Two moves per time step make a difference

Thomas Erlebach, Frank Kammer, Kelin Luo, Andrej Sajenko, Jakob T. Spooner

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

13 Citaten (Scopus)
12 Downloads (Pure)


A temporal graph is a graph whose edge set can change over time. We only require that the edge set in each time step forms a connected graph. The temporal exploration problem asks for a temporal walk that starts at a given vertex, moves over at most one edge in each time step, visits all vertices, and reaches the last unvisited vertex as early as possible. We show in this paper that every temporal graph with n vertices can be explored in O(n1.75) time steps provided that either the degree of the graph is bounded in each step or the temporal walk is allowed to make two moves per step. This result is interesting because it breaks the lower bound of Ω(n2) steps that holds for the worst-case exploration time if only one move per time step is allowed and the graph in each step can have arbitrary degree. We complement this main result by a logarithmic inapproximability result and a proof that for sparse temporal graphs (i.e., temporal graphs with O(n) edges in the underlying graph) making O(1) moves per time step can improve the worst-case exploration time at most by a constant factor.

Originele taal-2Engels
Titel46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
RedacteurenChristel Baier, Ioannis Chatzigiannakis, Paola Flocchini, Stefano Leonardi
UitgeverijSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Aantal pagina's14
ISBN van elektronische versie9783959771092
StatusGepubliceerd - 1 jul. 2019
Extern gepubliceerdJa
Evenement46th International Colloquium on Automata, Languages, and Programming, ICALP 2019 - Patras, Griekenland
Duur: 9 jul. 201912 jul. 2019

Publicatie series

NaamLeibniz International Proceedings in Informatics, LIPIcs
ISSN van geprinte versie1868-8969


Congres46th International Colloquium on Automata, Languages, and Programming, ICALP 2019


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