{"id":181616,"date":"2024-03-13T09:10:00","date_gmt":"2024-03-13T08:10:00","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=181616"},"modified":"2024-03-06T21:49:45","modified_gmt":"2024-03-06T20:49:45","slug":"decomposition-tree-understanding-and-utilizing-its-power","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/decomposition-tree-understanding-and-utilizing-its-power","title":{"rendered":"Decomposition Tree: Understanding and Utilizing its Power"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"181616\" class=\"elementor elementor-181616\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-700ad3b e-flex e-con-boxed e-con\" data-id=\"700ad3b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-362ce4a elementor-widget elementor-widget-heading\" data-id=\"362ce4a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">In graph theory, a decomposition tree is a decomposition of a graph into separators, connected in a tree. Proposed by Paul Seymour and Neil Robertson in their theory of graph minors, it is seen as a key concept offering a unique perspective for solving a variety of problems.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9ce8ad6 elementor-widget elementor-widget-text-editor\" data-id=\"9ce8ad6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>So what does<strong> tree decomposition or decomposition tree mean in data science?<\/strong> Find out in this article.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6a31654 e-flex e-con-boxed e-con\" data-id=\"6a31654\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a48f335 elementor-widget elementor-widget-heading\" data-id=\"a48f335\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">What is tree decomposition?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a2a93b2 elementor-widget elementor-widget-text-editor\" data-id=\"a2a93b2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>A <strong>tree decomposition<\/strong> of a graph consists in dividing the graph into substructures called &#8220;trees&#8221;. Each tree structure is associated with a set of vertices and represents a coherent region of the graph. Trees are then<strong> linked by specific relationships, creating an overall tree structure of the graph.<\/strong><\/p><p>To better understand tree decomposition, we also need to consider its components:<\/p><ul><li><strong>Local trees:<\/strong> each local tree consists of a set of vertices and their adjacent edges. These trees represent coherent subgraphs of the global graph.<\/li><li><strong>Separators:<\/strong> Separators are the sets of vertices that separate different tree structures. They act as connecting points between local trees, helping to build the tree structure.<\/li><li><strong>Connecting edges:<\/strong> These edges link separators and local trees, creating the hierarchy of the tree decomposition.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6e3754d elementor-widget elementor-widget-image\" data-id=\"6e3754d\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/09\/decomposition-tree-1.jpg\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8b257dc e-flex e-con-boxed e-con\" data-id=\"8b257dc\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-12e8273 elementor-widget elementor-widget-heading\" data-id=\"12e8273\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Why use tree decomposition?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c0cbc4e elementor-widget elementor-widget-text-editor\" data-id=\"c0cbc4e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>This method can be used to solve a combinatorial optimization problem where the graph is part of the data. The idea is to solve the initial problem on each of the subsets of the decomposition, then merge the results into the tree using dynamic programming methods.<\/p><p>It is then possible to apply tree decomposition in various digital domains:<\/p><ul><li><strong>Algorithm optimization<\/strong>: this structure facilitates the design of algorithms for difficult problems such as graph traversal, pattern matching and NP-hard problem solving.<\/li><li><strong>Network analysis:<\/strong> in the analysis of social, biological or communication networks, tree decomposition enables the discovery of structured sub-groups and key interactions.<\/li><li><strong>Database design<\/strong>: tree decomposition can be used to optimize join and query operations in relational databases.<\/li><li><strong>Computational biology:<\/strong> in computational biology, it can help model relationships between genes, proteins and metabolic pathways.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-01b49da elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"01b49da\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/power-bi-training\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Learn how to use tree decomposition<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ab70d5 elementor-widget elementor-widget-image\" data-id=\"6ab70d5\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/09\/decomposition-tree-2.jpg\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-374d158 e-flex e-con-boxed e-con\" data-id=\"374d158\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fd5d6be elementor-widget elementor-widget-heading\" data-id=\"fd5d6be\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">How do I create a tree structure on Power Bi?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-73ea0fd elementor-widget elementor-widget-text-editor\" data-id=\"73ea0fd\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>Tree decomposition<\/strong> can be a powerful way of effectively analyzing and <a href=\"https:\/\/datascientest.com\/en\/kibana-what-is-it\">visualizing hierarchical data.<\/a> This technique presents the relationships between different categories of data in the form of a tree structure. Here&#8217;s how to create a<strong> tree decomposition in Power BI:<\/strong><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3d38616 elementor-widget elementor-widget-heading\" data-id=\"3d38616\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-medium\"><b>Step 1: data preparation<\/b>.<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1e3faca elementor-widget elementor-widget-text-editor\" data-id=\"1e3faca\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Organized data is essential for any data project. Make sure your data is organized and sorted into different categories, separating &#8220;parent&#8221; data from &#8220;child&#8221; data.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2ba89e1 elementor-widget elementor-widget-heading\" data-id=\"2ba89e1\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-medium\">Step 2: Creating the hierarchy<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-427600e elementor-widget elementor-widget-text-editor\" data-id=\"427600e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Once you&#8217;ve organized your data, import it into <strong>Power Bi.<\/strong> Once imported, use the &#8220;Fields&#8221; pane on the right to select the table containing your data. Right-click on the &#8220;Parent Category&#8221; column and select &#8220;New Hierarchy&#8221;. Then drag the &#8220;Child Category&#8221; column into the new hierarchy. Don&#8217;t hesitate to rename this new hierarchy to make your work easier.