On the Complexity Landscape of Connected f-Factor Problems

D 2016

On the Complexity Landscape of Connected f-Factor Problems

GANIAN, Robert, N. S. NARAYANASWAMY, Sebastian ORDYNIAK, C. S. RAHUL, M. S. RAMANUJAN et. al.

Basic information

Original name

On the Complexity Landscape of Connected f-Factor Problems

Authors

GANIAN, Robert (203 Czech Republic, guarantor, belonging to the institution), N. S. NARAYANASWAMY (356 India), Sebastian ORDYNIAK (40 Austria), C. S. RAHUL (356 India) and M. S. RAMANUJAN (356 India)

Edition

Germany, 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016, August 22-26, p. "41:1"-"41:14", 14 pp. 2016

Publisher

Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

RIV identification code

RIV/00216224:14330/16:00093949

Organization unit

Faculty of Informatics

ISBN

978-3-95977-016-3

ISSN

DOI

http://dx.doi.org/10.4230/LIPIcs.MFCS.2016.41

Keywords in English

algorithms; vertex deletion problems

Abstract

V originále

Given an n-vertex graph G and a function f:V(G) -> {0, ..., n-1}, an f-factor is a subgraph H of G such that deg_H(v)=f(v) for every vertex v in V(G); we say that H is a connected f-factor if, in addition, the subgraph H is connected. A classical result of Tutte (1954) is the polynomial time algorithm to check whether a given graph has a specified f-factor. However, checking for the presence of a connected f-factor is easily seen to generalize Hamiltonian Cycle and hence is NP-complete. In fact, the Connected f-Factor problem remains NP-complete even when f(v) is at least n^epsilon for each vertex v and epsilon<1; on the other side of the spectrum, the problem was known to be polynomial-time solvable when f(v) is at least n/3 for every vertex v. In this paper, we extend this line of work and obtain new complexity results based on restricting the function f. In particular, we show that when f(v) is required to be at least n/(log n)^c, the problem can be solved in quasi-polynomial time in general and in randomized polynomial time if c <= 1. We also show that when c>1, the problem is NP-intermediate.

Citovat

GANIAN, Robert, N. S. NARAYANASWAMY, Sebastian ORDYNIAK, C. S. RAHUL and M. S. RAMANUJAN. On the Complexity Landscape of Connected f-Factor Problems. Online. In Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier. 41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016, August 22-26. Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016, p. "41:1"-"41:14", 14 pp. ISBN 978-3-95977-016-3. Available from: https://dx.doi.org/10.4230/LIPIcs.MFCS.2016.41.

@inproceedings{1376049,
   author = {Ganian, Robert and Narayanaswamy, N. S. and Ordyniak, Sebastian and Rahul, C. S. and Ramanujan, M. S.},
   address = {Germany},
   booktitle = {41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016, August 22-26},
   doi = {http://dx.doi.org/10.4230/LIPIcs.MFCS.2016.41},
   editor = {Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
   keywords = {algorithms; vertex deletion problems},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Germany},
   isbn = {978-3-95977-016-3},
   pages = {"41:1"-"41:14"},
   publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik},
   title = {On the Complexity Landscape of Connected f-Factor Problems},
   year = {2016}
}

TY  - JOUR
ID  - 1376049
AU  - Ganian, Robert - Narayanaswamy, N. S. - Ordyniak, Sebastian - Rahul, C. S. - Ramanujan, M. S.
PY  - 2016
TI  - On the Complexity Landscape of Connected f-Factor Problems
PB  - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik
CY  - Germany
SN  - 9783959770163
KW  - algorithms
KW  - vertex deletion problems
N2  - Given an n-vertex graph G and a function f:V(G) -> {0, ..., n-1}, an f-factor is a subgraph H of G such that deg_H(v)=f(v) for every vertex v in V(G); we say that H is a connected f-factor if, in addition, the subgraph H is connected. A classical result of Tutte (1954) is the polynomial time algorithm to check whether a given graph has a specified f-factor. However, checking for the presence of a connected f-factor is easily seen to generalize Hamiltonian Cycle and hence is NP-complete. In fact, the Connected f-Factor problem remains NP-complete even when f(v) is at least n^epsilon for each vertex v and epsilon<1; on the other side of the spectrum, the problem was known to be polynomial-time solvable when f(v) is at least n/3 for every vertex v. In this paper, we extend this line of work and obtain new complexity results based on restricting the function f. In particular, we show that when f(v) is required to be at least n/(log n)^c, the problem can be solved in quasi-polynomial time in general and in randomized polynomial time if c <= 1. We also show that when c>1, the problem is NP-intermediate.
ER  -

GANIAN, Robert, N. S. NARAYANASWAMY, Sebastian ORDYNIAK, C. S. RAHUL and M. S. RAMANUJAN. On the Complexity Landscape of Connected f-Factor Problems. Online. In Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier. \textit{41st International Symposium on Mathematical Foundations of Computer Science, MFCS 2016, August 22-26}. Germany: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016, p.~''41:1''-''41:14'', 14 pp. ISBN~978-3-95977-016-3. Available from: https://dx.doi.org/10.4230/LIPIcs.MFCS.2016.41.

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