On the approximation of maximum satisfiability
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
New ${\bf \frac{3}{4}}$-Approximation Algorithms for the Maximum Satisfiability Problem
SIAM Journal on Discrete Mathematics
Tight bound on Johnson's algorithm for maximum satisfiability
Journal of Computer and System Sciences
Approximation algorithms
Simplified tight analysis of Johnson's algorithm
Information Processing Letters
Yet another algorithm for dense max cut: go greedy
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Improved approximation algorithms for MAX NAE-SAT and MAX SAT
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Randomized variants of Johnson's algorithm for MAX SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Bounds on greedy algorithms for MAX SAT
ESA'11 Proceedings of the 19th European conference on Algorithms
Simpler 3/4-approximation algorithms for MAX SAT
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
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We consider the performance of two classic approximation algorithms which work by scanning the input and greedily constructing a solution. We investigate whether running these algorithms on a random permutation of the input can increase their performance ratio. We obtain the following results: 1. Johnson's approximation algorithm for MAX-SAT is one of the first approximation algorithms to be rigorously analyzed. It has been shown that the performance ratio of this algorithm is 2/3. We show that when executed on a random permutation of the variables, the performance ratio of this algorithm is improved to 2/3 + c for some c 0 This resolves an open problem of Chen, Friesen and Zhang [JCSS 1999]. (See also the paper by Poloczek and Schnitger in these proceedings for related results on this algorithm and its variants). 2. Motivated by the above improvement, we consider the performance of the greedy algorithm for MAX-CUT whose performance ratio is 1/2. Our hope was that running the greedy algorithm on a random permutation of the vertices would result in a 1/2 + c approximation algorithm. However, it turns out that in this case the performance of the algorithm remains 1/2. This resolves an open problem of Mathieu and Schudy [SODA 2008].