Industrial Engineering and Economics News
Department of Industrial Engineering and Economics started to issue Working Paper series, which reports recent outcomes of our research, in Publication section of this web site. The latest issue is 2016-1: Yotaro TAKAZAWA and Shinji MIZUNO. A 2-approximation algorithm for the minimum knapsack problem with a forcing graph.
Carnes and Shmoys  presented a 2-approximation algorithm for the minimum knapsack problem. We extend their algorithm to the minimum knapsack problem with a forcing graph (MKPFG), which has a forcing constraint for each edge in the graph. The forcing con-straint means that at least one item (vertex) of the edge must be packed in the knapsack. The problem is strongly NP-hard, since it includes the vertex cover problem as a special case. Generalizing the proposed algorithm, we also present an approximation algorithm for the covering integer program with 0-1 variables.
Following issues of Working Paper will appear as soon as available.