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Questions about approximation algorithms.

2
votes
In 2016–2018, in a series of papers, Dinur, Khot, Kindler, Minzer and Safra show that Vertex Cover is NP-hard to approximate to any factor better than $\sqrt{2}$, thus improving Dinur and Safra's earl …
answered Mar 15 '19 by Yuval Filmus
13
votes
2answers
A set-function $f$ is monotone submodular if for all $A,B$, $$ f(A) + f(B) \geq f(A \cup B) + f(A \cap B). $$ A stronger property is $$ \begin{multline*} f(A) + f(B) + f(C) + f(A\cup B\cup C) \geq \\ …
asked Apr 2 '12 by Yuval Filmus
7
votes
Higher-order discrete derivatives of set functions are explored in Submodularity, supermodularity and higher-order monotonicities of pseudo-boolean functions. According to them, the strict third-order …
answered Apr 2 '12 by Yuval Filmus
10
votes
There are many open algorithmic problems. All problems below (other than the last bullet) are NP-hard, so we are interested in the best approximation ratio we can achieve in polynomial time. The follo …
answered Feb 23 '15 by Yuval Filmus