We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 0-1 knapsack set, the mixed 0-1 knapsack set, the integer ...
We consider the standard semidefinite programming (SDP) relaxation for vertex cover to which all hypermetric inequalities supported on at most k vertices have been added. We show t...
We find the largest for which any simple closed path in the universal cover R2 \ Z2 of R2 \ Z2, equipped with the natural lifted metric from the Euclidean two dimensional plane,...
Crowder et al. (Oper. Res. 31 (1983) 803–834) conjectured that the separation problem for cover inequalities for binary integer programs is polynomially solvable. We show that t...
Diego Klabjan, George L. Nemhauser, Craig A. Tovey
The 0-1 Multidimensional Knapsack Problem (0-1 MKP) is a wellknown (and strongly NP-hard) combinatorial optimization problem with many applications. Up to now, the majority of upp...