An O ∗ ( 3.5 3 3 k ) -time parameterized algorithm for the 3-set packing problem

A parameterized algorithm for the well-known NP-complete problem 3- set packing is presented. The algorithm is based on the following new approaches: (1) an efficient algorithm for problem instances in which one element is known for each of the 3-sets in a solution packing (i.e., type-1  instances);...

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Bibliographic Details
Published in:Theoretical computer science Vol. 412; no. 18; pp. 1745 - 1753
Main Authors: Wang, Jianxin, Feng, Qilong, Chen, Jianer
Format: Journal Article Conference Proceeding
Language:English
Published: Oxford Elsevier B.V 15.04.2011
Elsevier
Subjects:
3-set packing
[formula omitted]-universal set
Algorithmics. Computability. Computer arithmetics
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Designs and configurations
Divide and conquer
Exact sciences and technology
Mathematics
Miscellaneous
Sciences and techniques of general use
Theoretical computing
( n , k ) -universal set
3-set packing
Divide and conquer
Upper bound
Packing
Computer theory
(n. k)-universal set
Decomposition method
NP complete problem
Algorithm
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:A parameterized algorithm for the well-known NP-complete problem 3- set packing is presented. The algorithm is based on the following new approaches: (1) an efficient algorithm for problem instances in which one element is known for each of the 3-sets in a solution packing (i.e., type-1  instances); (2) an efficient algorithm for problem instances in which at least two elements are known for each of the 3-sets in a solution packing (i.e., type-2  instances); and (3) an effective decomposition of a general instance of 3 -set packing into two instances of type-1 and type-2, respectively, whose base sets are disjoint. This technique results in an improved parameterized algorithm of running time O ∗ ( 3.5 3 3 k ) for the 3 -set packing problem, improving the previous best upper bound O ∗ ( 4.6 1 3 k ) .
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2010.12.048