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Exact and approximation algorithms for covering timeline in temporal graphs

Author

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  • Riccardo Dondi

    (Università degli Studi di Bergamo)

  • Alexandru Popa

    (University of Bucharest)

Abstract

We consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The problem has been proved to be NP-hard, even for several restrictions of the time domain and vertex degree. We present novel algorithmic contributions for the problem and we give an approximation algorithm of factor $$O(T \log {n})$$ O ( T log n ) , on a temporal graph of T timestamps and n vertices. We focus then on the NP-hard restriction of the problem, where at most one temporal edge is defined in each timestamp. For this restriction we present a $$4(T-1)$$ 4 ( T - 1 ) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution.

Suggested Citation

  • Riccardo Dondi & Alexandru Popa, 2025. "Exact and approximation algorithms for covering timeline in temporal graphs," Annals of Operations Research, Springer, vol. 351(1), pages 609-628, August.
    • Handle: RePEc:spr:annopr:v:351:y:2025:i:1:d:10.1007_s10479-024-05993-8
    DOI: 10.1007/s10479-024-05993-8
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