Abstract
Abstract A tournament is a digraph T = (V, E) in which, for every pair of vertices, u and v, exactly one of (u, v), (v, u) is in E. Two classical theorems about tournaments are that every tournament has a Hamiltonian path, and every strongly connected tournament has a Hamiltonian cycle. Furthermore, it is known how to find these in polynomial time. In this paper we discuss the parallel complexity of these problems. Our main result is that constructing a Hamiltonian path in a general tournament and a Hamiltonian cycle in a strongly connected tournament are both in NC. In addition, we give an NC algorithm for finding a Hamiltonian path with one fixed endpoint. In finding fast parallel algorithms, we also obtain new proofs for the theorems.
Published Version
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