The directed ring loading with penalty cost

Abstract

We study the directed ring loading problem with penalty cost, which is to select some of given multicast requests represented by hyperedges with different demands and embed them in a directed ring, such that the sum of the maximum congestion among all links on the ring and the total penalty cost of the unselected multicast requests is minimized. We prove that this problem is NP-hard even if the demand is divisible, and then design a 1.582-approximation algorithm for the demand divisible case and a 3-approximation algorithm for the demand indivisible case, respectively. As a consequence, for any ε > 0, we present a (1.582+ε)-approximation algorithm for the case where every multicast request contains exactly one sink.