On characterization of maximal independent sets via quadratic optimization

Authors:
Foad Mahdavi Pajouh;Balabhaskar Balasundaram;Oleg A. Prokopyev
Affiliations:
School of Industrial Engineering & Management, Oklahoma State University, Stillwater, USA 74078;School of Industrial Engineering & Management, Oklahoma State University, Stillwater, USA 74078;Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, USA 15261
Venue:
Journal of Heuristics
Year:
2013

Citing 16
Cited 0

Experiments in quadratic 0-1 programming

Mathematical Programming: Series A and B
Computational aspects of a branch and bound algorithm for quadratic zero-one programming

Computing
Variable neighborhood search

Computers and Operations Research
Solving quadratic (0,1)-problems by semidefinite programs and cutting planes

Mathematical Programming: Series A and B
Tabu Search

Tabu Search
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints

SIAM Journal on Optimization
Evolution towards the Maximum Clique

Journal of Global Optimization
Finding independent sets in a graph using continuous multivariable polynomial formulations

Journal of Global Optimization
Pseudo-boolean optimization

Discrete Applied Mathematics
Ellipsoidal Approach to Box-Constrained Quadratic Problems

Journal of Global Optimization
Lower Bound Improvement and Forcing Rule for Quadratic Binary Programming

Computational Optimization and Applications
On a Polynomial Fractional Formulation for Independence Number of a Graph

Journal of Global Optimization
Local search heuristics for Quadratic Unconstrained Binary Optimization (QUBO)

Journal of Heuristics
Global equilibrium search applied to the unconstrained binary quadratic optimization problem

Optimization Methods & Software
Global optimality conditions for quadratic 0-1 optimization problems

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

This article investigates the local maxima properties of a box-constrained quadratic optimization formulation of the maximum independent set problem in graphs. Theoretical results characterizing binary local maxima in terms of certain induced subgraphs of the given graph are developed. We also consider relations between continuous local maxima of the quadratic formulation and binary local maxima in the Hamming distance-1 and distance-2 neighborhoods. These results are then used to develop an efficient local search algorithm that provides considerable speed-up over a typical local search algorithm for the binary Hamming distance-2 neighborhood.