Disentangling the Computational Complexity of Network Untangling

We study the network untangling problem introduced by Rozenshtein et al. (Data Min. Knowl. Disc. 35(1), 213–247, 2021), which is a variant of  Vertex Cover on temporal graphs–graphs whose edge set changes over discrete time steps. They introduce two problem variants. The goal is to select at most k...

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Bibliographic Details
Published in:Theory of computing systems Vol. 68; no. 1; pp. 103 - 121
Main Authors: Froese, Vincent, Kunz, Pascal, Zschoche, Philipp
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2024
Springer Nature B.V
Subjects:
Apexes
Complexity
Computer Science
Data mining
Graph theory
Graphs
Intervals
Parameters
Theory of Computation
Temporal graph mining
Parameterized algorithmics
Complexity dichotomy
ISSN:1432-4350, 1433-0490
Online Access:Get full text
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Summary:We study the network untangling problem introduced by Rozenshtein et al. (Data Min. Knowl. Disc. 35(1), 213–247, 2021), which is a variant of  Vertex Cover on temporal graphs–graphs whose edge set changes over discrete time steps. They introduce two problem variants. The goal is to select at most k time intervals for each vertex such that all time-edges are covered and (depending on the problem variant) either the maximum interval length or the total sum of interval lengths is minimized. This problem has data mining applications in finding activity timelines that explain the interactions of entities in complex networks. Both variants of the problem are NP-hard. In this paper, we initiate a multivariate complexity analysis involving the following parameters: number of vertices, lifetime of the temporal graph, number of intervals per vertex, and the interval length bound. For both problem versions, we (almost) completely settle the parameterized complexity for all combinations of those four parameters, thereby delineating the border of fixed-parameter tractability.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-023-10150-y