On the all-pairs-shortest-path problem in unweighted undirected graphs
R Seidel - Journal of computer and system sciences, 1995 - Elsevier
Journal of computer and system sciences, 1995•Elsevier
We present an algorithm, APD, that solves the distance version of the all-pairs-shortest-path
problem for undirected, unweighted n-vertex graphs in time O (M (n) log n), where M (n)
denotes the time necessary to multiply two n× n matrices of small integers (which is currently
known to be o (n2. 376)). We also address the problem of actually finding a shortest path
between each pair of vertices and present a randomized algorithm that matches APD in its
simplicity and in its expected running time.
problem for undirected, unweighted n-vertex graphs in time O (M (n) log n), where M (n)
denotes the time necessary to multiply two n× n matrices of small integers (which is currently
known to be o (n2. 376)). We also address the problem of actually finding a shortest path
between each pair of vertices and present a randomized algorithm that matches APD in its
simplicity and in its expected running time.
We present an algorithm, APD, that solves the distance version of the all-pairs-shortest-path problem for undirected, unweighted n-vertex graphs in time O(M(n) log n), where M(n) denotes the time necessary to multiply two n × n matrices of small integers (which is currently known to be o(n2.376)). We also address the problem of actually finding a shortest path between each pair of vertices and present a randomized algorithm that matches APD in its simplicity and in its expected running time.
Elsevier
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