A parameterized view on matroid optimization problems
Matroid theory gives us powerful techniques for understanding combinatorial optimization problems and for designing polynomial-time algorithms. However, several natural matroid problems, such as 3-matroid intersection, are NP-hard. Here we investigate these problems from the parameterized complexity...
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| Vydáno v: | Theoretical computer science Ročník 410; číslo 44; s. 4471 - 4479 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
Oxford
Elsevier B.V
17.10.2009
Elsevier |
| Témata: | |
| ISSN: | 0304-3975, 1879-2294 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Matroid theory gives us powerful techniques for understanding combinatorial optimization problems and for designing polynomial-time algorithms. However, several natural matroid problems, such as 3-matroid intersection, are NP-hard. Here we investigate these problems from the parameterized complexity point of view: instead of the trivial
n
O
(
k
)
time brute force algorithm for finding a
k
-element solution, we try to give algorithms with uniformly polynomial (i.e.,
f
(
k
)
⋅
n
O
(
1
)
) running time. The main result is that if the ground set of a represented linear matroid is partitioned into blocks of size
ℓ
, then we can determine in randomized time
f
(
k
,
ℓ
)
⋅
n
O
(
1
)
whether there is an independent set that is the union of
k
blocks. As a consequence, algorithms with similar running time are obtained for other problems such as finding a
k
-element set in the intersection of
ℓ
matroids, or finding
k
terminals in a network such that each of them can be connected simultaneously to the source by
ℓ
disjoint paths. |
|---|---|
| Bibliografie: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0304-3975 1879-2294 |
| DOI: | 10.1016/j.tcs.2009.07.027 |