Stability in circular arc graphs

Martin Charles Golumbic; Peter L. Hammer

doi:10.1016/0196-6774(88)90023-5

Stability in circular arc graphs

Martin Charles Golumbic, Peter L. Hammer

Research output: Contribution to journal › Article › peer-review

Abstract

An algorithm is presented which finds a maximum stable set of a family of n arcs on a circle in O(nlogn) time given the arcs as an unordered list of their endpoints or in O(n) time if they are already sorted. If we are given only the circular arc graph without a circular arc representation for it, then a maximum stable set can be found in O(n + δe) time where n, e, and δ are the number of vertices, edges, and minimum vertex degree, respectively. Our algorithms are based on a simple neighborhood reduction theorem which allows one to reduce any circular arc graph to a special canonical form.

Original language	English
Pages (from-to)	314-320
Number of pages	7
Journal	Journal of Algorithms
Volume	9
Issue number	3
DOIs	https://doi.org/10.1016/0196-6774(88)90023-5
State	Published - Sep 1988
Externally published	Yes

Bibliographical note

Funding Information:
*This work was first presented by the authors at the First International Japan Conference on Graph Theory and Applications, (Hakone, Japan), June 1986. +This research was sponsored in part by the U.S. Air Force Office of Scientific Research Grant AF 0271 and by the National Science Foundation Grant NSF ECS 8503212.

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Computational Theory and Mathematics

Access to Document

10.1016/0196-6774(88)90023-5

Cite this

@article{16a849cdbf2f411bafbb4bf62c8fefa4,

title = "Stability in circular arc graphs",

abstract = "An algorithm is presented which finds a maximum stable set of a family of n arcs on a circle in O(nlogn) time given the arcs as an unordered list of their endpoints or in O(n) time if they are already sorted. If we are given only the circular arc graph without a circular arc representation for it, then a maximum stable set can be found in O(n + δe) time where n, e, and δ are the number of vertices, edges, and minimum vertex degree, respectively. Our algorithms are based on a simple neighborhood reduction theorem which allows one to reduce any circular arc graph to a special canonical form.",

author = "Golumbic, {Martin Charles} and Hammer, {Peter L.}",

note = "Funding Information: *This work was first presented by the authors at the First International Japan Conference on Graph Theory and Applications, (Hakone, Japan), June 1986. +This research was sponsored in part by the U.S. Air Force Office of Scientific Research Grant AF 0271 and by the National Science Foundation Grant NSF ECS 8503212.",

year = "1988",

month = sep,

doi = "10.1016/0196-6774(88)90023-5",

language = "English",

volume = "9",

pages = "314--320",

journal = "Journal of Algorithms",

issn = "0196-6774",

publisher = "Academic Press Inc.",

number = "3",

}

TY - JOUR

T1 - Stability in circular arc graphs

AU - Golumbic, Martin Charles

AU - Hammer, Peter L.

N1 - Funding Information: *This work was first presented by the authors at the First International Japan Conference on Graph Theory and Applications, (Hakone, Japan), June 1986. +This research was sponsored in part by the U.S. Air Force Office of Scientific Research Grant AF 0271 and by the National Science Foundation Grant NSF ECS 8503212.

PY - 1988/9

Y1 - 1988/9

N2 - An algorithm is presented which finds a maximum stable set of a family of n arcs on a circle in O(nlogn) time given the arcs as an unordered list of their endpoints or in O(n) time if they are already sorted. If we are given only the circular arc graph without a circular arc representation for it, then a maximum stable set can be found in O(n + δe) time where n, e, and δ are the number of vertices, edges, and minimum vertex degree, respectively. Our algorithms are based on a simple neighborhood reduction theorem which allows one to reduce any circular arc graph to a special canonical form.

AB - An algorithm is presented which finds a maximum stable set of a family of n arcs on a circle in O(nlogn) time given the arcs as an unordered list of their endpoints or in O(n) time if they are already sorted. If we are given only the circular arc graph without a circular arc representation for it, then a maximum stable set can be found in O(n + δe) time where n, e, and δ are the number of vertices, edges, and minimum vertex degree, respectively. Our algorithms are based on a simple neighborhood reduction theorem which allows one to reduce any circular arc graph to a special canonical form.

UR - http://www.scopus.com/inward/record.url?scp=0011478346&partnerID=8YFLogxK

U2 - 10.1016/0196-6774(88)90023-5

DO - 10.1016/0196-6774(88)90023-5

M3 - Article

AN - SCOPUS:0011478346

SN - 0196-6774

VL - 9

SP - 314

EP - 320

JO - Journal of Algorithms

JF - Journal of Algorithms

IS - 3

ER -

Stability in circular arc graphs

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this