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 -