Confining sets and avoiding bottleneck cases: A simple maximum independent set algorithm in degree-3 graphs

Authors:
Mingyu Xiao;Hiroshi Nagamochi
Affiliations:
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo, Kyoto 606-8501, Japan
Venue:
Theoretical Computer Science
Year:
2013

Citing 12
Cited 0

An O(20.304n) Algorithm for Solving Maximum Independent Set Problem

IEEE Transactions on Computers
Finding maximum independent sets in sparse and general graphs

Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Labeled Search Trees and Amortized Analysis: Improved Upper Bounds for NP-Hard Problems

Algorithmica
Measure and conquer: a simple O(20.288n) independent set algorithm

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Faster computation of maximum independent set and parameterized vertex cover for graphs with maximum degree 3

Journal of Discrete Algorithms
Pathwidth of cubic graphs and exact algorithms

Information Processing Letters
An O*(1.0977n) exact algorithm for MAX INDEPENDENT SET in sparse graphs

IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Further improvement on maximum independent set in degree-4 graphs

COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Fast Algorithms for max independent set

Algorithmica
Linear kernels in linear time, or how to save k colors in O(n2) steps

WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
A simple and fast algorithm for maximum independent set in 3-degree graphs

WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
A faster algorithm for finding maximum independent sets in sparse graphs

LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics

Quantified Score

Hi-index	5.23

Visualization

Abstract

We present an O^*(1.0836^n)-time algorithm for finding a maximum independent set in an n-vertex graph with degree bounded by 3, which improves all previous running time bounds for this problem. Our approach has the following two features. Without increasing the number of reduction/branching rules to get an improved time bound, we first successfully extract the essence from the previously known reduction rules such as domination, which can be used to get simple algorithms. More formally, we introduce a procedure for computing ''confining sets'', which unifies several known reducible subgraphs and covers new reducible subgraphs. Second we identify those instances that generate the worst recurrence among all recurrences of our branching rules as ''bottleneck instances'' and prove that bottleneck instances cannot appear consecutively after each branching operation.