On the minimum feedback vertex set problem: Exact and enumeration algorithms

Fedor V. Fomin; Serge Gaspers; Artem V. Pyatkin; Igor Razgon

doi:10.1007/s00453-007-9152-0

On the minimum feedback vertex set problem: Exact and enumeration algorithms

Fedor V. Fomin, Serge Gaspers, Artem V. Pyatkin, Igor Razgon

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

100 Scopus citations

Abstract

We present a time O(1.7548 ⁿ) algorithm finding a minimum feedback vertex set in an undirected graph on n vertices. We also prove that a graph on n vertices can contain at most 1.8638 ⁿ minimal feedback vertex sets and that there exist graphs having 105 ^n/10≈1.5926 ⁿ minimal feedback vertex sets.

Original language	English
Pages (from-to)	293-307
Number of pages	15
Journal	Algorithmica
Volume	52
Issue number	2
DOIs	https://doi.org/10.1007/s00453-007-9152-0
State	Published - 1 Oct 2008
Externally published	Yes

Keywords

Exact exponential algorithm
Maximum induced forest
Minimum feedback vertex set
Number of minimal feedback vertex sets

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

Access to Document

10.1007/s00453-007-9152-0

Cite this

@article{90ad5dc26a824930ab6e22652ad613d6,

title = "On the minimum feedback vertex set problem: Exact and enumeration algorithms",

abstract = "We present a time O(1.7548 n) algorithm finding a minimum feedback vertex set in an undirected graph on n vertices. We also prove that a graph on n vertices can contain at most 1.8638 n minimal feedback vertex sets and that there exist graphs having 105 n/10≈1.5926 n minimal feedback vertex sets.",

keywords = "Exact exponential algorithm, Maximum induced forest, Minimum feedback vertex set, Number of minimal feedback vertex sets",

author = "Fomin, {Fedor V.} and Serge Gaspers and Pyatkin, {Artem V.} and Igor Razgon",

year = "2008",

month = oct,

day = "1",

doi = "10.1007/s00453-007-9152-0",

language = "English",

volume = "52",

pages = "293--307",

journal = "Algorithmica",

issn = "0178-4617",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - On the minimum feedback vertex set problem

T2 - Exact and enumeration algorithms

AU - Fomin, Fedor V.

AU - Gaspers, Serge

AU - Pyatkin, Artem V.

AU - Razgon, Igor

PY - 2008/10/1

Y1 - 2008/10/1

N2 - We present a time O(1.7548 n) algorithm finding a minimum feedback vertex set in an undirected graph on n vertices. We also prove that a graph on n vertices can contain at most 1.8638 n minimal feedback vertex sets and that there exist graphs having 105 n/10≈1.5926 n minimal feedback vertex sets.

AB - We present a time O(1.7548 n) algorithm finding a minimum feedback vertex set in an undirected graph on n vertices. We also prove that a graph on n vertices can contain at most 1.8638 n minimal feedback vertex sets and that there exist graphs having 105 n/10≈1.5926 n minimal feedback vertex sets.

KW - Exact exponential algorithm

KW - Maximum induced forest

KW - Minimum feedback vertex set

KW - Number of minimal feedback vertex sets

UR - http://www.scopus.com/inward/record.url?scp=50849102034&partnerID=8YFLogxK

U2 - 10.1007/s00453-007-9152-0

DO - 10.1007/s00453-007-9152-0

M3 - Article

AN - SCOPUS:50849102034

SN - 0178-4617

VL - 52

SP - 293

EP - 307

JO - Algorithmica

JF - Algorithmica

IS - 2

ER -

On the minimum feedback vertex set problem: Exact and enumeration algorithms

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this