Improved algorithms for weighted and unweighted set splitting problems

Authors:
Jianer Chen;Songjian Lu
Affiliations:
Department of Computer Science, Texas A&M University, College Station, TX;Department of Computer Science, Texas A&M University, College Station, TX
Venue:
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Year:
2007

Citing 13
Cited 1

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

Journal of the ACM (JACM)
A fast and simple randomized parallel algorithm for the maximal independent set problem

Journal of Algorithms
Approximability of maximum splitting of k-sets and some other Apx-complete problems

Information Processing Letters
Outward rotations: a tool for rounding solutions of semidefinite programming relaxations, with applications to MAX CUT and other problems

STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint

Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties

Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
An Improved Learning Algorithm for Augmented Naive Bayes

PAKDD '01 Proceedings of the 5th Pacific-Asia Conference on Knowledge Discovery and Data Mining
Splitters and near-optimal derandomization

FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved algorithms for path, matching, and packing problems

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
Parameterized Complexity

Parameterized Complexity

Randomized disposal of unknowns and implicitly enforced bounds on parameters

IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we study parameterized algorithms for the set splitting problem, for both weighted and unweighted versions. First, we develop a new and effective technique based on a probabilistic method that allows us to develop a simpler and more efficient (deterministic) kernelization algorithm for the unweighted set splitting problem. We then propose a randomized algorithm for the weighted set splitting problem that is based on a new subset partition technique and has its running time bounded by O*(2k), which even significantly improves the previously known upper bound for the unweigthed set splitting problem. We also show that our algorithm can be de-randomized, thus derive the first fixed parameter tractable algorithm for the weighted set splitting problem.