Computational geometry: an introduction
Computational geometry: an introduction
An introduction to parallel algorithms
An introduction to parallel algorithms
Simple linear time recognition of unit interval graphs
Information Processing Letters
Solving the shortest-paths problem on bipartite permutation graphs efficiently
Information Processing Letters
Unified all-pairs shortest path algorithms in the chordal hierarchy
Discrete Applied Mathematics
Solving the all-pairs-shortest-length problem on chordal bipartite graphs
Information Processing Letters
Fast Estimation of Diameter and Shortest Paths (Without Matrix Multiplication)
SIAM Journal on Computing
Communications of the ACM
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Improved algorithm for all pairs shortest paths
Information Processing Letters
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We present an algorithm for the all pairs shortest distance problem on permutation graphs. Given a permutation model for the graph on n vertices, after O(n) preprocessing the algorithm will deliver answers to distance queries in O(1) time. In the EREW PRAM model, preprocessing can be accomplished in O(logn) time with O(n) work. Where the distance between query vertices is k, a path can be delivered in O(k) time. The method is based on reduction to bipartite permutation graphs, a further reduction to unit interval graphs, and a coordinatization of unit interval graphs.