Wenceslas Fernandez de la Vega, Marek Karpinski

We prove that the subdense instances of MAX-CUT of average

degree Omega(n/logn) posses a polynomial time approximation scheme (PTAS).

We extend this result also to show that the instances of general 2-ary

maximum constraint satisfaction problems (MAX-CSP) of the same average

density have PTASs. Our results ...
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Wenceslas Fernandez de la Vega, Marek Karpinski

We prove existence of approximation schemes for instances of MAX-CUT with $\Omega(\frac{n^2}{\Delta})$ edges which work in $2^{O^\thicksim(\frac{\Delta}{\varepsilon^2})}n^{O(1)}$ time. This entails in particular existence of quasi-polynomial approximation schemes (QPTASs) for mildly sparse instances of MAX-CUT with $\Omega(\frac{n^2}{\operatorname{polylog} n})$ edges. The result depends on new sampling method for smoothed linear programs that ... more >>>

Alexander Golovnev, Siyao Guo, Spencer Peters, Noah Stephens-Davidowitz

We study a natural and quite general model of branch-and-bound algorithms. In this model, an algorithm attempts to minimize (or maximize) a function $f : D \to \mathbb{R}_{\geq 0}$ by making oracle queries to a heuristic $h_f$ satisfying

\[

\min_{x \in S} f(x) \leq h_f(S) \leq \gamma \cdot ...
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