1.0957-Approximation Algorithm for Random MAX-3SAT

A 7/8-Approximation Algorithm for MAX 3SAT?

We describe a randomized approximation algorithm which takes an instance of MAX 3SAT as input. If the instance—a collection of clauses each of length at most three—is satisfiable, then the expected weight of the assignment found is at least 7=8 of optimal. We provide strong evidence (but not a proof) that the algorithm performs equally well on arbitrary MAX 3SAT instances. Our algorithm uses se...

Approximation Algorithm for Random MAX-kSAT

We provide a rigorous analysis of a greedy approximation algorithm for the maximum random k-SAT (MAX-R-kSAT) problem. The algorithm assigns variables one at a time in a predefined order. A variable is assigned TRUE if it occurs more often positively than negatively; otherwise, it is assigned FALSE. After each variable assignment, problem instance is simplified and a new variable is selected. We...

Approximation Algorithm for the Max-Cut Problem

In this project, we investigated several approximation algorithms for the Max-Cut problem. Our main approach to this problem is a semideenite program (GW) based algorithm that has a performance guarantee of at least 0.878 of the optimal cut. We also show that we can perform exhaustive local search on top of the GW to enhance the result. Our results show that the running time of the local search...

An Efficient Approximation Algorithm for Max-Cut

Significant research effort has been devoted in the study of approximation algorithms for NP-hard problems. Ap-proximation algorithm for Max-Cut problem with performance guarantee of 0. 87856 is long known. In this work we study balanced Max-Cut problem. We give a balancing factor ? for given ? such that the approximate solution is at least 0. 87856 times the optimal ?-balanced cut and it is it...

A .699-approximation algorithm for Max-Bisection