Multiple-Source Shortest Paths in Embedded Graphs
نویسندگان
چکیده
منابع مشابه
Multiple-Source Shortest Paths in Embedded Graphs
Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time with high probability, so that the shortest-path distance from any vertex on the boundary of f to any other vertex in G can be retrieved in O(log n) time. Ou...
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Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe an algorithm to preprocess the graph in O(gn log n) time, so that the shortest-path distance from any vertex on the boundary of f to any other vertex in G can be retrieved in O(log n) time. Our result directly generalizes th...
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We present an algorithm for the Single Source Shortest Paths (SSSP) problem in directed Hminor free graphs. For every fixed H, if G is a graph with n vertices having integer edge lengths and s is a designated source vertex of G, the algorithm runs in Õ(n √ 11.5−2 logL) ≤ O(n logL) time, where L is the absolute value of the smallest edge length. The algorithm computes shortest paths and the dist...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2013
ISSN: 0097-5397,1095-7111
DOI: 10.1137/120864271