Affiliation:
1. nstitut polytechnique de Paris, T´el´ecom Paris, 91123 Palaiseau, FRANCE
2. Laboratoire Interdisciplinaire des Sciences du Num´erique (UMR 9015), CNRS, Universit´e Paris-Saclay, 91400 Orsay FRANCE
Abstract
The decision problems of the existence of a Hamiltonian cycle or of a Hamiltonian path in a given directed or undirected graph, and of the existence of a truth assignment satisfying a given Boolean formula C, are well-known NP-complete problems. Here we study the problems of the uniqueness of a Hamiltonian cycle or path in an undirected, directed or oriented graph, and show that they have the same complexity, up to polynomials, as the problem U-SAT of the uniqueness of an assignment satisfying C. As a consequence, these Hamiltonian problems are NP-hard and belong to the class DP, like U-SAT.
Publisher
World Scientific and Engineering Academy and Society (WSEAS)
Reference17 articles.
1. J.-P. BARTHELEMY, G. D. COHEN and ´ A. C. LOBSTEIN: Algorithmic Complexity and Communication Problems, London: University College of London, 1996.
2. A. BLASS and Y. GUREVICH: On the unique satisfiability problem, Information and Control, Vol. 55, pp. 80-88, 1982.
3. C. CALABRO, R. IMPAGLIAZZO, V. KABANETS and R. PATURI: The complexity of Unique k-SAT: an isolation lemma for k-CNFs, Journal of Computer and System Sciences, Vol. 74, pp. 386–393, 2008.
4. S. A. COOK: The complexity of theoremproving procedures, Proceedings of 3rd Annual ACM Symposium on Theory of Computing, pp. 151–158, 1971.
5. T. CORMEN: Algorithmic complexity, in: K. H. Rosen (ed.) Handbook of Discrete and Combinatorial Mathematics, pp. 1077–1085, Boca Raton: CRC Press, 2000.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献