Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
MAX-CUT has a randomized approximation scheme in dense graphs
Random Structures & Algorithms
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Random sampling and approximation of MAX-CSPs
Journal of Computer and System Sciences - STOC 2002
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Linear time approximation schemes for the Gale-Berlekamp game and related minimization problems
Proceedings of the forty-first annual ACM symposium on Theory of computing
Online ranking for tournament graphs
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Approximation schemes for the betweenness problem in tournaments and related ranking problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Randomized greedy: new variants of some classic approximation algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Semi-supervised learning using greedy max-cut
The Journal of Machine Learning Research
| Hi-index | 0.00 |
We study dense instances of MaxCut and its generalizations. Following a long list of existing, diverse and often sophisticated approximation schemes, we propose taking the naïve greedy approach; we prove that when the vertices are considered in random order, our algorithms are still approximation schemes. Our algorithms may be simple, but the analysis is not. It relies on smoothing the vertices defining the partial cuts and on proving certain martingale properties. We also give a simpler proof of the result from Alon, Fernandez de la Vega, Kannan, and Karpinski [1] that dense problems have sample complexity Õ (1/ε4). Like previous work, our results generalize to dense maximum constraint satisfaction problems.