Exact "Fast" Algorithm for the Maximum Independent Set Problem - Easy Theory

Here we give a "fast" algorithm for solving the maximum independent set problem for an arbitrary graph, which is NP-complete in this general case. The key to getting a much faster algorithm is to break the graph up into "classes" of vertices based on their degree, and recurse appropriately on each.

Timeline: 0:00 - Intro + Example 2:07 - Brute Force Algorithm 4:00 - Vertices of Degree 0 or 1 10:10 - Vertices of Degree at least 3 13:40 - Vertices of Degree 2 17:35 - Final Runtime

Easy Theory Website: https://www.easytheory.org Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join Donation (appears on streams): https://streamlabs.com/easytheory1/tip Paypal: https://paypal.me/easytheory Patreon: https://www.patreon.com/easytheory Discord: https://discord.gg/SD4U3hs

#easytheory

Youtube Live Streaming (Sundays) - subscribe for when these occur.

Merch: Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122 Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang

If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1

▶SEND ME THEORY QUESTIONS◀ ryan.e.dougherty@icloud.com

▶ABOUT ME◀ I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes. ... https://www.youtube.com/watch?v=6jdWxjTASms