Constant Factor Approximation for Subset Feedback Set Problems via a new LP relaxation

We consider subset feedback edge and vertex set problems in undirected graphs. The input to these problems is an undirected graph G = (V, E) and a set S = {s1, s2, . . . , sk} ⊂ V of k terminals. A cycle in G is interesting if it contains a terminal. In the Subset Feedback Edge Set problem (SubsetFES) the input graph is edge-weighted and the goal is to remove a minimum weight set of edges such that no interesting cycle remains. In the Subset Feedback Vertex Set problem (Subset-FVS) the input graph is node-weighted and the goal is to remove a minimum weight set of nodes such that no interesting cycle remains. A 2-approximation is known for Subset-FES [12] and a 8approximation is known for Subset-FVS [13]. The algorithm and analysis for Subset-FVS is complicated. One reason for the difficulty in addressing feedback set problems in undirected graphs has been the lack of LP relaxations with constant factor integrality gaps; the natural LP has an integrality gap of Θ(log n). In this pap...

• Type: Journal
• Year: 2016
• Where: SODA
• Authors: Chandra Chekuri, Vivek Madan
• Keywords: Algorithms, SODA 2016