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Sliding into the Future: Investigating Sliding Windows in Temporal Graphs (Invited Talk)

Authors Nina Klobas , George B. Mertzios , Paul G. Spirakis

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Author Details

Nina Klobas
  • Department of Computer Science, Durham University, UK
George B. Mertzios
  • Department of Computer Science, Durham University, UK
Paul G. Spirakis
  • Department of Computer Science, University of Liverpool, UK

Funding

  • Mertzios, George B.: Supported by the EPSRC grant EP/P020372/1.
  • Spirakis, Paul G.: Supported by the EPSRC grant EP/P02002X/1.

Cite As Get BibTex

Nina Klobas, George B. Mertzios, and Paul G. Spirakis. Sliding into the Future: Investigating Sliding Windows in Temporal Graphs (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.MFCS.2023.5

Abstract

Graphs are fundamental tools for modelling relations among objects in various scientific fields. However, traditional static graphs have limitations when it comes to capturing the dynamic nature of real-world systems. To overcome this limitation, temporal graphs have been introduced as a framework to model graphs that change over time. In temporal graphs the edges among vertices appear and disappear at specific time steps, reflecting the temporal dynamics of the observed system, which allows us to analyse time dependent patterns and processes. In this paper we focus on the research related to sliding time windows in temporal graphs. Sliding time windows offer a way to analyse specific time intervals within the lifespan of a temporal graph. By sliding the window along the timeline, we can examine the graph’s characteristics and properties within different time periods. 
This paper provides an overview of the research on sliding time windows in temporal graphs. Although progress has been made in this field, there are still many interesting questions and challenges to be explored. We discuss some of the open problems and highlight their potential for future research.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • General and reference → Surveys and overviews
Keywords
  • Temporal Graphs
  • Sliding Time Windows