<\/p><p><br \/>\ud83d\udca1Related articles:<\/p><table dir=\"ltr\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\" data-sheets-root=\"1\"><colgroup><col width=\"656\" \/><\/colgroup><tbody><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;DAX Power BI: all about the query programming language&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/dax-power-bi-all-about-the-query-programming-language\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/dax-power-bi-all-about-the-query-programming-language\" target=\"_blank\" rel=\"noopener\">DAX Power BI: all about the query programming language<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Dataflow Power BI: everything you need to know about the self-service ETL tool&quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/dataflow-power-bi-everything-you-need-to-know-about-the-self-service-etl-tool\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/dataflow-power-bi-everything-you-need-to-know-about-the-self-service-etl-tool\" target=\"_blank\" rel=\"noopener\">Dataflow Power BI: everything you need to know about the self-service ETL tool<\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Power BI Direct Query: All you need to know about this data query method &quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/power-bi-direct-query-all-you-need-to-know-about-this-data-query-method\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/power-bi-direct-query-all-you-need-to-know-about-this-data-query-method\" target=\"_blank\" rel=\"noopener\">Power BI Direct Query: All you need to know about this data query method <\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Power BI license: What does it cost? &quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/power-bi-license-how-much-does-the-microsoft-solution-cost\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/power-bi-license-how-much-does-the-microsoft-solution-cost\" target=\"_blank\" rel=\"noopener\">Power BI license: What does it cost? <\/a><\/td><\/tr><tr><td data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Power BI vs. Tableau: Two tools &quot;}\" data-sheets-hyperlink=\"https:\/\/datascientest.com\/en\/power-bi-vs-tableau\"><a class=\"in-cell-link\" href=\"https:\/\/datascientest.com\/en\/power-bi-vs-tableau\" target=\"_blank\" rel=\"noopener\">Power BI vs. Tableau: Two tools <\/a><\/td><\/tr><\/tbody><\/table>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2be3808 elementor-widget elementor-widget-heading\" data-id=\"2be3808\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-medium\">Step 3: using tree decomposition in visualizations<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4ac2ec4 elementor-widget elementor-widget-text-editor\" data-id=\"4ac2ec4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Now create a new page in Power BI by clicking on the &#8220;+ Page&#8221; icon at the bottom of the screen. Next, add a visualization, such as a table, bar chart or <a href=\"https:\/\/datascientest.com\/en\/mastering-data-visualization-a-deep-dive-into-pie-charts-in-excel\">pie chart.<\/a><\/p><p>In the visualization, drag the created hierarchy into the appropriate zones. Place it in the Axes or Legends fields, depending on the type of visualization you&#8217;ve chosen.<\/p><p><a href=\"https:\/\/datascientest.com\/en\/matplotlib-master-data-visualization-in-python\">When you display your visualization,<\/a> you&#8217;ll see the different hierarchical categories. You can now explore the levels by clicking on the expansion arrows to see the sub-categories.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a86c639 elementor-widget elementor-widget-heading\" data-id=\"a86c639\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-medium\">Step 4: Customization and formatting<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3a8d7fb elementor-widget elementor-widget-text-editor\" data-id=\"3a8d7fb\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Don&#8217;t forget to customize and format your visualization so that it&#8217;s aesthetically appealing and easy to understand. You can adjust colors, labels and titles to make your tree structure clearer.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-38bd135 elementor-widget elementor-widget-heading\" data-id=\"38bd135\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-medium\">Step 5: Sharing and publishing<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1a73743 elementor-widget elementor-widget-text-editor\" data-id=\"1a73743\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Once you&#8217;re satisfied with your <strong>tree decomposition visualization<\/strong>, you can save your report in <a href=\"https:\/\/datascientest.com\/en\/power-bi-desktop-download-and-installation-guide\">Power BI Desktop<\/a> and publish it on the<a href=\"https:\/\/datascientest.com\/en\/power-bi-service-how-to-create-a-learning-environment-for-training\"> Power BI service<\/a> for sharing with other users.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3520862 elementor-widget elementor-widget-image\" data-id=\"3520862\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/09\/tree-interaction-2.gif\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1869326 elementor-widget elementor-widget-text-editor\" data-id=\"1869326\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Tree decomposition is much more than just a theoretical concept in computer science. It represents a powerful strategy for tackling complex problems by breaking them down into more manageable structures<\/p><p>Its influence spans many fields, making it an invaluable tool for digital professionals and researchers alike.<\/p><p>Data science and its uses are transforming our daily lives and the way we work, and to stay competitive and efficient, training in these fields remains the best option. That&#8217;s why, if you&#8217;ve enjoyed this article and are considering a career in data science or Power Bi, don&#8217;t hesitate to discover our training courses on DataScientest.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e9991b8 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"e9991b8\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/power-bi-training\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Start a Power BI training<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-653da07 e-flex e-con-boxed e-con\" data-id=\"653da07\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-e112f70 elementor-widget elementor-widget-html\" data-id=\"e112f70\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"What is a tree decomposition?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"A tree decomposition of a graph consists in dividing the graph into substructures called \"treecences\". 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Proposed by Paul Seymour and Neil Robertson in their theory of graph minors, it is seen as a key concept offering a unique perspective for solving a variety of problems. So what does tree decomposition or decomposition [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":181617,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Decomposition Tree: Understanding and Utilizing its Power<\/title>\n<meta name=\"description\" content=\"Uncover the concept and practical applications of the decomposition tree in data analysis. 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