Domination analysis of algorithms for bipartite boolean quadratic programs

Abstract

For the bipartite boolean quadratic programming problem (BBQP) with m + n variables, an O(mn) algorithm is given to compute the average objective function value A of all solutions where as computing the median objective function value is shown to be NP-hard. Also, we show that any solution with objective function value no worse than A dominates at least 2m+n-2 solutions and this bound is the best possible. An O(mn) algorithm is given to identify such a solution. We then show that for any fixed rational number α = a/b > 1 and gcd(a,b) = 1, no polynomial time approximation algorithm exists for BBQP with dominance ratio larger than 1-2(1-α)/α(m+n), unless P=NP. Finally, it is shown that some powerful local search algorithms can get trapped at a local maximum with objective function value less than A. © 2013 Springer-Verlag.