Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization

We show that the NP-complete Feedback Vertex Set problem, which asks for the smallest set of vertices to remove from a graph to destroy all cycles, is deterministically solvable in O ( c k ⋅ m ) time. Here, m denotes the number of graph edges, k denotes the size of the feedback vertex set searched f...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Journal of computer and system sciences Ročník 72; číslo 8; s. 1386 - 1396
Hlavní autoři: Guo, Jiong, Gramm, Jens, Hüffner, Falk, Niedermeier, Rolf, Wernicke, Sebastian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.12.2006
Témata:
Feedback set problem
Fixed-parameter tractability
Graph algorithm
Graph modification problem
Iterative compression
Iterative compression
Feedback set problem
Fixed-parameter tractability
Graph modification problem
Graph algorithm
ISSN:0022-0000, 1090-2724
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:We show that the NP-complete Feedback Vertex Set problem, which asks for the smallest set of vertices to remove from a graph to destroy all cycles, is deterministically solvable in O ( c k ⋅ m ) time. Here, m denotes the number of graph edges, k denotes the size of the feedback vertex set searched for, and c is a constant. We extend this to an algorithm enumerating all solutions in O ( d k ⋅ m ) time for a (larger) constant d. As a further result, we present a fixed-parameter algorithm with runtime O ( 2 k ⋅ m 2 ) for the NP-complete Edge Bipartization problem, which asks for at most k edges to remove from a graph to make it bipartite.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2006.02.001