TY - GEN

T1 - All-pairs bottleneck paths for general graphs in truly sub-cubic time

AU - Vassilevska, Virginia

AU - Williams, Ryan

AU - Yuster, Raphael

PY - 2007

Y1 - 2007

N2 - In the all-pairs bottleneck paths (APBP) problem (a.k.a. all-pairs maximum capacity paths), one is given a directed graph with real non-negative capacities on its edges and is asked to determine, for all pairs of vertices s and t, the capacity of a single path for which a maximum amount of flow can be routed from s to t. The APBP problem was first studied in operations research, shortly after the introduction of maximum flows and all-pairs shortest paths. We present the first truly sub-cubic algorithm for APBP in general dense graphs. In particular, we give a procedure for computing the (max, min)-product of two arbitrary matrices over R (,-) in O(n2+/3) O(n2.792) time, where n is the number of vertices and is the exponent for matrix multiplication over rings. Using this procedure, an explicit maximum bottleneck path for any pair of nodes can be extracted in time linear in the length of the path.

AB - In the all-pairs bottleneck paths (APBP) problem (a.k.a. all-pairs maximum capacity paths), one is given a directed graph with real non-negative capacities on its edges and is asked to determine, for all pairs of vertices s and t, the capacity of a single path for which a maximum amount of flow can be routed from s to t. The APBP problem was first studied in operations research, shortly after the introduction of maximum flows and all-pairs shortest paths. We present the first truly sub-cubic algorithm for APBP in general dense graphs. In particular, we give a procedure for computing the (max, min)-product of two arbitrary matrices over R (,-) in O(n2+/3) O(n2.792) time, where n is the number of vertices and is the exponent for matrix multiplication over rings. Using this procedure, an explicit maximum bottleneck path for any pair of nodes can be extracted in time linear in the length of the path.

KW - Bottleneck path

KW - Matrix multiplication

KW - Maximum capacity path

KW - Subcubic

UR - http://www.scopus.com/inward/record.url?scp=35548966040&partnerID=8YFLogxK

U2 - 10.1145/1250790.1250876

DO - 10.1145/1250790.1250876

M3 - Conference contribution

AN - SCOPUS:35548966040

SN - 1595936319

SN - 9781595936318

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 585

EP - 589

BT - STOC'07

T2 - STOC'07: 39th Annual ACM Symposium on Theory of Computing

Y2 - 11 June 2007 through 13 June 2007

ER -