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...
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| Published in: | Journal of computer and system sciences Vol. 72; no. 8; pp. 1386 - 1396 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Inc
01.12.2006
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| ISSN: | 0022-0000, 1090-2724 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. |
| Author | Gramm, Jens Hüffner, Falk Niedermeier, Rolf Guo, Jiong Wernicke, Sebastian |
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| Keywords | Iterative compression Feedback set problem Fixed-parameter tractability Graph modification problem Graph algorithm |
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| Snippet | 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... |
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| SubjectTerms | Feedback set problem Fixed-parameter tractability Graph algorithm Graph modification problem Iterative compression |
| Title | Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization |
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