Prize-Collecting Steiner Networks via Iterative Rounding

In this paper we design an iterative rounding approach for the classic prize-collecting Steiner forest problem and more generally the prize-collecting survivable Steiner network design problem. We show as an structural result that in each iteration of our algorithm there is an LP variable in a basic feasible solution which is at least one-third-integral resulting a 3-approximation algorithm for this problem. In addition, we show this factor 3 in our structural result is indeed tight for prize-collecting Steiner forest and thus prize-collecting survivable Steiner network design. This especially answers negatively the previous belief that one might be able to obtain an approximation factor better than 3 for these problems using a natural iterative rounding approach. Our structural result is extending the celebrated iterative rounding approach of Jain [13] by using several new ideas some from more complicated linear algebra. The approach of this paper can be also applied to get a constant...

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: MohammadTaghi Hajiaghayi, Arefeh A. Nasri
• Keywords: Information Retrieval, Iterative Rounding Approach, LATIN 2010, Prize-collecting Steiner Forest, Prize-collecting Survivable Steiner