not high quality.

Results Mirror Helpful Content Update

They tested this system on half a billion webpages, analyzing the pages using different attributes such as document length, age of the content and the topic.

The age of the content isn’t about marking new content as low quality.

They simply analyzed web content by time and discovered that there was a huge jump in low quality pages beginning in 2023, coinciding with the growing popularity of the use of machine-generated content.

Analysis by topic revealed that certain topic areas tended to have higher quality pages, like the legal and government topics.

Interestingly is that they discovered a huge amount of low quality pages in the education space, which they said corresponded with sites that offered essays to students.

Google’s blog post written by Danny Sullivan shares:

“…our testing has found it will especially improve results related to online education…”

Three Language Quality Scores

Google’s Quality Raters Guidelines (PDF) uses four quality scores, low, medium, high and very high.

The researchers used three quality scores for testing of the new system, plus one more named undefined.

Documents rated as undefined were those that couldn’t be assessed, for whatever reason, and were removed.

The scores are rated 0, 1, and 2, with two being the highest score.

These are the descriptions of the Language Quality (LQ) Scores:

Text is incomprehensible or logically inconsistent.

Text is comprehensible but poorly written (frequent grammatical / syntactical errors).

Text is comprehensible and reasonably well-written (infrequent grammatical / syntactical errors).

Here is the Quality Raters Guidelines definitions of low quality:

Lowest Quality:

“MC is created without adequate effort, originality, talent, or skill necessary to achieve the purpose of the page in a satisfying way.

…little attention to important aspects such as clarity or organization.

monetization rather than creating original or effortful content to help users.

Filler” content may also be added, especially at the top of the page, forcing users to scroll down to reach the MC.

…The writing of this article is unprofessional, including many grammar and punctuation errors.”

The quality raters guidelines have a more detailed description of low quality than the algorithm.

What’s interesting is how the algorithm relies on grammatical and syntactical errors.

Syntax is a reference to the order of words.

Words in the wrong order sound incorrect, similar to how the Yoda character in Star Wars speaks (“Impossible to see the future is”).

Does the Helpful Content algorithm rely on grammar and syntax signals? If this is the algorithm then maybe that may play a role (but not the only role).

But I would like to think that the algorithm was improved with some of what’s in the quality raters guidelines between the publication of the research in 2023 and the rollout of the helpful content signal in 2023.

The Algorithm is “Powerful”

It’s a good practice to read what the conclusions are to get an idea if the algorithm is good enough to use in the search results.

Many research papers end by saying that more research has to be done or conclude that the improvements are marginal.

The most interesting papers are those that claim new state of the art results.

The researchers remark that this algorithm is powerful and outperforms the baselines.

What makes this a good candidate for a helpful content type signal is that it is a low resource algorithm that is web-scale.

In the conclusion they reaffirm the positive results:

“This paper posits that detectors trained to discriminate human vs. machine-written text are effective predictors of webpages’ language quality, outperforming a baseline supervised spam classifier.”

The conclusion of the research paper was positive about the breakthrough and expressed hope that the research will be used by others.

There is no mention of further research being necessary.

This research paper describes a breakthrough in the detection of low quality webpages.

The conclusion indicates that, in my opinion, there is a likelihood that it could make it into Google’s algorithm.

Because it’s described as a “web-scale” algorithm that can be deployed in a “low-resource setting” means that this is the kind of algorithm that could go live and run on a continual basis, just like the helpful content signal is said to do.

We don’t know if this is related to the helpful content update but it’s a certainly a breakthrough in the science of detecting low quality content.

Citations Google Research Page:

Generative Models are Unsupervised Predictors of Page Quality: A Colossal-Scale Study

Download the Google Research Paper

Generative Models are Unsupervised Predictors of Page Quality: A Colossal-Scale Study (PDF)

Featured image by Shutterstock/Asier Romero

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Protected Content Cannot Be Viewed On This Device

Screen Mirroring is a feature that lets users share the screen of one device with another device by using wireless technology. For example, if your Android smartphone and your computer support the Screen Mirroring feature, you can share the screen of your smartphone with your computer and watch the content on a larger screen. If you see the “Protected content cannot be viewed on this device” error message while mirroring your screen to your computer, the solutions provided in this article will help you.

