Local elimination algorithms for solving sparse discrete problems

The class of local elimination algorithms is considered that make it possible to obtain global information about solutions of a problem using local information. The general structure of local elimination algorithms is described that use neighborhoods of elements and the structural graph describing the problem structure; an elimination algorithm is also described. This class of algorithms includes local decomposition algorithms for discrete optimization problems, nonserial dynamic programming algorithms, bucket elimination algorithms, and tree decomposition algorithms. It is shown that local elimination algorithms can be used for solving optimization problems.