On-line and Dynamic Shortest Paths through Graph Decompositions
نویسندگان
چکیده
We describe algorithms for finding shortest paths and distances in a planar digraph which exploit the particular topology of the input graph. We give both sequential and parallel algorithms that work on a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. For outerplanar digraphs, for instance, the data structures can be updated after any such change in only O(log n) time, where n is the number of vertices of the digraph. The parallel algorithms presented here are the first known ones for solving this problem. Our results can be extended to hold for digraphs of genus o(n).
منابع مشابه
Fully Dynamic All Pairs All Shortest Paths
We consider the all pairs all shortest paths (APASP) problem, which maintains all of the multiple shortest paths for every vertex pair in a directed graph G = (V,E) with a positive real weight on each edge. We present a fully dynamic algorithm for this problem in which an update supports either weight increases or weight decreases on a subset of edges incident to a vertex. Our algorithm runs in...
متن کاملAll - Pairs Shortest Paths in O ( n 2 ) Time with High Probability
We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0, 1] is O(n2), in expectation and with high probability. This resolves a long-standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano [2006]....
متن کاملShortest paths on dynamic graphs
Among the variants of the well known shortest path problem, those that refer to a dynamically changing graphs are theoretically interesting, as well as computationally challenging. Applicationwise, there is an industrial need for computing point-to-point shortest paths on large-scale road networks whose arcs are weighted with a travelling time which depends on traffic conditions. We survey rece...
متن کاملA Faster Algorithm for Fully Dynamic Betweenness Centrality
We present a new fully dynamic algorithm for maintaining betweenness centrality (BC) of vertices in a directed graph G = (V,E) with positive edge weights. BC is a widely used parameter in the analysis of large complex networks. We achieve an amortized O(ν · log n) time per update, where n = |V | and ν bounds the number of distinct edges that lie on shortest paths through any single vertex. This...
متن کاملFully Dynamic Betweenness Centrality
We present fully dynamic algorithms for maintaining betweenness centrality (BC) of vertices in a directed graph G = (V,E) with positive edge weights. BC is a widely used parameter in the analysis of large complex networks. We achieve an amortized O(ν∗ · log n) time per update with our basic algorithm, and O(ν∗ · log n) time with a more complex algorithm, where n = |V |, and ν∗ bounds the number...
متن کامل