A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Using random sampling to find maximum flows in uncapacitated undirected graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Finding maximum flows in undirected graphs seems easier than bipartite matching
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Better random sampling algorithms for flows in undirected graphs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Random sampling in residual graphs
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Single-source unsplittable flow
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Journal of Computer and System Sciences
A case for adapting channel width in wireless networks
Proceedings of the ACM SIGCOMM 2008 conference on Data communication
Hi-index | 0.00 |
Traditionally, combinatorial optimization problems (such as maximum flow, maximum matching, etc.) have been studied for networks where each link has a fixed capacity. Recent research in wireless networking has shown that it is possible to design networks where the capacity of the links can be changed adaptively to suit the needs of specific applications. In particular, one gets a choice of having few high capacity outgoing links or many low capacity ones at any node of the network. This motivates us to have a re-look at the traditional combinatorial optimization problems and design algorithms to solve them in this new framework. In particular, we consider the problem of maximum bipartite flow , which has been studied extensively in the traditional network model. One of the motivations for studying this problem arises from the need to maximize the throughput of an infrastructure wireless network comprising base-stations (one set of vertices in the bipartition) and clients (the other set of vertices in the bipartition). We show that this problem has a significantly different combinatorial structure in this new network model from the classical one. While there are several polynomial time algorithms solving the maximum bipartite flow problem in traditional networks, we show that the problem is NP-hard in the new model. In fact, our proof extends to showing that the problem is APX-hard. We complement our lower bound by giving two algorithms for solving the problem approximately. The first algorithm is deterministic and achieves an approximation factor of O (logN ), where there are N nodes in the network, while the second algorithm (which is our main contribution) is randomized and achieves an approximation factor of $\frac{e}{e-1}$.