The Boolean quadric polytope: some characteristics, facets and relatives
Mathematical Programming: Series A and B
A branch and bound algorithm for the maximum clique problem
Computers and Operations Research
Quadratic 0/1 optimization and a decomposition approach for the placement of electronic circuits
Mathematical Programming: Series A and B
Adaptive Memory Tabu Search for Binary Quadratic Programs
Management Science
Solving quadratic (0,1)-problems by semidefinite programs and cutting planes
Mathematical Programming: Series A and B
Discrete Applied Mathematics
Hi-index | 0.00 |
We consider a still NP-complete partial case of the unconstrained binary quadratic optimization problem that can be described in terms of an undirected graph with red edges having negative weights and green edges having positive weights. The maximum vertex degree of the graph is three. It can be assumed w.l.o.g. that every vertex is incident to a red and a green edge. We are looking for a vertex cover with respect to the red edges which covers a subset of green edges of total weight as small as possible. We prove that for all connected such graphs except a subclass of special graphs having exactly five green edges it is possible to find a vertex cover with respect to the red edges for which the total weight of uncovered green edges is at least 1/4 fraction of the total weight of all green edges.