Computing All-Pairs Shortest Paths by Leveraging Low Treewidth
2012 ◽
Vol 43
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pp. 353-388
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Keyword(s):
Run Time
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We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both algorithms run in O(n^2 w_d) time, where w_d is the graph width induced by this vertex ordering. For graphs of constant treewidth, this yields O(n^2) time, which is optimal. On chordal graphs, the algorithms run in O(nm) time. In addition, we present a variant that exploits graph separators to arrive at a run time of O(n w_d^2 + n^2 s_d) on general graphs, where s_d
2019 ◽
Vol 11
(06)
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pp. 1950076
Keyword(s):
1998 ◽
Vol 1645
(1)
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pp. 170-175
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2012 ◽
Vol 8
(4)
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pp. 1-17
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2007 ◽
Vol 62
(2)
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pp. 74-92
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