TY - JOUR

T1 - Computing the k densest subgraphs of a graph

AU - Dondi, Riccardo

AU - Hermelin, Danny

N1 - Funding Information:
We thank anonymous reviewers for pointing out an error in an algorithm included in a previous version of the paper. We thank the anonymous reviewers of this version of the paper for many helpful suggestions and for pointing out reference [26].
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2023/1

Y1 - 2023/1

N2 - Computing cohesive subgraphs is a central problem in graph theory. While many formulations of cohesive subgraphs lead to NP-hard problems, finding a densest subgraph can be done in polynomial-time. As such, the densest subgraph model has emerged as the most popular notion of cohesiveness. Recently, the data mining community has started looking into the problem of computing k densest subgraphs in a given graph, rather than one. In this paper we consider a natural variant of the k densest subgraphs problem, where overlap between solution subgraphs is allowed with no constraint. We show that the problem is fixed-parameter tractable with respect to k, and admits a PTAS for constant k. Both these algorithms complement nicely the previously known O(nk) algorithm for the problem.

AB - Computing cohesive subgraphs is a central problem in graph theory. While many formulations of cohesive subgraphs lead to NP-hard problems, finding a densest subgraph can be done in polynomial-time. As such, the densest subgraph model has emerged as the most popular notion of cohesiveness. Recently, the data mining community has started looking into the problem of computing k densest subgraphs in a given graph, rather than one. In this paper we consider a natural variant of the k densest subgraphs problem, where overlap between solution subgraphs is allowed with no constraint. We show that the problem is fixed-parameter tractable with respect to k, and admits a PTAS for constant k. Both these algorithms complement nicely the previously known O(nk) algorithm for the problem.

KW - Algorithm design

KW - Algorithmic aspects of networks

KW - Algorithms

KW - Densest subgraph

KW - Network mining and analysis

UR - http://www.scopus.com/inward/record.url?scp=85138052736&partnerID=8YFLogxK

U2 - 10.1016/j.ipl.2022.106316

DO - 10.1016/j.ipl.2022.106316

M3 - Article

SN - 0020-0190

VL - 179

JO - Information Processing Letters

JF - Information Processing Letters

M1 - 106316

ER -