TY - JOUR
T1 - Maximum bipartite flow in networks with adaptive channel width
JF - Theoretical Computer Science
Y1 - 2011
A1 - Azar,Yossi
A1 - Mądry,Aleksander
A1 - Moscibroda,Thomas
A1 - Panigrahi,Debmalya
A1 - Srinivasan, Aravind
KW - Adaptive channel width
KW - graph algorithm
KW - Linear program rounding
KW - Maximum flow
KW - Wireless networks
AB - Traditionally, network optimization problems assume that each link in the network 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 a 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 classical network 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 fixed-capacity 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 fixed-capacity one. While there are several polynomial time algorithms for 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 ( log N ) , where N is the number of nodes in the network, while the second algorithm is randomized and achieves an approximation factor of e e − 1 .
VL - 412
SN - 0304-3975
UR - http://www.sciencedirect.com/science/article/pii/S0304397510005852
CP - 24
M3 - 10.1016/j.tcs.2010.10.023
ER -