We present several types of extended formulations for integer programs, based on irreducible integer solutions to Gomory’s group relaxations. We present an algorithm based on an iterative reformulation technique using these extended formulations. We give computational results for benchmark problems, which illustrate the primal and dual effect of the reformulation.

Let $L$ be a lattice in $ZZ^n$ of dimension $m$. We prove that there exist integer constants $D$ and $M$ which are basis-independent such that the total degree of any Graver element of $L$ is not greater than $m(n-m+1)MD$. The case $M=1$ occurs precisely when $L$ is saturated, and in this case the bound is a reformulation of a well-known bound given by several authors. As a corollary, we show t...

We prove a reformulation of the multiplicity upper bound conjecture and use that reformulation to prove it for three-dimensional simplicial complexes and homology manifolds with many vertices. We provide necessary conditions for a Cohen-Macaulay complex with many vertices to have a pure minimal free resolution and a characterization of flag complexes whose minimal free resolution is pure.

This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem. By using several results from parametric optimization we show that, apart from exceptional cases, all locally minimal points of the reformulation are differentiability points of the objective function. This ju...

Fluent merging is a reformulation technique for classical planning problems that can be applied automatically or semiautomatically. The reformulation strives to transform a planning task into a representation that allows a planning algorithm to find solutions more efficiently or to find solutions of better quality. This work introduces different approaches for fluent merging and evaluates them ...

The query reformulation approach (also called semantic query optimization) takes advantage of the semantic knowledge about the contents of databases for optimization. The basic idea is to use the knowledge to reformulate a query into a less expensive yet equivalent query. Previous work on semantic query optimization has shown the cost reduction that can be achieved by reformulation, we further ...