Protected content cannot be viewed on this device

Use the following solutions to fix the “Protected content cannot be viewed on this device” error on your Windows device.

Check if your system supports the Screen Mirroring technology

Check your network connection

Is your Network adapter enabled?

Disable your Firewall temporarily

Turn on the Media Streaming

Update or reinstall the Network and Display drivers

Uninstall and reinstall the Wireless Display feature

Let’s see all these fixes in detail.

1] Check if your system supports the Screen Mirroring technology

Before you use any of the solutions provided in this article, it is necessary to check if your system supports the Screen Mirroring feature or not. You can check this by using the DirectX Diagnostics Tool.

Follow the steps written below:

Open the Run command box (Win + R).

The DirectX Diagnostic Tool will appear on your screen.

Name your file or save it with the default name.

2] Check your network connection

To cast your screen from one device to another by using the Screen Mirroring technology, both of your devices should be connected to the same network. Check if both your devices are connected to the same network or not.

Also, check if your laptop is in flight mode or not. The flight mode disconnects a laptop from all wireless connections automatically. If you are in flight mode, turn it off.

3] Is your Network adapter enabled?

The root cause of this error message is the network issue. Hence, you have to troubleshoot your network in order to fix this problem. The network adapter is responsible for connecting your system to the wireless network, like WiFi. If it is disabled, you will not be able to connect to any WiFi signal until you enable it.

The steps are provided below:

Open the Control Panel.

Select Category in the View by mode.

After enabling the WiFi adapter, your system will connect to your WiFi network and you should be able to cast your screen.

4] Disable your Firewall temporarily

A Firewall is also one of the causes of the “Protected content cannot be viewed on this device” error on a PC while casting the screen. Temporarily disable your Firewall and see if it helps. If this works, you have to allow Cast through Windows Firewall. The steps for the same are explained below:

Select the same option from the search results.

Select the following options:

Cast to Device functionality

Connected Devices Platform

Select both the Private and Public checkboxes next to these options.

If you are using a third-party Firewall, contact their support to know how to allow a program.

5] Turn on the Media Streaming

Media Streaming allows users to send videos, music, and pictures to other computers and devices connected to the same network. You may not be able to use the Screen Mirroring feature on Windows 11/10 if this feature is turned off. The following steps will help you enable Media Streaming on Windows 11/10:

Open the Control Panel and switch your view to the Category mode.

Select Media streaming options from the left side.

After performing the above steps, check if the issue persists.

6] Update or reinstall the Network and Display drivers

Corrupted or outdated device drivers cause problems on a Windows device. Hence, it is suggested that all your device drivers should be up to date. The issue might also be occurring due to corrupted wireless or display drivers. Open the Optional Updates page in Windows 11/10 Settings and see if any update for your drivers is available. If yes, install it.

If an update is not available there, uninstall your Network and Display drivers, and reinstall them. After uninstalling the Network driver, you will not be able to access the internet. Therefore, first, visit the official website of the manufacturer and then download the latest version of the Network and Display drivers. After that, follow the steps written below:

Open the Device Manager.

Expand the Display adapters and Network adapters nodes.

Uninstall your display and WiFi divers.

Run the installer files to install these two drivers again. If the drivers are in INF format, use the Device Manager to install them.

7] Uninstall and reinstall the Wireless Display feature

If the issue still persists, uninstall and reinstall the Wireless Display feature. In Windows 11/10. Wireless Display is a built-in optional feature. Hence, users can install it if they want to do so. Uninstalling and reinstalling this feature can fix the issue. Go through the following instructions:

Open Windows 11/10 Settings.

Scroll down and locate Wireless Display and uninstall it.

Once you uninstall it, restart your computer.

After restarting your computer, install Wireless Display again via Optional features. This should help.

Read: How to improve Wireless Network Signal on Windows.

How do you fix protected content cannot be viewed on this device?

