Complexity of uniqueness and local search in quadratic 0-1 programming

Authors:
Panos M Pardalos;Somesh Jha
Affiliations:
Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA;Department of Computer Science, Carnegie-Mellon University, Pittsburgh, PA 15213, USA
Venue:
Operations Research Letters
Year:
1992

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Abstract

We prove that the problem of checking whether a quadratic 0-1 problem has a unique solution is NP-hard. Furthermore, we prove that finding the global minimum of quadratic 0-1 programming with unique solution remains an NP-hard problem. Regarding local search, we prove that the problem of finding a discrete local minimum for quadratic 0-1 problems, with two coordinates being fixed, is NP-hard. In addition, we discuss an algorithm for computing discrete local minima.