# Combinatorial Approximation Algorithms for MaxCut using Random Walks

@article{Kale2011CombinatorialAA, title={Combinatorial Approximation Algorithms for MaxCut using Random Walks}, author={Satyen Kale and C. Seshadhri}, journal={ArXiv}, year={2011}, volume={abs/1008.3938} }

We give the first combinatorial approximation algorithm for Maxcut that beats the trivial 0.5 factor by a constant. The main partitioning procedure is very intuitive, natural, and easily described. It essentially performs a number of random walks and aggregates the information to provide the partition. We can control the running time to get an approximation factor-running time tradeoff. We show that for any constant b > 1.5, there is an O(n^{b}) algorithm that outputs a (0.5+delta…

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## 22 Citations

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- 2010

It is shown that when executed on a random permutation of the variables, the performance ratio of Johnson’s approximation algorithm for MAX-SAT is improved to 2/3 + c for some c > 0.1 and the hope was that running the greedy algorithm on arandom permutations of the vertices would result in a 1/2+ c approximation algorithm.

### Randomized greedy: new variants of some classic approximation algorithms

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It is shown that when executed on a random permutation of the variables, the performance ratio of Johnson's approximation algorithm for MAX-SAT is improved to 2/3 + c for some c > 0 and the hope was that running the greedy algorithm on arandom permutations of the vertices would result in a 1/2 + c approximation algorithm, but it turns out that in this case the performance of the algorithm remains 1/ 2.

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It is shown that for any e > 0, any streaming algorithm that obtains a (1 + e)-approximation to the max cut value when edges arrive in adversarial order requires n1−O(e) space, implying that Ω(n) space is necessary to obtain an arbitrarily good approximation to themax cut value.

### Improved Combinatorial Approximation Algorithms for MAX CUT in Sparse Graphs

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- 2022

A new vertex decomposition of graphs is introduced, which is called tree-bipartite decomposition, which presents a linear-time ( 1 2 + n−1 2m )-approximation algorithm for the Max-Cut problem and a derivative is presented, which solves an open problem in their paper.

### Fast Distributed Approximation for Max-Cut

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These algorithms make non-trivial use of the greedy approach of Buchbinder et al. (SIAM Journal on Computing, 2015) for maximizing an unconstrained (non-monotone) submodular function, which may be of independent interest.

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