Faster Exploration of Degree-Bounded Temporal Graphs

Authors Thomas Erlebach , Jakob T. Spooner

Thumbnail PDF


  • Filesize: 449 kB
  • 13 pages

Document Identifiers

Author Details

Thomas Erlebach
  • Department of Informatics, University of Leicester, Leicester, England
Jakob T. Spooner
  • Department of Informatics, University of Leicester, Leicester, England

Cite AsGet BibTex

Thomas Erlebach and Jakob T. Spooner. Faster Exploration of Degree-Bounded Temporal Graphs. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 36:1-36:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


A temporal graph can be viewed as a sequence of static graphs indexed by discrete time steps. The vertex set of each graph in the sequence remains the same; however, the edge sets are allowed to differ. A natural problem on temporal graphs is the Temporal Exploration problem (TEXP): given, as input, a temporal graph G of order n, we are tasked with computing an exploration schedule (i.e., a temporal walk that visits all vertices in G), such that the time step at which the walk arrives at the last unvisited vertex is minimised (we refer to this time step as the arrival time). It can be easily shown that general temporal graphs admit exploration schedules with arrival time no greater than O(n^2). Moreover, it has been shown previously that there exists an infinite family of temporal graphs for which any exploration schedule has arrival time Omega(n^2), making these bounds tight for general TEXP instances. We consider restricted instances of TEXP, in which the temporal graph given as input is, in every time step, of maximum degree d; we show an O(n^2/log n) bound on the arrival time when d is constant, and an O(d log d * n^2/log n) bound when d is given as some function of n.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • temporal graph exploration
  • algorithmic graph theory
  • NP-complete problem


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Kenneth A. Berman. Vulnerability of scheduled networks and a generalization of Menger’s theorem. Networks, 28(3):125-134, 1996. URL:<125::AID-NET1>3.0.CO;2-P.
  2. Björn Brodén, Mikael Hammar, and Bengt J. Nilsson. Online and offline algorithms for the time-dependent TSP with time zones. Algorithmica, 39(4):299-319, 2004. URL:
  3. Binh-Minh Bui-Xuan, Afonso Ferreira, and Aubin Jarry. Computing shortest, fastest, and foremost journeys in dynamic networks. Int. J. Found. Comput. Sci., 14(2):267-285, 2003. URL:
  4. A. Casteigts, P. Flocchini, Quattrociocchi W., and N. Santoro. Time-varying graphs and dynamic networks. IJPEDS, 27(5):387-408, 2012. Google Scholar
  5. Thomas Erlebach, Michael Hoffmann, and Frank Kammer. On temporal graph exploration. In 42nd International Colloquium on Automata, Languages, and Programming (ICALP 2015), Part I, volume 9134 of Lecture Notes in Computer Science, pages 444-455. Springer, 2015. URL:
  6. Till Fluschnik, Hendrik Molter, Rolf Niedermeier, and Philipp Zschoche. Temporal graph classes: A view through temporal separators. CoRR, abs/1803.00882, 2018. URL:
  7. David Kempe, Jon M. Kleinberg, and Amit Kumar. Connectivity and inference problems for temporal networks. J. Comput. Syst. Sci., 64(4):820-842, 2002. URL:
  8. George B. Mertzios, Othon Michail, Ioannis Chatzigiannakis, and Paul G. Spirakis. Temporal network optimization subject to connectivity constraints. In 40th International Colloquium on Automata, Languages, and Programming (ICALP 2013), Part II, volume 7966 of Lecture Notes in Comptuer Science, pages 657-668. Springer, 2013. URL:
  9. Othon Michail. An introduction to temporal graphs: An algorithmic perspective. Internet Mathematics, 12(4):239-280, 2016. URL:
  10. Othon Michail and Paul G. Spirakis. Traveling salesman problems in temporal graphs. Theor. Comput. Sci., 634:1-23, 2016. URL:
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail