Abstract
Let G(V,E) be an unweighted undirected graph on |V | = n vertices. Let δ(u,v) denote the shortest distance between vertices u,v ∈ V. An algorithm is said to compute all-pairs t-approximate shortest-paths/distances, for some t ≥ 1, if for each pair of vertices u,v ∈ V, the path/distance reported by the algorithm is not longer/greater than t · δ(u,v).
This paper presents two randomized algorithms for computing all-pairs nearly 2-approximate distances. The first algorithm takes expected O(m 2/3 n log n + n 2) time, and for any u,v ∈ V reports distance no greater than 2δ(u,v) + 1. Our second algorithm requires expected O(n 2 log3/2) time, and for any u,v ∈ V reports distance bounded by 2δ(u,v)+3.
This paper also presents the first expected O(n 2) time algorithm to compute all-pairs 3-approximate distances.
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Baswana, S., Goyal, V., Sen, S. (2005). All-Pairs Nearly 2-Approximate Shortest-Paths in O(n 2 polylog n) Time. In: Diekert, V., Durand, B. (eds) STACS 2005. STACS 2005. Lecture Notes in Computer Science, vol 3404. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31856-9_55
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DOI: https://doi.org/10.1007/978-3-540-31856-9_55
Publisher Name: Springer, Berlin, Heidelberg
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