JACM, 29 (1), 24-32.

Artificial Intelligence, 14 (3), 263-313.

Information Sciences, 19 (3), 229-50.

"Artificial intelligence tasks which can be formulated as constraint satisfaction problems, with which this paper is for the most part concerned, are usually solved by backtracking. By examining the thrashing behavior that nearly always accompanies backtracking, identifying three of its causes and proposing remedies for them we are led to a class of algorithms which can profitably be used to eliminate local (node, arc and path) inconsistencies before any attempt is made to construct a complete solution. A more general paradigm for attacking these tasks is the alternation of constraint manipulation and case analysis producing an OR problem graph which may be searched in any of the usual ways.Many authors, particularly Montanan i and Waltz, have contributed to the development of these ideas; a secondary aim of this paper is to trace that history. The primary aim is to provide an accessible, unified framework, within which to present the algorithms including a new path consistency algorithm, to discuss their relationships and the many applications, both realized and potential, of network consistency algorithms."See also: sciencedirect.comArtificial Intelligence 8:99-118

Information Science 7:95-132

This paper explores new approaches to the symmetric traveling-salesman problem in which 1-trees, which are a slight variant of spanning trees, play an essential role. A 1-tree is a tree together with an additional vertex connected to the tree by two edges. We observe that (i) a tour is precisely a 1-tree in which each vertex has degree 2, (ii) a minimum 1-tree is easy to compute, and (iii) the transformation on “intercity distances” cij → Cij + πi + πj leaves the traveling-salesman problem invariant but changes the minimum 1-tree. Operations Research, 18, 1138–1162.