If you see the “Protected content cannot be viewed on this device,” first, check if your device supports Screen Mirroring or Miracast technology. If yes, it may be the fault of your display and network drivers. We have explained some fixes in this article to resolve this issue.

Why won’t my computer connect to my wireless display?

To connect your computer to your wireless display, make sure that both devices are connected to the same network. Also, it might be the fault of your network driver. Update or reinstall your network drivers. You can also use the solutions provided in this article to fix the issue.

Read next: Wireless Display not working on Windows.

New Youtube Content Age Restrictions & This Week’s Digital Marketing News

This week on Marketing O’Clock, Greg Finn, Mark Saltarelli, and Christine “Shep” Zirnheld discuss the biggest digital marketing news of the week along with insights and hot takes from the SEO and PPC communities.

Plus, marketers are going to be really thirsty ones they go back to the office.

LinkedIn Stories have finally launched and are sure to replace the water cooler in the hearts and minds of professionals.

If you’re unable to catch the episode on Spotify, be sure to watch the video version on the Search Engine Journal YouTube channel.

YouTube announced new enhancements to its age-restricted content policies.

Using automated tools to detect when videos are inappropriate, more YouTube videos will be flagged and users will have to create an account and confirm their age to watch.

None of the policies are changing, but creators whose inappropriate content went unnoticed before may see more videos flagged.

If a creator thinks their YouTube video was misclassified as inappropriate, they can request a human review of their content and it may be overridden.

Ahrefs Webmaster Tools

Ahrefs announced new Webmaster Tools that are free to all content creators.

The tools can monitor your site’s SEO health, give you more insight into your backlinks, and help you gain a better understanding of keywords that bring traffic to your site.

Ahrefs confirmed that the data collected from sites that are verified through Google Search Console may be used to improve Ahrefs CTR and Search Volume forecasting tools, but Webmasters can also choose to verify through a DNS record, HTML file, or HTML tag.

If you couldn’t make it to HubSpot’s virtual Inbound event this year, you’re in luck!

The team breaks down some of the most exciting new features announced at the event, including an enterprise-level CRM, new sales engagement tools, a new sales analysis tool, connected CPQ tools, and the ability to add free non-marketing contacts to the system

Google is further enhancing its local campaigns to emphasize online-offline purchases.

New features include Google My Business service attributes, a “Pick up later” option for items that are currently out of stock but will be restocked, and smart bidding optimization for in-store sales.

LinkedIn launched a redesigned interface this week with some enhanced features, including a new and improved design, better search results, and new messaging features.

The redesign also comes with the long-awaited LinkedIn stories feature with a question of the day and localized stickers.

In our take of the week segment, James Svoboda shared an extremely useful Google Ads recommendation he found in the account of his pest control client.

New Keyword Recommendation in a Pest Control account today.

— James Svoboda (@Realicity) September 22, 2023

Then, we share an ICYMI from James Webster for all the non-branded-believers out there.

Wherever you sit on the whole brand bidding debate you can’t argue with this data below 🤓

— James Webster (@PPC_Webster) September 18, 2023

We answer your burning digital marketing questions during our lightning round segment:

Who should follow the new Google Web Creators blog?

What kind of person would use voice search on a desktop?

When your Google Ads campaigns may have magically stopped running last week.

Where you can find the Conversion column in Google Ads if it’s missing.

Why TikTok’s time in the U.S still hasn’t come to an end.

How SMBs can leverage the new Facebook Business Suite.

If you enjoyed the show, be sure to head over to chúng tôi to read the full show notes and subscribe.

Featured Image Credit: Cypress North

The Pixel 5 Is Google’s Smartest Phone Since The Nexus 5

When Google unveiled the Pixel 5 alongside the Pixel 4a 5G at its Launch Night In event on September 30, I was perplexed. On paper and in pictures, the $699 Pixel 5 made little sense compared to the $499 Pixel 4a 5G, not to mention the Pixel 4 XL.  I struggled to understand why Google made a smaller phone with very similar specs for more money.

Michael Simon/IDG

A hole-punch camera helps Google keep the bezels nice and uniform on the Pixel 5.

