Binary Integer Program Reformulation: A Set System Approximation Approach

This paper presents a generic reformulation framework for binary integer programs (BIPs) without imposing additional specifications for the objective function or constraints. To facilitate such generality, we introduce a set system approximation theory designed to identify the tightest inner and outer approximations for any binary solution space using special types of set systems. This development … Read more

The Star Degree Centrality Problem: A Decomposition Approach

We consider the problem of identifying the induced star with the largest cardinality open neighborhood in a graph. This problem, also known as the star degree centrality (SDC) problem, has been shown to be 𝒩𝒫-complete. In this work, we first propose a new integer programming (IP) formulation, which has a fewer number of constraints and … Read more

Cutting Plane Algorithms for 0-1 Programming Based on Cardinality Cuts

Abstract: We present new valid inequalities for 0-1 programming problems that work in similar ways to well known cover inequalities. Discussion and analysis of these cuts is followed by their revision and use in integer programming as a new generation of cuts that excludes not only portions of polyhedra containing noninteger points, also parts with … Read more

Cardinality Cuts: New Cutting Planes for 0-1 Programming

We present new valid inequalities that work in similar ways to well known cover inequalities.The differences exist in three aspects. First difference is in the generation of the inequalities. The method used in generation of the new cuts is more practical in contrast to classical cover inequalities. Second difference is the more general applicability, i.e., … Read more

Search and Cut: New Class of Cutting Planes for 0-1 Programming

The basic principle of the cutting plane techniques is to chop away the portions of the solution space of the linear programming relaxation of an integer program that contain no integer solutions. this is true for both Gomory’s cutting planes, and other more recent cuts based on valid inequalities. Obtaining a partial or full description … Read more