|
|
|
|
LEADER |
02460 am a22003253u 4500 |
001 |
71698 |
042 |
|
|
|a dc
|
100 |
1 |
0 |
|a Christiano, Paul F.
|e author
|
100 |
1 |
0 |
|a Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
|e contributor
|
100 |
1 |
0 |
|a Massachusetts Institute of Technology. Department of Mathematics
|e contributor
|
100 |
1 |
0 |
|a Kelner, Jonathan Adam
|e contributor
|
100 |
1 |
0 |
|a Kelner, Jonathan Adam
|e contributor
|
100 |
1 |
0 |
|a Christiano, Paul F.
|e contributor
|
100 |
1 |
0 |
|a Madry, Aleksander
|e contributor
|
700 |
1 |
0 |
|a Kelner, Jonathan Adam
|e author
|
700 |
1 |
0 |
|a Madry, Aleksander
|e author
|
700 |
1 |
0 |
|a Spielman, Daniel A.
|e author
|
700 |
1 |
0 |
|a Teng, Shang-Hua
|e author
|
245 |
0 |
0 |
|a Electrical flows, Laplacian systems, and faster approximation of maximum flow in undirected graphs
|
260 |
|
|
|b Association for Computing Machinery,
|c 2012-07-18T20:23:57Z.
|
856 |
|
|
|z Get fulltext
|u http://hdl.handle.net/1721.1/71698
|
520 |
|
|
|a We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a system of linear equations in a Laplacian matrix, and thus may be approximately computed in nearly-linear time. Using this approach, we develop the fastest known algorithm for computing approximately maximum s-t flows. For a graph having n vertices and m edges, our algorithm computes a (1-ε)-approximately maximum s-t flow in time ~O(mn1/3ε-11/3). A dual version of our approach gives the fastest known algorithm for computing a (1+ε)-approximately minimum s-t cut. It takes ~O(m+n4/3ε-16/3) time. Previously, the best dependence on m and n was achieved by the algorithm of Goldberg and Rao (J. ACM 1998), which can be used to compute approximately maximum s-t flows in time ~O({m√nε-1), and approximately minimum s-t cuts in time ~O(m+n3/2ε-3).
|
520 |
|
|
|a National Science Foundation (U.S.) (NSF grants 0829878)
|
520 |
|
|
|a National Science Foundation (U.S.) (NSF grant 0843915)
|
520 |
|
|
|a National Science Foundation (U.S.) (0915487)
|
520 |
|
|
|a National Science Foundation (U.S.) (NSF grant 0915487)
|
520 |
|
|
|a United States. Office of Naval Research (ONR grant N00014-11-1-0053)
|
546 |
|
|
|a en_US
|
655 |
7 |
|
|a Article
|
773 |
|
|
|t Proceedings of the 43rd annual ACM symposium on Theory of Computing, STOC '11
|