Feedback edge sets in temporal graphs

Roman Haag; Hendrik Molter; Rolf Niedermeier; Malte Renken

doi:10.1016/j.dam.2021.09.029

Feedback edge sets in temporal graphs

Roman Haag, Hendrik Molter, Rolf Niedermeier, Malte Renken

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

9 Scopus citations

Abstract

The classical, linear-time solvable FEEDBACK EDGE SET problem is concerned with finding a minimum number of edges intersecting all cycles in a (static, unweighted) graph. We provide a first study of this problem in the setting of temporal graphs, where edges are present only at certain points in time. We find that there are four natural generalizations of FEEDBACK EDGE SET, all of which turn out to be NP-hard. We also study the tractability of these problems with respect to several parameters (solution size, lifetime, and number of graph vertices, among others) and obtain some parameterized hardness but also fixed-parameter tractability results.

Original language	English
Pages (from-to)	65-78
Number of pages	14
Journal	Discrete Applied Mathematics
Volume	307
DOIs	https://doi.org/10.1016/j.dam.2021.09.029
State	Published - 30 Jan 2022
Externally published	Yes

Keywords

Dynamic programming
Fixed-parameter tractability
MSO
NP-complete problems
Temporal cycles
Temporal paths

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2021.09.029

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title = "Feedback edge sets in temporal graphs",

abstract = "The classical, linear-time solvable FEEDBACK EDGE SET problem is concerned with finding a minimum number of edges intersecting all cycles in a (static, unweighted) graph. We provide a first study of this problem in the setting of temporal graphs, where edges are present only at certain points in time. We find that there are four natural generalizations of FEEDBACK EDGE SET, all of which turn out to be NP-hard. We also study the tractability of these problems with respect to several parameters (solution size, lifetime, and number of graph vertices, among others) and obtain some parameterized hardness but also fixed-parameter tractability results.",

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AU - Molter, Hendrik

AU - Niedermeier, Rolf

AU - Renken, Malte

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Y1 - 2022/1/30

N2 - The classical, linear-time solvable FEEDBACK EDGE SET problem is concerned with finding a minimum number of edges intersecting all cycles in a (static, unweighted) graph. We provide a first study of this problem in the setting of temporal graphs, where edges are present only at certain points in time. We find that there are four natural generalizations of FEEDBACK EDGE SET, all of which turn out to be NP-hard. We also study the tractability of these problems with respect to several parameters (solution size, lifetime, and number of graph vertices, among others) and obtain some parameterized hardness but also fixed-parameter tractability results.

AB - The classical, linear-time solvable FEEDBACK EDGE SET problem is concerned with finding a minimum number of edges intersecting all cycles in a (static, unweighted) graph. We provide a first study of this problem in the setting of temporal graphs, where edges are present only at certain points in time. We find that there are four natural generalizations of FEEDBACK EDGE SET, all of which turn out to be NP-hard. We also study the tractability of these problems with respect to several parameters (solution size, lifetime, and number of graph vertices, among others) and obtain some parameterized hardness but also fixed-parameter tractability results.

KW - Dynamic programming

KW - Fixed-parameter tractability

KW - MSO

KW - NP-complete problems

KW - Temporal cycles

KW - Temporal paths

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SP - 65

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Feedback edge sets in temporal graphs

Abstract

Keywords

ASJC Scopus subject areas

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