منابع مشابه
Shortest Paths in Distance-regular Graphs
We aim here at introducing a new point of view of the Laplacian of a graph, Γ. With this purpose in mind, we consider L as a kernel on the finite space V (Γ), in the context of the Potential Theory. Then we prove that L is a nice kernel, since it verifies some fundamental properties as maximum and energy principles and the equilibrium principle on any proper subset of V (Γ). If Γ is a proper se...
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Consider a random regular graph with degree d and of size n. Assign to each edge an i.i.d. exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edges on the shortest-weight paths between a fixed vertex and all the other vertices, as well as between any pair of vertices. Namely, for any fixed d ≥ 3, we show that the longe...
متن کاملImproved Bounds for Shortest Paths in Dense Distance Graphs
We study the problem of computing shortest paths in so-called dense distance graphs. Every planar graph G on n vertices can be partitioned into a set of O(n/r) edge-disjoint regions (called an r-division) with O(r) vertices each, such that each region has O( √ r) vertices (called boundary vertices) in common with other regions. A dense distance graph of a region is a complete graph containing a...
متن کاملFaster shortest paths in dense distance graphs, with applications
We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the linear-time shortest-path algorithm of Henzinger, Klein, Subramanian, and Rao [STOC’94]. The second is Fakcharoenphol and Rao’s algorithm [FOCS’01] for emulating Dijkstra’s algorithm on the dense distance graph (DDG). A DDG is defined for a decomposition of a planar graph G...
متن کاملShortest Paths In Unweighed Graphs
When dealing with shortest paths in weighed or unweighed graphs, one may solve one-to-one, one-to-all or all-to-all instances. But the known algorithms compute one single shortest path of the considered instance. This article describes a new algorithm (patent pending) designed to compute all the shortest paths between two vertices of a directed, strongly connected and unweighed graph G, contain...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2000
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0269