A successful algorithm for the undirected Hamiltonian path problem

In this paper a polynomial algorithm called the Minram algorithm is presented which finds a Hamiltonian Path in an undirected graph with high frequency of success for graphs up to 1000 nodes. It first reintroduces the concept described in [13] and then explains the algorithm. Computational comparison with the algorithm by Posa [10] is given.It is shown that a Hamiltonian Path is a spanning arborescence with zero ramification index. Given an undirected graph, the Minram algorithm starts by finding a spanning tree which defines a unique spanning arborescence. By suitable pivots it locates a locally minimal value of the ramification index. If this local minima corresponds to zero ramification index then the algorithm is considered to have ended successfully, else a failure is reported.Computational performance of the algorithm on randomly generated Hamiltonian graphs is given. The random graphs used as test problems were generated using the procedure explained in Section 6.1. Comparison with our version of the Posa algorithm which we call Posa-ran algorithm [10] is also made.     

关于Udo Simon猜测的注记

设ψ:S2→Sn为线性满的极小浸入,Gauss曲率K满足1/10≤K≤1/6。若K不是常数,则n=6,且ψ的准线φ0至少有2个不同的分歧点。作为它的推论,如果1/7相似文献   

Induced formal deformations and the Cohen-Macaulay property

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Multi-Valued Fields. II

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