论文信息 - An algorithm for finding hamilton paths and cycles in random graphs

An algorithm for finding hamilton paths and cycles in random graphs

This paper describes a polynomial time algorithm HAM that searches for Hamilton cycles in undirected graphs. On a random graph its asymptotic probability of success is that of the existence of such a cycle. If all graphs withn vertices are considered equally likely, then using dynamic programming on failure leads to an algorithm with polynomial expected time. The algorithm HAM is also used to solve the symmetric bottleneck travelling salesman problem with probability tending to 1, asn tends to ∞.Various modifications of HAM are shown to solve several Hamilton path problems.

B. Bollobás | A. Frieze | T. Fenner

[1] M. Held,et al. A dynamic programming approach to sequencing problems , 1962, ACM National Meeting.

[2] P. Erdos,et al. On the strength of connectedness of a random graph , 1964 .

[3] Leslie G. Valiant,et al. Fast probabilistic algorithms for hamiltonian circuits and matchings , 1977, STOC '77.

[4] Eli Shamir,et al. How many random edges make a graph hamiltonian? , 1983, Comb..

[5] T.I. Fenner,et al. On the existence of Hamiltonian cycles in a class of random graphs , 1983, Discret. Math..

[6] János Komlós,et al. Limit distribution for the existence of hamiltonian cycles in a random graph , 1983, Discret. Math..

[7] Béla Bollobás,et al. Almost all Regular Graphs are Hamiltonian , 1983, European journal of combinatorics (Print).

[8] Béla Bollobás,et al. Random Graphs , 1985 .

[9] Alan M. Frieze. Limit Distribution for the Existence of Hamiltonian Cycles in Random Bipartite Graphs , 1985, Eur. J. Comb..

[10] Béla Bollobás,et al. On matchings and hamiltonian cycles in random graphs Annals of Discrete Mathematics 28 , 1985 .

[11] A. Frieze. ON MATCHINGS AND HAMILTON CYCLES IN RANDOM GRAPHS , 1988 .