Vertex cover gets faster and harder on low degree graphs

Akanksha Agrawal; Sathish Govindarajan; Neeldhara Misra

doi:10.1007/978-3-319-08783-2_16

Vertex cover gets faster and harder on low degree graphs

Akanksha Agrawal, Sathish Govindarajan, Neeldhara Misra

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of two Hamiltonian Paths. We show the latter problem to be NP-complete, and also give an algorithm to find a vertex cover of size at most k, on graphs of maximum degree four, whose running time is 1.2637 ^k n ^O(1).

Original language	English
Title of host publication	Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings
Publisher	Springer Verlag
Pages	179-190
Number of pages	12
ISBN (Print)	9783319087825
DOIs	https://doi.org/10.1007/978-3-319-08783-2_16
State	Published - 1 Jan 2014
Externally published	Yes
Event	20th International Computing and Combinatorics Conference, COCOON 2014 - Atlanta, GA, United States Duration: 4 Aug 2014 → 6 Aug 2014

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	8591 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	20th International Computing and Combinatorics Conference, COCOON 2014
Country/Territory	United States
City	Atlanta, GA
Period	4/08/14 → 6/08/14

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-319-08783-2_16

Cite this

Agrawal, A., Govindarajan, S., & Misra, N. (2014). Vertex cover gets faster and harder on low degree graphs. In Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings (pp. 179-190). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8591 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-08783-2_16

Agrawal, Akanksha ; Govindarajan, Sathish ; Misra, Neeldhara. / Vertex cover gets faster and harder on low degree graphs. Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings. Springer Verlag, 2014. pp. 179-190 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{a502a6c125c84b80acf4be4062354820,

title = "Vertex cover gets faster and harder on low degree graphs",

abstract = "The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of two Hamiltonian Paths. We show the latter problem to be NP-complete, and also give an algorithm to find a vertex cover of size at most k, on graphs of maximum degree four, whose running time is 1.2637 k n O(1).",

author = "Akanksha Agrawal and Sathish Govindarajan and Neeldhara Misra",

year = "2014",

month = jan,

day = "1",

doi = "10.1007/978-3-319-08783-2_16",

language = "English",

isbn = "9783319087825",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "179--190",

booktitle = "Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings",

address = "Germany",

note = "20th International Computing and Combinatorics Conference, COCOON 2014 ; Conference date: 04-08-2014 Through 06-08-2014",

}

Agrawal, A, Govindarajan, S & Misra, N 2014, Vertex cover gets faster and harder on low degree graphs. in Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8591 LNCS, Springer Verlag, pp. 179-190, 20th International Computing and Combinatorics Conference, COCOON 2014, Atlanta, GA, United States, 4/08/14. https://doi.org/10.1007/978-3-319-08783-2_16

Vertex cover gets faster and harder on low degree graphs. / Agrawal, Akanksha; Govindarajan, Sathish; Misra, Neeldhara.
Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings. Springer Verlag, 2014. p. 179-190 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8591 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Vertex cover gets faster and harder on low degree graphs

AU - Agrawal, Akanksha

AU - Govindarajan, Sathish

AU - Misra, Neeldhara

PY - 2014/1/1

Y1 - 2014/1/1

N2 - The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of two Hamiltonian Paths. We show the latter problem to be NP-complete, and also give an algorithm to find a vertex cover of size at most k, on graphs of maximum degree four, whose running time is 1.2637 k n O(1).

AB - The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric objects, often turns out to be exactly the vertex cover problem on restricted classes of graphs. In this work we explore a particular instance of such a phenomenon. We consider the problem of hitting all axis-parallel slabs induced by a point set P, and show that it is equivalent to the problem of finding a vertex cover on a graph whose edge set is the union of two Hamiltonian Paths. We show the latter problem to be NP-complete, and also give an algorithm to find a vertex cover of size at most k, on graphs of maximum degree four, whose running time is 1.2637 k n O(1).

UR - http://www.scopus.com/inward/record.url?scp=84904733131&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-08783-2_16

DO - 10.1007/978-3-319-08783-2_16

M3 - Conference contribution

AN - SCOPUS:84904733131

SN - 9783319087825

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 179

EP - 190

BT - Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings

PB - Springer Verlag

T2 - 20th International Computing and Combinatorics Conference, COCOON 2014

Y2 - 4 August 2014 through 6 August 2014

ER -

Agrawal A, Govindarajan S, Misra N. Vertex cover gets faster and harder on low degree graphs. In Computing and Combinatorics - 20th International Conference, COCOON 2014, Proceedings. Springer Verlag. 2014. p. 179-190. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-08783-2_16

Vertex cover gets faster and harder on low degree graphs

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this