Complexity of a Class of Nonlinear Combinatorial Problems Related to Their Linear Counterparts

European Journal of Operational Research, Vol. 73, No. 3, pp. 569-576, March 1994

8 Pages Posted: 8 Apr 2008 Last revised: 10 May 2017

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Wieslaw Kubiak

University of Toronto

Date Written: 1994

Abstract

The ultimate purpose of our analysis is to show that for any class of linear combinatorial problems assumed to be NP-hard, the class of their strictly nonlinear counterparts is also NP-hard. In this paper, we set the framework, and prove the result for a class of linear integer programming problems with bounded feasible sets and their nonlinear counterparts. We also discuss briefly the complications that may arise when the feasible set is unbounded, and as a result some strictly nonlinear problems become easy even though their linear versions are hard.

Keywords: Complexity theory, Integer programming, Combinatorial optimization, Nonlinear objective functions, NP-hard

JEL Classification: M11, C61

Suggested Citation

Sethi, Suresh and Kubiak, Wieslaw, Complexity of a Class of Nonlinear Combinatorial Problems Related to Their Linear Counterparts (1994). European Journal of Operational Research, Vol. 73, No. 3, pp. 569-576, March 1994, Available at SSRN: https://ssrn.com/abstract=1117345

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Wieslaw Kubiak

University of Toronto ( email )

105 St George Street
Toronto, Ontario M5S 3G8
Canada

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
27
Abstract Views
529
PlumX Metrics