Certifying algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs

Authors:
Haim Kaplan;Yahav Nussbaum
Affiliations:
The Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;The Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 14
Cited 1

Recognizing interval digraphs and interval bigraphs in polynomial time

Discrete Applied Mathematics
LEDA: a platform for combinatorial and geometric computing

LEDA: a platform for combinatorial and geometric computing
Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs

SIAM Journal on Computing
PC trees and circular-ones arrangements

Theoretical Computer Science - Computing and combinatorics
A certifying algorithm for the consecutive-ones property

SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Certifying LexBFS Recognition Algorithms for Proper Interval Graphs and Proper Interval Bigraphs

SIAM Journal on Discrete Mathematics
Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs

SIAM Journal on Computing
Polynomial time recognition of unit circular-arc graphs

Journal of Algorithms
Recognition and computation of minimal triangulations for AT-free claw-free and co-comparability graphs

Discrete Applied Mathematics
Unit Circular-Arc Graph Representations and Feasible Circulations

SIAM Journal on Discrete Mathematics
Interval bigraphs and circular arc graphs

Journal of Graph Theory
Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms

Journal of Computer and System Sciences
Certifying algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs

WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
A simpler linear-time recognition of circular-arc graphs

SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory

Normal Helly circular-arc graphs and its subclasses

Discrete Applied Mathematics

Quantified Score

Hi-index	0.05

Visualization

Abstract

We give two new linear-time algorithms, one for recognizing proper circular-arc graphs and the other for recognizing unit circular-arc graphs. Both algorithms provide either a model for the input graph, or a certificate that proves that such a model does not exist and can be authenticated in O(n) time. No other previous algorithm for each of these two graph classes provides a certificate for its result.