I also get what Google is trying to do. Google is calling it “the ultimate 5G Google phone,” but its focus isn’t on gimmicky features like Motion Sense or Active Edge, or even niche camera tricks that show off Google’s AI prowess. Rather, the Pixel 5 is about taking the high-end Pixel experience and distilling it in a smart and stylish package that challenges the very definition of a flagship.

A design without compromises

Much like the Galaxy S20 and S20 FE, the Pixel 5 and 4a are extremely similar phones. Both have a small hole-punch camera in the upper left corner that looks a lot better than the Pixel 4’s giant forehead or the 3 XL’s notch.

The Pixel 5 has subtle enhancements that give it an almost luxurious feel. The aluminum back, Simply Sage color, and chrome power button all add a touch of luxury compared to the plastic 4a. It doesn’t quite feel as metallic as the original Pixel duo to the paint over the wireless-charging-friendly plastic, but it has a very nice texture. It’s downright Apple-like, a comparison I never thought I’d make for a Pixel phone. It’s like the iPhone 11 versus the Pro, or the XR versus the XS. 

Michael Simon/IDG

The camera bump is a lot less bumpy on the Pixel 5.

The Pixel 5 is also the first Android phone I’ve used that actually has uniform bezels around the screen. Google is using a flexible OLED to bend the display under itself and reduce the chin, a surprising and impressive bit of engineering for a phone that doesn’t cost a thousand bucks. While it seems like a small thing, once you turn it on for the first time, you won’t look at another Android phone the same way. Even the Galaxy Note 20 Ultra doesn’t have quite the same visual appeal after switching over from the Pixel 5.

Altogether, the $699 Pixel 5 is the first phone Google has made that actually feels like a premium device. At just $200 more than the Pixel 4a 5G, it’s a smart addition to the lineup.

The same but different

The Pixel 5 has the same Snapdragon 765G processor as the Pixel 4a 5G, but overall, the Pixel 5 feels like the faster phone. That’s because it has a bit more RAM (8GB vs 6GB) and a faster display (90Hz vs 60Hz), more seemingly small changes that make a big difference.

Michael Simon/IDG

The chrome power button brings a touch of class to the Pixel 5.

But what really gives the Pixel 5 its edge over other phones in its class (and higher, to be honest), as always, is its camera. The Pixel 5 has the same general dual-camera array as the Pixel 4 XL, though the secondary telephoto lens has been swapped out for an ultra-wide one. It’s something of a matter of preference, though I’d personally like both of them in the Pixel 6. But even with a different lens, the results aren’t categorically different from those of the Pixel 5 versus the 4XL. Photos take a touch longer to process due to the slower CPU, but for the most part, the experience is very similar to that of the previous Pixels.

Michael Simon/IDG

The back of the Pixel 5 isn’t quite metallic, but it has a nice texture.

The feature is Android

As expected, the Pixel 5 ships with Android 11 on board, and it feels very much like Google designed it strictly for the new Pixels. The gesture navigation feels better than ever with less bottom bezel, and the optimizations make the Pixel 5 feel like a phone with a much faster chip and much bigger battery. A new Extreme Battery Saver mode will help your Pixel last for up to two days by disabling features, throttling the processor, and limiting notifcations by prioritizing apps.

Michael Simon/IDG

The Pixel 5 dispenses of the ugly chin that previous Pixel phones had.

With the Pixel 5, Android is the premium feature. It reminds me of the last great Nexus phone, the Nexus 5. At the time it was the launch device for Android 4.4 KitKat, and it showcased the new design, improved performance, and Google now Launcher. It wasn’t flashy or over-the-top, but it got the job done. 

And so it is with the Pixel 5. I’ll get into the camera and performance in my full review, but on a high level, Google dispensed with the gimmicks and focused on the things that matter. We finally have a true alternative to the Galaxy S20 and iPhone 12 that leans on the things Google does best. It could lead to some truly impressive phones to come.

Topological Sort: Python, C++ Algorithm Example

What is Topological Sort Algorithm?

