A fast parallel algorithm for the maximal independent set problem
Journal of the ACM (JACM)
Journal of Combinatorial Theory Series A
P-Complete Approximation Problems
Journal of the ACM (JACM)
Complexity of Partial Satisfaction
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the approximation of maximum satisfiability
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Fast Approximation Algorithms on Maxcut, k-Coloring, and k-Color Ordering for VLSI Applications
IEEE Transactions on Computers
On greedy construction heuristics for the MAX-CUT problem
International Journal of Computational Science and Engineering
Advanced Scatter Search for the Max-Cut Problem
INFORMS Journal on Computing
Bounding Probability of Small Deviation: A Fourth Moment Approach
Mathematics of Operations Research
Note on maximal bisection above tight lower bound
Information Processing Letters
Overlaying multiple maps efficiently
CIT'04 Proceedings of the 7th international conference on Intelligent Information Technology
Max-cut parameterized above the edwards-erdős bound
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A spanning tree-based encoding of the MAX CUT problem for evolutionary search
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
Bisections above tight lower bounds
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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The maximum cut problem is known to be an important NP-complete problem with many applications. The authors investigate this problem (which they call the normal maximum cut problem) and a variant of it (which is referred to as the connected maximum cut problem). They show that any n-vertex e-edge graph admits a cut with at least the fraction 1/2+1/2n of its edges, thus improving the ratio 1/2+2/e known before. It is shown that it is NP-complete to decide if a given graph has a normal maximum cut with at least a fraction (1/2+ epsilon ) of its edges, where the positive constant epsilon can be taken smaller than any value chosen. The authors present an approximation algorithm for the normal maximum cut problem on any graph that runs in O((e log e+n log n)/p+log p*log n) parallel time using p(1or=por=e+n) processors that guarantees a ratio of at least (1/2+1/2n), given a matching of size e/n in G. The authors take up the connected maximum cut problem and show that, unlike the normal maximum cut problem, this problem admits an infinity of instances where the fraction of the edges in the connected maximum cut is arbitrarily close to zero. They then show that the connected maximum cut problem is NP-complete even for planar graphs, in clear contrast to the normal maximum cut problem, which is solvable in polynomial time on planar graphs.