Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Journal of Global Optimization
Non-monotone submodular maximization under matroid and knapsack constraints
Proceedings of the forty-first annual ACM symposium on Theory of computing
Conflict Resolution in the Scheduling of Television Commercials
Operations Research
Maximizing Nonmonotone Submodular Functions under Matroid or Knapsack Constraints
SIAM Journal on Discrete Mathematics
Improved approximation algorithms for maximum graph partitioning problems extended abstract
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
| Hi-index | 0.00 |
Given a directed graph $G$ and an arc weight function $w: E(G)\rightarrow\mathbb{R}_+$, the maximum directed cut problem ({\sc max dicut}) is that of finding a directed cut $\delta (X)$ with maximum total weight. In this paper we consider a version of {\sc max dicut}---{\sc max dicut} with given sizes of parts or {\sc max dicut with gsp}---whose instance is that of {\sc max dicut} plus a positive integer $p$, and it is required to find a directed cut $\delta (X)$ having maximum weight over all cuts $\delta (X)$ with $|X|=p$. Our main result is a $0.5$-approximation algorithm for solving the problem. The algorithm is based on a tricky application of the pipage rounding technique developed in some earlier papers by two of the authors and a remarkable structural property of basic solutions to a linear relaxation. The property is that each component of any basic solution is an element of a set $\{0,\delta,1/2,1-\delta,1 \}$, where $\delta$ is a constant that satisfies $0