We study the approximability of three versions of the Steiner tree problem. For the first one where the input graph is only supposed connected, we show that it is not approximable within better than | \ | for any ∊ ∈ (0, 1), where and are the vertex-set of the input graph and the set of...

Given an instance of a weighted combinatorial optimization problem and its feasible solution, the usual inverse problem is to modify as little as possible (with respect to a fixed norm) the given weight system to make the given feasible solution optimal. We focus on its 0-1 version, which is to...

In this paper, we study the on-line version of the bin-packing problem. We analyze the approximation behavior of an on-line bin-packing algorithm under an approximation criterion called differential ratio. We are interested in two types of results : the differential competitivity ratio...