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References

  1. Eric Aaron, Danny Krizanc, and Elliot Meyerson. DMVP: foremost waypoint coverage of time-varying graphs. In Proceedings of the 40th International Workshop on Graph-Theoretic Concepts in Computer Science (WG), pages 29-41, 2014. Google Scholar
  2. Eleni C. Akrida, Leszek Gasieniec, George B. Mertzios, and Paul G. Spirakis. Ephemeral networks with random availability of links: The case of fast networks. Journal of Parallel and Distributed Computing, 87:109-120, 2016. Google Scholar
  3. Eleni C. Akrida, Leszek Gasieniec, George B. Mertzios, and Paul G. Spirakis. The complexity of optimal design of temporally connected graphs. Theory of Computing Systems, 61(3):907-944, 2017. Google Scholar
  4. Eleni C. Akrida, George B. Mertzios, Paul G. Spirakis, and Viktor Zamaraev. Temporal vertex cover with a sliding time window. Journal of Computer and System Sciences, 107:108-123, 2020. Google Scholar
  5. Julien Baste, Binh-Minh Bui-Xuan, and Antoine Roux. Temporal matching. Theor. Comput. Sci., 806:184-196, 2020. Google Scholar
  6. Matthias Bentert, Anne-Sophie Himmel, Hendrik Molter, Marco Morik, Rolf Niedermeier, and René Saitenmacher. Listing all maximal k-plexes in temporal graphs. In Proceedings of the 2018 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), pages 41-46, 2018. Google Scholar
  7. Binh-Minh Bui-Xuan, Afonso Ferreira, and Aubin Jarry. Computing shortest, fastest, and foremost journeys in dynamic networks. International Journal of Foundations of Computer Science, 14(2):267-285, 2003. Google Scholar
  8. Arnaud Casteigts and Paola Flocchini. Deterministic algorithms in dynamic networks: Problems, analysis, and algorithmic tools. Technical report, Defence R&D Canada, 2013. Google Scholar
  9. Arnaud Casteigts, Paola Flocchini, Walter Quattrociocchi, and Nicola Santoro. Time-varying graphs and dynamic networks. International Journal of Parallel, Emergent and Distributed Systems, 27(5):387-408, 2012. Google Scholar
  10. Arnaud Casteigts, Anne-Sophie Himmel, Hendrik Molter, and Philipp Zschoche. Finding temporal paths under waiting time constraints. Algorithmica, 83(9):2754-2802, 2021. Google Scholar
  11. Jiehua Chen, Hendrik Molter, Manuel Sorge, and Ondrej Suchý. Cluster editing in multi-layer and temporal graphs. In Proceedings of the 29th International Symposium on Algorithms and Computation (ISAAC), volume 123, pages 24:1-24:13, 2018. Google Scholar
  12. Andrea E. F. Clementi, Claudio Macci, Angelo Monti, Francesco Pasquale, and Riccardo Silvestri. Flooding time of edge-markovian evolving graphs. SIAM Journal on Discrete Mathematics, 24(4):1694-1712, 2010. Google Scholar
  13. Germán Creamer, Ryan Rowe, Shlomo Hershkop, and Salvatore J. Stolfo. Segmentation and automated social hierarchy detection through email network analysis. In Advances in Web Mining and Web Usage Analysis, 9th International Workshop on Knowledge Discovery on the Web, WebKDD 2007, Lecture Notes in Computer Science, pages 40-58, 2007. Google Scholar
  14. Jessica A. Enright, Kitty Meeks, George B. Mertzios, and Viktor Zamaraev. Deleting edges to restrict the size of an epidemic in temporal networks. Journal of Computer and System Sciences, 119:60-77, 2021. Google Scholar
  15. Thomas Erlebach, Michael Hoffmann, and Frank Kammer. On temporal graph exploration. Journal of Computer and System Sciences, 119:1-18, 2021. Google Scholar
  16. Afonso Ferreira. Building a reference combinatorial model for MANETs. IEEE Network, 18(5):24-29, 2004. Google Scholar
  17. Paola Flocchini, Bernard Mans, and Nicola Santoro. Exploration of periodically varying graphs. In Proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC), pages 534-543, 2009. Google Scholar
  18. Subhankar Ghosal and Sasthi C Ghosh. Channel assignment in mobile networks based on geometric prediction and random coloring. In Proceedings of the 40th IEEE Conference on Local Computer Networks (LCN), pages 237-240, 2015. Google Scholar
  19. George Giakkoupis, Thomas Sauerwald, and Alexandre Stauffer. Randomized rumor spreading in dynamic graphs. In Proceedings of the 41st International Colloquium on Automata, Languages and Programming (ICALP), pages 495-507, 2014. Google Scholar
  20. Leonidas J. Guibas, Nikola Milosavljevic, and Arik Motskin. Connected dominating sets on dynamic geometric graphs. Comput. Geom., 46(2):160-172, 2013. Google Scholar
  21. Thekla Hamm, Nina Klobas, George B. Mertzios, and Paul G. Spirakis. The complexity of temporal vertex cover in small-degree graphs. In Thirty-Sixth AAAI Conference on Artificial Intelligence, AAAI 2022, February 22 - March 1, 2022, pages 10193-10201, 2022. Google Scholar