Topological Sorting is also known as Kahn’s algorithm and is a popular Sorting Algorithm. Using a directed graph as input, Topological Sort sorts the nodes so that each appears before the one it points to.

This algorithm is applied on a DAG (Directed Acyclic Graph) so that each node appears in the ordered array before all other nodes are pointed to it. This algorithm follows some rules repeatedly until the sort is completed.

To simplify, look at the following example:

Directed Graph

Here, we can see that “A” has no indegree. It means the edge that points to a node. “B” and “C” have a pre-requisite of “A”, then “E” has a pre-requisite of “D” and “F” nodes. Some of the nodes are dependent on other nodes.

Here’s another representation of the above Graph:

Dependency of each node (Linear Ordering)

So, when we pass the DAG (Directed Acyclic Graph) to the topological sort, it will give us an array with linear ordering, where the first element has no dependency.

This example shows a graph with a cycle:

Here’re the steps to do this:

Step 1) Find the node with zero incoming edges, a node with zero degrees.

Step 2) Store that zeroes in-degree node in a Queue or Stack and removes the node from the Graph.

Step 3) Then delete the outgoing edge from that node.

This will decrement the in-degree count for the next node.

Topological ordering requires that the graph data structure will not have any cycle.

A graph will be considered a DAG if it follows these requirements:

One or more nodes with an indegree value of zero.

Graph doesn’t contain any cycle

As long as there’re nodes in the Graph and the Graph is still DAG, we will run the above three steps. Otherwise, the algorithm will fall into the cyclic dependency, and Kahn’s Algorithm won’t be able to find a node with zero in-degree.

How Topological Sort Works

Here, we will use “Kahn’s Algorithm” for the topological sort. Let’s say we have the following Graph:

Here’re the steps for Kahn’s Algorithm:

Step 1) Calculate the indegree or incoming edge of all nodes in the Graph.


Indegree means the directed edges pointing to the node.

Outdegree means the directed edges that come from a node.

Here’s the indegree and outdegree of the above Graph:

Step 2) Find the node with zero indegrees or zero incoming edges.

The node with zero indegree means no edges are coming toward that node. Node “A” has zero indegrees, meaning there’s no edge pointing to node “A”.

So, we will do the following actions:

Remove this node and its outdegree edges (outgoing edges)

Place the node in the Queue for ordering.

Update the in-degree count of the neighbor node of “A.”

Step 3) We need to find a node with an indegree value of zero. In this example, “B” and “C” have zero indegree.

Here, we can take either of these two. Let’s take “B” and delete it from the Graph.

Then update the indegree values of other nodes.

After performing these operations, our Graph and Queue will look like the following:

Step 4) Node “C” has no incoming edge. So, we will remove node “C” from the Graph and push it into the Queue.

We can also delete the edge that is outgoing from “C”.

Now, our Graph will look like this:

Step 5) We can see that nodes “D” and “F” have the indegree of zero. We will take a node and put it in the Queue.

Let’s take out “D” first. Then the indegree count for node “E” will be 1. Now, there’ll be no node from D to E.

We need to do the same for node “F”, our result will be like the following:

Step 6) The indegree (ingoing edges) and outdegree (outgoing edges) of node “E” became zero. So, we have met all the pre-requisite for node “E”.

Here, we l put “E” at the end of the Queue. So, we don’t have any nodes left, so the algorithm ends here.

Pseudo Code for Topological Sorting

Here’s the pseudo-code for the topological sort while using Kahn’s Algorithm.

function TopologicalSort( Graph G ): for each node in G: calculate the indegree start = Node with 0 indegree G.remove(start) topological_list = [start] While node with O indegree present: topological_list.append(node) G.remove(node) Update Indegree of present nodes Return topological_list

Topological sort can also be implemented using the DFS (Depth First Search) method. However, that approach is the recursive method. Kahn’s algorithm is more efficient than the DFS approach.

