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An FPT Algorithm for Temporal Graph Untangling

Authors Riccardo Dondi , Manuel Lafond

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Author Details

Riccardo Dondi
  • Università degli studi di Bergamo, Italy
Manuel Lafond
  • Université de Sherbrooke, Canada

Acknowledgements

We thank the referees of the paper that help us to improve the presentation.

Cite AsGet BibTex

Riccardo Dondi and Manuel Lafond. An FPT Algorithm for Temporal Graph Untangling. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.IPEC.2023.12

Abstract

Several classical combinatorial problems have been considered and analysed on temporal graphs. Recently, a variant of Vertex Cover on temporal graphs, called MinTimelineCover, has been introduced to summarize timeline activities in social networks. The problem asks to cover every temporal edge while minimizing the total span of the vertices (where the span of a vertex is the length of the timestamp interval it must remain active in). While the problem has been shown to be NP-hard even in very restricted cases, its parameterized complexity has not been fully understood. The problem is known to be in FPT under the span parameter only for graphs with two timestamps, but the parameterized complexity for the general case is open. We settle this open problem by giving an FPT algorithm that is based on a combination of iterative compression and a reduction to the Digraph Pair Cut problem, a powerful problem that has received significant attention recently.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Graph algorithms analysis
  • Mathematics of computing → Graph theory
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Temporal Graphs
  • Vertex Cover
  • Graph Algorithms
  • Parameterized Complexity

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