# Talk:Branch and bound

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## Disjoint subregions

Do the subregions created during the branch and bound heuristic have to be mutually disjoint? - Strictly speaking, the sub-regions need not be mutually disjoint. However, intersecting sub-domains will only but introduce additional overhead.

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)

## Universal Bounding Algorithm

The article says: There is no universal bounding algorithm that works for all problems, and there is little hope that one will ever be found;

It seems to me that, not only has no algorithm ever been found, but moreover that there does not even exist such a "universal" bounding algorithm, even in principle. For example, consider a set where f(x)=0 for all x except one xi chosen at random with f(xi)=1. Without any further information, the only way to be sure and find xi is to check every element, right? Perhaps someone with more knowledge of this field can advise, thanks. 67.9.148.47 (talk) 06:08, 16 February 2009 (UTC)

## Original reference link

There is a text reference to the original "invetor" but not the exact ref. I think it's this one :

A. H. Land & A. G. Doig: An automatic method of solving discrete programming problems. Econometrica 28(3): 497-520, July 1960

If someone can check and add it at the end of the article, that would be nice.

I don't have access to the book, but other sources refer to it, so I guess this is the correct citation. – Adrianwn (talk) 15:38, 23 July 2010 (UTC)