  The aim of this paper is to provide a review of structural decomposition
methods in discrete optimization and to give a unified framework in the form of
local elimination algorithms (LEA). This paper is organized as follows. Local
elimination algorithms for discrete optimization (DO) problems (DOPs) with
constraints are considered; a classification of dynamic programming
computational procedures is given. We introduce Elimination Game and
Elimination tree. Application of bucket elimination algorithm from constraint
satisfaction (CS) to solving DOPs is done. We consider different local
elimination schemes and related notions. Clustering that merges several
variables into single meta-variable defines a promising approach to solve DOPs.
This allows to create a quotient (condensed) graph and apply a local block
elimination algorithm. In order to describe a block elimination process, we
introduce Block Elimination Game. We discuss the connection of aforementioned
local elimination algorithmic schemes and a way of transforming the directed
acyclic graph (DAG) of computational LEA procedure to the tree decomposition.