C++ Implementation of Topological Sorting

using namespace std; class graph{ int vertices; public: graph(int vertices){ } void createEdge(int u, int v){ adjecentList[u].push_back(v); } void TopologicalSort(){

for(int i=0;i<vertices;i++){ for(itr=adjecentList[i].begin(); itr!=adjecentList[i].end();itr++){ indegree_count[*itr]++; } } for(int i=0; i<vertices;i++){ if(indegree_count[i]==0){ Q.push(i); } } int visited_node = 0; while(!Q.empty()){ int u = Q.front(); Q.pop(); order.push_back(u);

for(itr=adjecentList[u].begin(); itr!=adjecentList[u].end();itr++){ if(–indegree_count[*itr]==0){ Q.push(*itr); } } visited_node++; } if(visited_node!=vertices){ cout<<“There’s a cycle present in the Graph.nGiven graph is not DAG”<<endl; return; } for(int i=0; i<order.size();i++){ cout<<order[i]<<“t”; } } }; int main(){ graph G(6); G.createEdge(0,1); G.createEdge(0,2); G.createEdge(1,3); G.createEdge(1,5); G.createEdge(2,3); G.createEdge(2,5); G.createEdge(3,4); G.createEdge(5,4); G.TopologicalSort(); }

Output: 0 1 2 3 5 4 Python Implementation of Topological Sorting from collections import defaultdict class graph: def __init__(self, vertices): self.adjacencyList = defaultdict(list) self.Vertices = vertices # No. of vertices # function to add an edge to adjacencyList def createEdge(self, u, v): self.adjacencyList[u].append(v) # The function to do Topological Sort. def topologicalSort(self): total_indegree = [0]*(self.Vertices) for i in self.adjacencyList: for j in self.adjacencyList[i]: total_indegree[j] += 1 queue = [] for i in range(self.Vertices): if total_indegree[i] == 0: queue.append(i) visited_node = 0 order = [] while queue: u = queue.pop(0) order.append(u) for i in self.adjacencyList[u]: total_indegree[i] -= 1 if total_indegree[i] == 0: queue.append(i) visited_node += 1 if visited_node != self.Vertices: print("There's a cycle present in the Graph.nGiven graph is not DAG") else: print(order) G = graph(6) G.createEdge(0,1) G.createEdge(0,2) G.createEdge(1,3) G.createEdge(1,5) G.createEdge(2,3) G.createEdge(2,5) G.createEdge(3,4) G.createEdge(5,4) G.topologicalSort() Output: [0, 1, 2, 3, 5, 4] Cyclic Graphs of Topological Sort Algorithm

A graph containing a cycle can’t be topologically ordered. As the cyclic Graph has the dependency in a cyclic manner.

For example, check this Graph:

This Graph is not DAG (Directed Acyclic Graph) because A, B, and C create a cycle. If you notice, there’s no node with zero in-degree value.

According to Kahn’s Algorithm, if we analyze the above Graph:

Find a node with zero indegrees (no incoming edges).

However, in the above Graph, there’s no node with zero in degrees. Every node has an in-degree value greater than 0.

Return an empty queue, as it could not find any node with zero in degrees.

We can detect cycles using the topological ordering with the following steps:

Step 1) Perform topological Sorting.

Step 2) Calculate the total number of elements in the topologically sorted list.

Step 3) If the number of elements equals the total number of vertex, then there’s no cycle.

Step 4) If it’s not equal to the number of vertices, then there’s at least one cycle in the given graph data structure.

Complexity Analysis of Topological Sort

There are two types of complexity in algorithms. They’re

Time Complexity

Space Complexity

These complexities are represented with a function that provides a general complexity.

Time Complexity: All time complexity is the same for Topological Sorting. There are worst, average, and best-case scenarios for time complexity.

The time complexity for topological Sorting is O(E + V), here, E means the number of Edges in the Graph, and V means the number of vertices in the Graph.

Let’s break through this complexity:

Step 1) At the beginning, we will calculate all the indegrees. To do that, we need to go through all the edges, and initially, we will assign all V vertex indegrees to zero. So, the incremental steps we complete will be O(V+E).

Step 2) We will find the node with zero indegree value. We need to search from the V number of the vertex. So, the steps completed will be O(V).

Step 3) For each node with zero indegrees, we will remove that node and decrement the indegree. Performing this operation for all the nodes will take O(E).

