Matching is as easy as matrix inversion
Combinatorica
Maximizing the number of unused colors in the vertex coloring problem
Information Processing Letters
New ${\bf \frac{3}{4}}$-Approximation Algorithms for the Maximum Satisfiability Problem
SIAM Journal on Discrete Mathematics
Efficient approximation algorithms for semidefinite programs arising from MAX CUT and COLORING
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Recycling queries in PCPs and in linearity tests (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Non-oblivious Local Search for MAX 2-CCSP with Application to MAX DICUT
WG '97 Proceedings of the 23rd International Workshop on Graph-Theoretic Concepts in Computer Science
Gadgets Approximation, and Linear Programming
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
A combinatorial algorithm for MAX CSP
Information Processing Letters
Non-monotone submodular maximization under matroid and knapsack constraints
Proceedings of the forty-first annual ACM symposium on Theory of computing
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Submodular secretary problem and extensions
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
SIAM Journal on Discrete Mathematics
Maximizing Non-monotone Submodular Functions
SIAM Journal on Computing
Journal of Combinatorial Optimization
Submodular secretary problem and extensions
ACM Transactions on Algorithms (TALG)
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We describe several combinatorial algorithms for the maximum directed cut problem. Among our results is a simple linear time 9/20-approximation algorithm for the problem, and a somewhat slower ½-approximation algorithm that uses a bipartite matching routine. No better combinatorial approximation algorithms are known even for the easier maximum cut problem for undirected graphs. Our algorithms do not use linear programming, nor semidefinite programming. They are based on the observation that the maximum directed cut problem is equivalent to the problem of finding a maximum independent set in the line graph of the input graph, and that the linear programming relaxation of the problem is equivalent to the problem of finding a maximum fractional independent set of that line graph. The maximum fractional independent set problem can be easily reduced to a bipartite matching problem. As a consequence of this relation, we also get that the maximum directed cut problem for bipartite digraphs can be solved in polynomial time.