A kernelization algorithm for d-Hitting Set
For a given parameterized problem, π, a kernelization algorithm is a polynomial-time pre-processing procedure that transforms an arbitrary instance of π into an equivalent one whose size depends only on the input parameter(s). The resulting instance is called a problem kernel. In this paper, a kerne...
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| Vydáno v: | Journal of computer and system sciences Ročník 76; číslo 7; s. 524 - 531 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
01.11.2010
|
| Témata: | |
| ISSN: | 0022-0000, 1090-2724 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | For a given parameterized problem,
π, a kernelization algorithm is a polynomial-time pre-processing procedure that transforms an arbitrary instance of
π into an equivalent one whose size depends only on the input parameter(s). The resulting instance is called a problem kernel. In this paper, a kernelization algorithm for the 3-Hitting Set problem is presented along with a general kernelization for
d-Hitting Set. For 3-Hitting Set, an arbitrary instance is reduced into an equivalent one that contains at most
5
k
2
+
k
elements. This kernelization is an improvement over previously known methods that guarantee cubic-order kernels. Our method is used also to obtain quadratic kernels for several other problems. For a constant
d
⩾
3
, a kernelization of
d-Hitting Set is achieved by a non-trivial generalization of the 3-Hitting Set method, and guarantees a kernel whose order does not exceed
(
2
d
−
1
)
k
d
−
1
+
k
. |
|---|---|
| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 0022-0000 1090-2724 |
| DOI: | 10.1016/j.jcss.2009.09.002 |