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In this paper, we present an (optimal) linear-time algorithm that decides whether a bipartite permutation graph can be partitioned into one or more induced Hamiltonian subgraphs each of which contains at least k vertices for a given k, and if so, obtains such a partition. We then give an efficient parallelization of the algorithm. We also investigate the problem of partitioning arbitrary directed...
In this paper we present optimal sequential and parallel algorithms for the shortest-paths problems on strongly ordered bipartite (permutation) graphs. The parallel algorithm runs in O(log n) time on a CREW PRAM and is both time-optimal and work-optimal. With a published procedure as a subroutine, this work immediately leads to an optimal O(n 2 ) time algorithm for the all-pairs shortest-paths...
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