Exact and approximation algorithms for covering timeline in temporal graphs

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 contributio...

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Published in:	Annals of operations research Vol. 351; no. 1; pp. 609 - 628
Main Authors:	Dondi, Riccardo, Popa, Alexandru
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.08.2025 Springer Nature B.V
Subjects:	Algorithms Apexes Approximation Business and Management Combinatorics Graph theory Graphs Linear programming Operations Research/Decision Theory Original Research Theory of Computation Timeline cover Temporal graph FPT algorithm NP-hard problem Approximation algorithm
ISSN:	0254-5330, 1572-9338
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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 ) , 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 ) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution.
AbstractList	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(Tlogn), 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) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution. 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 ) , 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 ) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution. 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.
Author	Dondi, Riccardo Popa, Alexandru
Author_xml	– sequence: 1 givenname: Riccardo orcidid: 0000-0002-6124-2965 surname: Dondi fullname: Dondi, Riccardo email: riccardo.dondi@unibg.it organization: Dipartimento di Lettere, Filosofia, Comunicazione, Università degli Studi di Bergamo – sequence: 2 givenname: Alexandru surname: Popa fullname: Popa, Alexandru email: alexandru.popa@fmi.unibuc.ro organization: Department of Computer Science, University of Bucharest
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SubjectTerms	Algorithms Apexes Approximation Business and Management Combinatorics Graph theory Graphs Linear programming Operations Research/Decision Theory Original Research Theory of Computation
Title	Exact and approximation algorithms for covering timeline in temporal graphs
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