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Partial Temporal Vertex Cover with Bounded Activity Intervals

Authors Riccardo Dondi , Fabrizio Montecchiani , Giacomo Ortali , Tommaso Piselli , Alessandra Tappini

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Temporal Graphs
  • Temporal Vertex Cover
  • Parameterized Complexity
  • Approximation Algorithms

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Abstract

Different variants of Vertex Cover have recently garnered attention in the context of temporal graphs. One of these variants is motivated by the need to summarize timeline activities in social networks. Here, the activities of individual vertices, representing users, are characterized by time intervals. In this paper, we explore a scenario where the temporal span of each vertex’s activity interval is bounded by an integer 𝓁, and the objective is to maximize the number of (temporal) edges that are covered. We establish the APX-hardness of this problem and the NP-hardness of the corresponding decision problem, even under the restricted condition where the temporal domain comprises only two timestamps and each edge appears at most once. Subsequently, we delve into the parameterized complexity of the problem, offering two fixed-parameter algorithms parameterized by: (i) the number k of temporal edges covered by the solution, and (ii) the number h of temporal edges not covered by the solution. Finally, we present a polynomial-time approximation algorithm achieving a factor of 3/4.

Cite As Get BibTex

Riccardo Dondi, Fabrizio Montecchiani, Giacomo Ortali, Tommaso Piselli, and Alessandra Tappini. Partial Temporal Vertex Cover with Bounded Activity Intervals. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SAND.2024.11

Author Details

Riccardo Dondi
  • Università degli Studi di Bergamo, Italy
Fabrizio Montecchiani
  • Università degli Studi di Perugia, Italy
Giacomo Ortali
  • Università degli Studi di Perugia, Italy
Tommaso Piselli
  • Università degli Studi di Perugia, Italy
Alessandra Tappini
  • Università degli Studi di Perugia, Italy

Funding

This work was partially supported by: (i) MUR PRIN Proj. 2022TS4Y3N - "EXPAND: scalable algorithms for EXPloratory Analyses of heterogeneous and dynamic Networked Data"; (ii) MUR PRIN Proj. 2022ME9Z78 - "NextGRAAL: Next-generation algorithms for constrained GRAph visuALization"; (iii) University of Perugia, Fondi di Ricerca di Ateneo, edizione 2021, project "AIDMIX - Artificial Intelligence for Decision making: Methods for Interpretability and eXplainability".

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