  22. Klaus Heeger, Danny Hermelin, George B. Mertzios, Hendrik Molter, Rolf Niedermeier, and Dvir Shabtay. Equitable scheduling on a single machine. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI), pages 11818-11825. AAAI Press, 2021. Google Scholar
  23. Anne-Sophie Himmel, Hendrik Molter, Rolf Niedermeier, and Manuel Sorge. Adapting the bron-kerbosch algorithm for enumerating maximal cliques in temporal graphs. Social Network Analysis and Mining, 7(1):35:1-35:16, 2017. Google Scholar
  24. David Kempe, Jon M. Kleinberg, and Amit Kumar. Connectivity and inference problems for temporal networks. Journal of Computer and System Sciences, 64(4):820-842, 2002. Google Scholar
  25. Nina Klobas, George B. Mertzios, Hendrik Molter, Rolf Niedermeier, and Philipp Zschoche. Interference-free walks in time: temporally disjoint paths. Auton. Agents Multi Agent Syst., 37(1), 2023. Google Scholar
  26. Nina Klobas, George B. Mertzios, Hendrik Molter, and Paul G. Spirakis. The complexity of computing optimum labelings for temporal connectivity. In 47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022, August 22-26, 2022, Vienna, Austria, volume 241, pages 62:1-62:15, 2022. Google Scholar
  27. Jure Leskovec, Jon M. Kleinberg, and Christos Faloutsos. Graph evolution: Densification and shrinking diameters. ACM Transactions on Knowledge Discovery from Data, 1(1), 2007. Google Scholar
  28. Subhrangsu Mandal and Arobinda Gupta. Approximation algorithms for permanent dominating set problem on dynamic networks. In Distributed Computing and Internet Technology - 14th International Conference, ICDCIT 2018, Bhubaneswar, India, January 11-13, 2018, Proceedings, volume 10722 of Lecture Notes in Computer Science, pages 265-279. Springer, 2018. Google Scholar
  29. Andrea Marino and Ana Silva. Coloring temporal graphs. Journal of Computer and System Sciences, 123:171-185, 2022. Google Scholar
  30. George B. Mertzios, Othon Michail, and Paul G. Spirakis. Temporal network optimization subject to connectivity constraints. Algorithmica, 81(4):1416-1449, 2019. Google Scholar
  31. George B Mertzios, Hendrik Molter, Rolf Niedermeier, Viktor Zamaraev, and Philipp Zschoche. Computing maximum matchings in temporal graphs. In Proceedings of the 37th International Symposium on Theoretical Aspects of Computer Science (STACS), volume 154, pages 27:1-27:14, 2020. Google Scholar
  32. George B. Mertzios, Hendrik Molter, Malte Renken, Paul G. Spirakis, and Philipp Zschoche. The complexity of transitively orienting temporal graphs. In Proceedings of the 46th International Symposium on Mathematical Foundations of Computer Science (MFCS), pages 75:1-75:18, 2021. Google Scholar
  33. George B. Mertzios, Hendrik Molter, and Viktor Zamaraev. Sliding window temporal graph coloring. Journal of Computer and System Sciences, 120:97-115, 2021. Google Scholar
  34. Othon Michail and Paul G. Spirakis. Traveling salesman problems in temporal graphs. Theoretical Computer Science, 634:1-23, 2016. Google Scholar
  35. Ram Samudrala and John Moult. A graph-theoretic algorithm for comparative modeling of protein structure11edited by f. cohen. Journal of Molecular Biology, 279(1):287-302, 1998. Google Scholar
  36. John Kit Tang, Mirco Musolesi, Cecilia Mascolo, and Vito Latora. Characterising temporal distance and reachability in mobile and online social networks. Computer Communication Review, 40(1):118-124, 2010. Google Scholar
  37. Tiphaine Viard, Matthieu Latapy, and Clémence Magnien. Computing maximal cliques in link streams. Theoretical Computer Science, 609:245-252, 2016. Google Scholar
  38. John Whitbeck, Marcelo Dias de Amorim, Vania Conan, and Jean-Loup Guillaume. Temporal reachability graphs. In The 18th Annual International Conference on Mobile Computing and Networking, Mobicom'12, Istanbul, Turkey, August 22-26, 2012, pages 377-388. ACM, 2012. Google Scholar
  39. Feng Yu, Amotz Bar-Noy, Prithwish Basu, and Ram Ramanathan. Algorithms for channel assignment in mobile wireless networks using temporal coloring. In Proceedings of the 16th ACM international conference on Modeling, analysis & simulation of wireless and mobile systems (MSWiM), pages 49-58, 2013. Google Scholar
  40. Philipp Zschoche, Till Fluschnik, Hendrik Molter, and Rolf Niedermeier. The complexity of finding small separators in temporal graphs. Journal of Computer and System Sciences, 107:72-92, 2020. Google Scholar
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