On the Sample Complexity of MAX-CUT

Increasingly Cautious Optimism for Practical PAC-MDP Exploration

Exploration strategy is an essential part of learning agents in model-based Reinforcement Learning. R-MAX and V-MAX are PAC-MDP strategies proved to have polynomial sample complexity; yet, their exploration behavior tend to be overly cautious in practice. We propose the principle of Increasingly Cautious Optimism (ICO) to automatically cut off unnecessarily cautious exploration, and apply ICO t...

Approximation Complexity of Nondense Instances of MAX-CUT

We prove existence of approximation schemes for instances of MAXCUT with Ω( 2 ∆ ) edges which work in 2 O ( ∆ ε2 ) nO(1) time. This entails in particular existence of quasi-polynomial approximation schemes (QPTASs) for mildly sparse instances of MAX-CUT with Ω( n 2 polylogn) edges. The result depends on new sampling method for smoothed linear programs that approximate MAX-CUT. On the other hand...

Learning the best algorithm for max-cut, clustering, and other partitioning problems

Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation algorithms and heuristics. Although the best algorithm to use typically depends on the specific application domain, a worst-case analysis is often used to compare al...

MAX-CUT and MAX-BISECTION are NP-hard on unit disk graphs

We prove that the max-cut and max-bisection problems are NP-hard on unit disk graphs. We also show that λ-precision graphs are planar for λ > 1/ √ 2 and give a dichotomy theorem for max-cut computational complexity on λ-precision unit disk graphs.

New Worst-Case Upper Bounds for MAX-2-SAT with Application to MAX-CUT