Average Update Times for Fully-Dynamic All-Pairs Shortest PathsI
نویسندگان
چکیده
We study the fully-dynamic all pairs shortest path problem for graphs with arbitrary non-negative edge weights. It is known for digraphs that an update of the distance matrix costs O(n2.75 polylog(n)) worst-case time [Thorup, STOC ’05] and O(n2 log(n)) amortized time [Demetrescu and Italiano, J.ACM ’04] where n is the number of vertices. We present the first average-case analysis of the undirected problem. For a random update we show that the expected time per update is bounded by O(n4/3+ε) for all ε > 0. If the graph is outside the critical window, we prove even smaller bounds.
منابع مشابه
Average Update Times for Fully-Dynamic All-Pairs Shortest Paths
We study the fully-dynamic all pairs shortest path problem for graphs with arbitrary non-negative edge weights. It is known for digraphs that an update of the distance matrix costs Õ(n) worst-case time [Thorup, STOC ’05] and Õ(n) amortized time [Demetrescu and Italiano, J.ACM ’04] where n is the number of vertices. We present the first average-case analysis of the undirected problem. For a rand...
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