NP-Complete Reductions: Clique, Independent Set, Vertex Cover, and Dominating Set

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The previous version had a flawed definition (for Vertex Cover), which has been fixed here.

Table of Contents:

00:00 - Introduction and Prerequisites:
00:28 - Independent Set Definition
01:17 - Reducing Independent Set to/from Clique
02:53 - Vertex Cover Definition
03:39 - Reducing Independent Set to/from Vertex Cover
04:24 - Reduction Compositions
05:00 - NP-Hard and NP-Complete Definitions
06:02 - Proving additional problems NP-Hard
07:09 - Dominating Set Definition
08:13 - Reducing Vertex Cover to Dominating Set
12:38 - Up Next
  1. Algorithms with Attitude
  2. algorithms
  3. data structures
  4. David Scot Taylor
  5. Clique
  6. NP-Complete
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Комментарии
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Thank you for painting such a clear picture of something I struggled to understand!

furkan-sahin
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man you are smart and funny and explain well! thank you so much for your free videos and your great attitude. i declare you as my official teacher

ropopal
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I'm not sure which part of my comprehension went wrong, but what makes vertex cover different from dominating set? They seem pretty much the same.

laolun
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Any approximate time in the future you are thinking of covering Approximation Algorithms?

cagan
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Am I wrong in saying that the independent set is the graph compliment of clique, while the independent set is the vertex complement of vertex over?

extremeforlife
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What about partial reductions to restricted 2sats to deduce restricted 3sats that make it easy to solve the main 3sat problem. To fiddly and approach for humans but not ai.

JikeWimblik
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Why we need 3 nodes for vertex cover we could do in 2 also. 6 and 3. why 4 is there ? 6 is connected to 1, 2, 4, 5, 7 and 3 is connected to 7 and 5

vidhisanghavi
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If a problem is NP-Hard, does that make it automatically np-complete?

yunoletmehaveaname
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what is, , between two things not in the set? and to something not in the set? are they both not different ? at 3:55

rohandevaki
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how are you telling a independent set? there is no edge between 6 and 3, isnt it also a independent set?, why didnt you include it ? at 0:38

rohandevaki
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you are just reading it, no proper explaination

rohandevaki