Data-independent neighborhood functions and strict local optima

Authors:
Derek E. Armstrong;Sheldon H. Jacobson
Affiliations:
BAE Systems, 3811 North Fairfax Drive, Arlington, VA 22203, USA;Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street (MC-244), Urbana, IL 61801-2906, USA
Venue:
Discrete Applied Mathematics
Year:
2005

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Abstract

The paper proves that data-independent neighborhood functions with the smooth property (all strict local optima are global optima) for maximum 3-satisfiability (MAX 3-SAT) must contain all possible solutions for large instances. Data-independent neighborhood functions with the smooth property for 0-1 knapsack are shown to have size with the same order of magnitude as the cardinality of the solution space. Data-independent neighborhood functions with the smooth property for traveling salesman problem (TSP) are shown to have exponential size. These results also hold for certain polynomially solvable sub-problems of MAX 3-SAT, 0-1 knapsack and TSP.