TY - GEN
T1 - Maximum bipartite flow in networks with adaptive channel width
AU - Azar, Yossi
AU - Ma̧dry, Aleksander
AU - Moscibroda, Thomas
AU - Panigrahi, Debmalya
AU - Srinivasan, Aravind
N1 - Funding Information:
We are grateful to Chandra Chekuri for suggesting an alternative approach for our problem based on submodular functions. We also thank the anonymous referees for helpful comments. The first author’s research is supported in part by the Israeli Science Foundation (grant No. 1404/10). The second author’s research is supported by a Fulbright Science and Technology Award, by NSF contract CCF-0829878 and by ONR grant N00014-05-1-0148. The fourth author’s research is supported in part by NSF contract CCF-0635286. The fifth author’s research is supported in part by NSF ITR Award CNS-0426683, NSF Award CNS-0626636, and NSF Award CNS-1010789.
PY - 2009
Y1 - 2009
N2 - 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 .
AB - 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 .
UR - http://www.scopus.com/inward/record.url?scp=70449092014&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-02930-1_29
DO - 10.1007/978-3-642-02930-1_29
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AN - SCOPUS:70449092014
SN - 3642029299
SN - 9783642029295
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 351
EP - 362
BT - Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings
Y2 - 5 July 2009 through 12 July 2009
ER -