@inproceedings{2e35d0ef1c224484a05e8808b8120822,

title = "Constant factor approximation for subset feedback set problems via a new LP relaxation",

abstract = "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} c V of k terminals. A cycle in G is interesting if it contains a terminal. In the Subset Feedback Edge Set problem (Subset-FES) 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 8-approximation 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(logn). In this paper, we introduce new LP relaxations for subset-FES and Subset-FVS and show that their integrality gap is at most 13. Our LP formulation and rounding are simple although the analysis is non-obvious.",

author = "Chandra Chekuri and Vivek Madan",

year = "2016",

doi = "10.1137/1.9781611974331.ch58",

language = "English (US)",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery",

pages = "808--820",

editor = "Robert Krauthgamer",

booktitle = "27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016",

address = "United States",

note = "27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 ; Conference date: 10-01-2016 Through 12-01-2016",

}