Exact and approximation algorithms for covering timeline in temporal graphs

Riccardo Dondi () and Alexandru Popa ()
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Riccardo Dondi: Università degli Studi di Bergamo
Alexandru Popa: University of Bucharest

Annals of Operations Research, 2025, vol. 351, issue 1, No 23, 609-628

Abstract: 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.

Keywords: Timeline cover; Temporal graph; NP-hard problem; Approximation algorithm; FPT algorithm (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10479-024-05993-8

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