Step 4) Finally, we will check if there is any cycle or not. We will check whether the total number of elements in the sorted array is equal to the total number of nodes. It will take O(1).

So, these were the individual time complexity for each step of the topological Sorting or topological ordering. We can say that the time complexity from the above calculation will be O( V + E ); here, O means the complexity function.

Space Complexity: We needed O(V) spaces for running the topological sorting algorithm.

Here are the steps where we needed the space for the program:

We had to calculate all the indegrees of nodes present in the Graph. As the Graph has a total of V nodes, we need to create an array of size V. So, the space required was O(V).

A Queue data structure was used to store the node with zero indegree. We removed the nodes with zero indegree from the original Graph and placed them in the Queue. For this, the required space was O(V).

The array is named “order.” That stored the nodes in topological order. That also required O(V) spaces.

These were the individual space complexity. So, we need to maximize these spaces in the run time.

Space complexity stands for O(V), where V means the number of the vertex in the Graph.

Application of Topological Sort

There’s a huge use for Topological Sorting. Here are some of them:

It is used when Operating system needs to perform the resource allocation.

Finding a cycle in the Graph. We can validate if the Graph is DAG or not with topological sort.

Sentence ordering in the auto-completion apps.

It is use for detecting deadlocks.

Different type of Scheduling or course scheduling uses the topological sort.

Resolving dependencies. For example, if you try to install a package, that package might also need other packages. Topological ordering finds out all the necessary packages to install the current package.

Linux uses the topological sort in the “apt” to check the dependency of the packages.

Why Your Freelance Content Marketer Is Letting You Down

The most successful SMBs recognize that at some point they’ll need to expand and delegate certain tasks, like content marketing. Creating and promoting content for your business is essentially a full-time job. It starts small when you initially deploy it, but it doesn’t take long for it to grow.

Here are some of the common reasons why freelance content marketers could be disappointing you, along with tips for finding one that will exceed your expectations:

1. Difficulty Hitting Volume Needs

A brand that gradually incorporates content marketing into its strategy is likely focused on writing just a little bit of content initially. It usually starts with blog posts or emails, or even content marketing ebooks. If the content gains traction and the business grows, the frequency and variety of content should increase along with the growing demand from readers.

Initially, a freelance content marketer should have the capacity to manage smaller content needs on their own. As your business grows, they may not be able to juggle all of your projects and assignments – especially if they’re working with other clients and their schedule is already pretty full.

It can be frustrating to spend time creating deployment plans for content, only to find out that your content writer has no availability during that time. At some point, you should consider either bringing on additional content marketers and writers, or moving your content production over to an agency that won’t have any trouble meeting your content volume needs.

2. Trouble with Specializations

Brands utilize content in a lot of forms, and there are dozens of content formats you can use for marketing. As your content needs expand, you’ll need to lean more heavily on your content marketer for a wider variety of projects.

Unfortunately, it’s not uncommon for freelance content marketers to specialize only in certain types of content or in a very narrow niche. Those who have broader skill sets may still lack the experience needed to produce a type of content you need, such as an infographic. That certainly doesn’t mean they’re incapable of handling the project for you, but working on new projects that are outside their scope may take a bit more time to complete.

There are also quality concerns involved with inexperienced freelancers, compared to what an established content agency could provide with a staff of experienced writers and marketers.

3. Maintaining Momentum

In all the time I’ve spent researching content, I’ve come across countless microsites and branded content built around one-off campaigns. Seeing all that great content abandoned after its usefulness for the brand ran its course is particularly saddening.

Wasted content opportunities are often the result of a mindset where companies are solely focused on launching the campaign and barreling toward the finish line. Once the campaign is over, there’s no strategy to move forward with the content created before the launch, so they just leave it stagnant in forgotten pockets of the internet.

In the event you do want to move forward and maintain that campaign’s momentum, you would be hard-pressed to do so with a freelance content marketer. Trying to maintain momentum across multiple campaigns is quite a challenge since your freelancer has a limited number of working hours in the day and they can only produce so much content within that timeframe.

