Optimal parallel computations for halin graphs
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Optimal parallel algorithms are given for two hard problems (the Hamiltonian cycle and the travelling salesman problem) restricted to graphs having a simple structure — Halin graphs. These problems were previously investigated for Halin graphs from the sequential point of view [1,5,6]. The travelling salesman problem (the computation of the shortest Hamiltonian cycle) for the Halin graph is interesting because such a graph can contain an exponential number of Hamiltonian cycles. Two tree-oriented algorithmic techniques are used: computation of products for paths of the tree (which gives log2n time algorithm for the Hamiltonian cycle) and a special parallel pebble game (giving log2n time for the travelling salesman problem).
KeywordsFunction dePe Travel Salesman Problem Hamiltonian Cycle Planar Embedding Parallel Random Access Machine
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