An O*(3.533k)-time parameterized algorithm for the 3-set packing problem

Authors:
Jianxin Wang;Qilong Feng;Jianer Chen
Affiliations:
School of Information Science and Engineering, Central South University, Changsha 410083, PR China;School of Information Science and Engineering, Central South University, Changsha 410083, PR China;School of Information Science and Engineering, Central South University, Changsha 410083, PR China and Department of Computer Science and Engineering, Texas A&M University, College Station, TX 778 ...
Venue:
Theoretical Computer Science
Year:
2011

Citing 12
Cited 0

Storing a Sparse Table with 0(1) Worst Case Access Time

Journal of the ACM (JACM)
Color-coding

Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Splitters and near-optimal derandomization

FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
An efficient parameterized algorithm for m-set packing

Journal of Algorithms
Using Nondeterminism to Design Efficient Deterministic Algorithms

Algorithmica
Improved algorithms for path, matching, and packing problems

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Faster Algebraic Algorithms for Path and Packing Problems

ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Improved Parameterized Set Splitting Algorithms: A Probabilistic Approach

Algorithmica
A faster parameterized algorithm for set packing

Information Processing Letters
Divide-and-color

WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Greedy localization and color-coding: improved matching and packing algorithms

IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation

Quantified Score

Hi-index	5.23

Visualization

Abstract

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^*(3.53^3^k) for the 3-set packing problem, improving the previous best upper bound O^*(4.61^3^k).