Subset feedback vertex set is fixed-parameter tractable
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Enumerating minimal subset feedback vertex sets
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
An FPT algorithm for edge subset feedback edge set
Information Processing Letters
Fast algorithms for hard graph problems: bidimensionality, minors, and local treewidth
GD'04 Proceedings of the 12th international conference on Graph Drawing
Fixed-parameter tractability for the subset feedback set problem and the S-cycle packing problem
Journal of Combinatorial Theory Series B
Disjoint cycles intersecting a set of vertices
Journal of Combinatorial Theory Series B
Directed subset feedback vertex set is fixed-parameter tractable
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
An exact algorithm for subset feedback vertex set on chordal graphs
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
| Hi-index | 0.00 |
We present an 8-approximation algorithm for the problem of finding a minimum weight subset feedback vertex set (or subset-fvs, in short). The input in this problem consists of an undirected graph G=(V,E) with vertex weights c(v) and a subset of vertices S called special vertices. A cycle is called interesting if it contains at least one special vertex. A subset of vertices is called a subset-fvs with respect to S if it intersects every interesting cycle. The goal is to find a minimum weight subset-fvs. The best previous algorithm for the general case provided only a logarithmic approximation factor. The minimum weight subset-fvs problem generalizes two NP-complete problems: the minimum weight feedback vertex set problem in undirected graphs and the minimum weight multiway vertex cut problem. The main tool that we use in our algorithm and its analysis is a new version of multicommodity flow, which we call relaxed multicommodity flow. Relaxed multicommodity flow is a hybrid of multicommodity flow and multiterminal flow.