Talk:Branch and bound

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Do the subregions created during the branch and bound heuristic have to be mutually disjoint?

According to the book "The Traveling Salesman Problem - A Computational Study" by David L. Applegate, Robert E. Bixby, Vasek Chvátal, and William J. Cook (Chap 1, pag 41) the branch-and-bound approach has its origin in work on the Traveling Salesman Problem. The concept was introduced in the late 1950s (Bock 1958, Croes, 1958), even though the name branch-and-bound appeared only in a 1963 paper by Little et al. (1963).

F. Bock. An algorithm for solving “traveling-salesman” and related network optimization problems. Research Report, Armour Research Foundation, 1958.

G. A. Croes. A method for solving traveling-salesman problems. Operations Research, 6:791–812, 1958.

J. D. C. Little, K. G. Murty, D. W. Sweeney, and C. Karel. An algorithm for the traveling salesman problem. Operations Research, 11:972–989, 1963.

I think that partitioning a given node is sort of implied, making the resulting regions mutually disjoint by definition. Cyberia 05:10, 26 May 2007 (UTC)