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Heuristics for Covering the Timeline in Temporal Graphs

Authors Riccardo Dondi , Rares-Ioan Mateiu , Alexandru Popa

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LIPIcs.TIME.2025.8.pdf
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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Mathematical optimization
  • Theory of computation → Discrete optimization
Keywords
  • Temporal Networks
  • Activity Timeline
  • Vertex Cover
  • Heuristic
  • Dynamic Programming

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Abstract

We consider a variant of the Vertex Cover problem on temporal graphs, called Minimum Timeline Cover (k-MinTimelineCover). Temporal graphs are used to model complex systems, describing how edges (relations) change in a discrete time domain. The k-MinTimelineCover problem has been introduced in complex data summarization and synthesis jobs. Given a temporal graph G, k-MinTimelineCover asks to define k activity intervals for each vertex, such that each temporal edge is covered by at least one active interval. The objective function is the minimization of the sum of interval lengths. k-MinTimelineCover is NP-hard and even hard to approximate within any factor for k > 1. While the literature has mainly focused on the cases k = 1, in this contribution we consider the case k > 1. We first present an ILP formulation that is able to solve the problem on moderate size instances. Then we develop an efficient heuristic, based on local search which is built on top of the solution of an existing literature method. 
Finally, we present an experimental evaluation of our algorithms on synthetic data sets, that shows in particular that our heuristic has a consistent improvement on the state-of-the art method.

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Riccardo Dondi, Rares-Ioan Mateiu, and Alexandru Popa. Heuristics for Covering the Timeline in Temporal Graphs. In 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 355, pp. 8:1-8:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.TIME.2025.8

Author Details

Riccardo Dondi
  • Università degli Studi di Bergamo, Italy
Rares-Ioan Mateiu
  • Department of Computer Science, University of Bucharest, Romania
Alexandru Popa
  • Department of Computer Science, University of Bucharest, Romania

References

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