If you want to build lasting campaigns while maintaining your editorial calendar across the board, don’t overwhelm your freelance content writer with this massive task. Instead, consider developing a larger content marketing crew to balance your content production and prevent your current writer from burning out.

4. Inability to Show ROI

There’s a pervasive myth in our industry that says it’s difficult to show returns on content marketing efforts. Honestly, my head might explode if I keep hearing this. It’s completely possible for you to tie content to every stage of the buyer’s journey and measure your returns.

The problem is, if you feel like your freelance content marketer should be the one responsible for showing those returns, then you might feel disappointed with the results.

Your content marketer’s primary role is help you develop strategies for content marketing and produce content as a part of that strategy. Unless your agreement specifically states that they’re responsible for metrics and reporting, and for hitting specific returns, then this isn’t really in their wheelhouse.

This shouldn’t be your largest concern when it comes to content marketing, anyway. The return on your investment will be mediocre at best if you don’t give the talented people you hire the freedom to create masterful stories that connect your audience to your brand.

5. Critical Dependability

Brands often want to form close relationships with those who handle their content marketing. A good relationship means the freelancer will have a thorough understanding of the company’s style guide – voice, mission, values, and brand position – and that insight will shine through in the marketing content they produce for the brand.

If something critical or last-minute comes up, like a press release or a topic that must be covered quickly, you want to be able to get content up and running right away.

When you work with a freelance content marketer however, you may find yourself at the mercy of their limited schedule. Even if they have few or no other clients taking up time throughout their day, they may not be working at the moment or maybe they left the house on any given day.

Trying to find a freelance content marketer who is just as responsive as a well-staffed content marketing agency is a fruitless task, so your alternatives are to hire more freelancers or sign up with an agency to insure you won’t miss deadlines in the future.

6. Limitation on Distribution

By definition, a content marketer is primarily a distributor who sits at the intersection of content, marketing, SEO, social, and PR. Their goal is to make the content go farther. Freelance content marketers have evolved to offer more services to their clients, and in many cases, they perform the actual researching and writing of content in addition to distributing and promoting it.

A great content marketer is highly skilled in multiple areas, including writing, domain or industry expertise, and promotion or networking skills.

At the far end of the spectrum, contrary to the previously-mentioned textbook definition sits the other type of content marketer, who is predominantly a writer but not much of a distributor.

Promotion and distribution is a critical part of content marketing. Even the best content with maximum value for your audience won’t gain traction if it’s not being promoted. Therein lies a major source of frustration for business owners who invest in content marketing but never see increases in traffic or engagement.

This is why it’s so important to find a freelance content marketer or agency that is capable of handling the promotion of the content after it goes live. This includes:

Understanding the channels used by the audience for targeted promotion

Leveraging extra distribution channels for pushing out content

Utilizing tools for promotion and distribution such as chúng tôi and even Buffer

Finding and promoting to influencers using tools like chúng tôi and NinjaOutreach

Repurposing content in a variety of formats to expand reach into different audience segments

7. Strategic Pivoting

A majority of marketers struggle to create engaging content. If you find yourself among that group, with limited engagement on some or most of your content, realize that you’re not alone.

You shouldn’t feel let down by your freelance content marketer over this, since not every piece of content you produce will knock it out of the ballpark. Still, you want a content marketer or agency that knows how to pivot if the current strategy is floundering.

The ability to analyze why content topics may have done poorly and implement ways to recover from that is a critical asset that you’ll want to rely on when it comes to your content marketing team.


There’s a vast, overarching problem of quality when working with an individual freelance marketer. You’re more likely to get reduced quality in strategy, as they tend to focus on the writing and not the planning. You’re also not likely to see a quality approach to research, writing, and distribution among your average freelance writer.

If you feel let down by the performance of your current content marketer, it doesn’t necessarily have to mean the end of a relationship. Examine the issues, uncover the potential causes of the problem, and get back on track.

Sometimes, your company may just be growing beyond what a freelancer can reasonably handle, which means it could be time to upgrade to an agency that can handle your volume and needs.

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