Feedback vertex sets on restricted bipartite graphs

Authors:
Wei Jiang;Tian Liu;Chaoyi Wang;Ke Xu
Affiliations:
Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing 100871, Chi ...;Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing 100871, Chi ...;Key Laboratory of High Confidence Software Technologies, Ministry of Education, Institute of Software, School of Electronic Engineering and Computer Science, Peking University, Beijing 100871, Chi ...;National Lab of Software Development Environment, Beihang University, Beijing 100191, China
Venue:
Theoretical Computer Science
Year:
2013

Citing 30
Cited 0

A graph theoretic approach to statistical data security

SIAM Journal on Computing
Optimization of Pearl's method of conditioning and greedy-like approximation algorithms for the vertex feedback set problem

Artificial Intelligence
A linear-time algorithm for the weighted feedback vertex problem on interval graphs

Information Processing Letters
Approximation Algorithms for the Feedback Vertex Set Problem with Applications to Constraint Satisfaction and Bayesian Inference

SIAM Journal on Computing
Almost exact minimum feedback vertex set in meshes and butterflies

Information Processing Letters
Graph classes: a survey

Graph classes: a survey
Feedback vertex set in hypercubes

Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
An Approximation Algorithm for Feedback Vertex Sets in Tournaments

SIAM Journal on Computing
An Approximation Algorithm for Feedback Vertex Sets in Tournaments

SIAM Journal on Computing
New bounds on the size of the minimum feedback vertex set in meshes and butterflies

Information Processing Letters
A Min-Max Theorem on Feedback Vertex Sets

Mathematics of Operations Research
Minimum feedback vertex sets in shuffle-based interconnection networks

Information Processing Letters
Feedback vertex sets in star graphs

Information Processing Letters
Operating Systems Concepts with Java

Operating Systems Concepts with Java
Minimum weight feedback vertex sets in circle graphs

Information Processing Letters
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms

Algorithmica - Parameterized and Exact Algorithms
A fixed-parameter algorithm for the directed feedback vertex set problem

Journal of the ACM (JACM)
Improved algorithms for feedback vertex set problems

Journal of Computer and System Sciences
An efficient algorithm for minimum feedback vertex sets in rotator graphs

Information Processing Letters
Randomized algorithms for the loop cutset problem

Journal of Artificial Intelligence Research
Backdoors to typical case complexity

IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Linear programming based approximation algorithms for feedback set problems in bipartite tournaments

Theoretical Computer Science
Two hardness results on feedback vertex sets

FAW-AAIM'11 Proceedings of the 5th joint international frontiers in algorithmics, and 7th international conference on Algorithmic aspects in information and management
Tractable feedback vertex sets in restricted bipartite graphs

COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Feedback vertex sets in rotator graphs

ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
On feedback vertex set new measure and new structures

SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Improved approximation algorithm for the feedback set problem in a bipartite tournament

Operations Research Letters
Independent domination on tree convex bipartite graphs

FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
A REVIEW OF TREE CONVEX SETS TEST

Computational Intelligence

Quantified Score

Hi-index	5.23

Visualization

Abstract

A feedback vertex set (FVS) in a graph is a subset of vertices whose complement induces a forest. Finding a minimum FVS is NP-complete on bipartite graphs, but tractable on convex bipartite graphs and on chordal bipartite graphs. A bipartite graph is called tree convex, if a tree is defined on one part of the vertices, such that for every vertex in the other part, its neighborhood induces a subtree. When the tree is a path, a triad or a star, the bipartite graph is called convex bipartite, triad convex bipartite or star convex bipartite, respectively. We show that: (1) FVS is tractable on triad convex bipartite graphs; (2) FVS is NP-complete on star convex bipartite graphs and on tree convex bipartite graphs where the maximum degree of vertices on the tree is at most three.