Your rugby mates don't need to know your colleagues: Triadic closure with edge colors

Laurent Bulteau; Niels Grüttemeier; Christian Komusiewicz; Manuel Sorge

doi:10.1016/j.jcss.2021.03.001

Your rugby mates don't need to know your colleagues: Triadic closure with edge colors

Laurent Bulteau, Niels Grüttemeier, Christian Komusiewicz, Manuel Sorge

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

1 Scopus citations

Abstract

Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong such that at most k edges are weak and for each induced P₃ in G at least one edge is weak. We study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced P₃ may receive two strong labels as long as they are different. In Edge-List Multi-STC and Vertex-List Multi-STC we may restrict the set of permitted colors for each edge of G. We show that, under the Exponential Time Hypothesis (ETH), Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time 2^o(|V|²). We proceed with a parameterized complexity analysis in which we extend previous algorithms and kernelizations for STC [11,14] to the three variants or outline the limits of such an extension.

Original language	English
Pages (from-to)	75-96
Number of pages	22
Journal	Journal of Computer and System Sciences
Volume	120
DOIs	https://doi.org/10.1016/j.jcss.2021.03.001
State	Published - 1 Sep 2021
Externally published	Yes

Keywords

Edge coloring
Exponential time hypothesis
Fixed-parameter tractability
Kernelization
Social network analysis

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1016/j.jcss.2021.03.001

Cite this

@article{2249ce6a66a94c28a5666aaf6ea72173,

title = "Your rugby mates don't need to know your colleagues: Triadic closure with edge colors",

abstract = "Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong such that at most k edges are weak and for each induced P3 in G at least one edge is weak. We study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced P3 may receive two strong labels as long as they are different. In Edge-List Multi-STC and Vertex-List Multi-STC we may restrict the set of permitted colors for each edge of G. We show that, under the Exponential Time Hypothesis (ETH), Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time 2o(|V|2). We proceed with a parameterized complexity analysis in which we extend previous algorithms and kernelizations for STC [11,14] to the three variants or outline the limits of such an extension.",

keywords = "Edge coloring, Exponential time hypothesis, Fixed-parameter tractability, Kernelization, Social network analysis",

author = "Laurent Bulteau and Niels Gr{\"u}ttemeier and Christian Komusiewicz and Manuel Sorge",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = sep,

day = "1",

doi = "10.1016/j.jcss.2021.03.001",

language = "English",

volume = "120",

pages = "75--96",

journal = "Journal of Computer and System Sciences",

issn = "0022-0000",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Your rugby mates don't need to know your colleagues

T2 - Triadic closure with edge colors

AU - Bulteau, Laurent

AU - Grüttemeier, Niels

AU - Komusiewicz, Christian

AU - Sorge, Manuel

PY - 2021/9/1

Y1 - 2021/9/1

N2 - Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong such that at most k edges are weak and for each induced P3 in G at least one edge is weak. We study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced P3 may receive two strong labels as long as they are different. In Edge-List Multi-STC and Vertex-List Multi-STC we may restrict the set of permitted colors for each edge of G. We show that, under the Exponential Time Hypothesis (ETH), Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time 2o(|V|2). We proceed with a parameterized complexity analysis in which we extend previous algorithms and kernelizations for STC [11,14] to the three variants or outline the limits of such an extension.

AB - Given an undirected graph G=(V,E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong such that at most k edges are weak and for each induced P3 in G at least one edge is weak. We study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced P3 may receive two strong labels as long as they are different. In Edge-List Multi-STC and Vertex-List Multi-STC we may restrict the set of permitted colors for each edge of G. We show that, under the Exponential Time Hypothesis (ETH), Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time 2o(|V|2). We proceed with a parameterized complexity analysis in which we extend previous algorithms and kernelizations for STC [11,14] to the three variants or outline the limits of such an extension.

KW - Edge coloring

KW - Exponential time hypothesis

KW - Fixed-parameter tractability

KW - Kernelization

KW - Social network analysis

UR - https://www.scopus.com/pages/publications/85103310136

U2 - 10.1016/j.jcss.2021.03.001

DO - 10.1016/j.jcss.2021.03.001

M3 - Article

AN - SCOPUS:85103310136

SN - 0022-0000

VL - 120

SP - 75

EP - 96

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

ER -

Your rugby mates don't need to know your colleagues: Triadic closure with edge colors

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this