LIPIcs.ESA.2024.11.pdf
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How to Reduce Temporal Cliques to Find Sparse Spanners
Authors
Sebastian Angrick 
,
Ben Bals ,
Tobias Friedrich ,
Hans Gawendowicz ,
Niko Hastrich ,
Nicolas Klodt ,
Pascal Lenzner ,
Jonas Schmidt ,
George Skretas ,
Armin Wells
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Volume:
32nd Annual European Symposium on Algorithms (ESA 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: European Symposium on Algorithms (ESA) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-09-23
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Author Details
- Faculty of Digital Engineering, Hasso Plattner Institute, University of Potsdam, Germany
- Faculty of Digital Engineering, Hasso Plattner Institute, University of Potsdam, Germany
- Faculty of Digital Engineering, Hasso Plattner Institute, University of Potsdam, Germany
- Faculty of Digital Engineering, Hasso Plattner Institute, University of Potsdam, Germany
- Faculty of Digital Engineering, Hasso Plattner Institute, University of Potsdam, Germany
- Faculty of Digital Engineering, Hasso Plattner Institute, University of Potsdam, Germany
- Faculty of Digital Engineering, Hasso Plattner Institute, University of Potsdam, Germany
- Faculty of Digital Engineering, Hasso Plattner Institute, University of Potsdam, Germany
Cite As Get BibTex
Sebastian Angrick, Ben Bals, Tobias Friedrich, Hans Gawendowicz, Niko Hastrich, Nicolas Klodt, Pascal Lenzner, Jonas Schmidt, George Skretas, and Armin Wells. How to Reduce Temporal Cliques to Find Sparse Spanners. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ESA.2024.11
Abstract
Many real-world networks, such as transportation or trade networks, are dynamic in the sense that the edge-set may change over time, but these changes are known in advance. This behavior is captured by the temporal graphs model, which has recently become a trending topic in theoretical computer science. A core open problem in the field is to prove the existence of linear-size temporal spanners in temporal cliques, i.e., sparse subgraphs of complete temporal graphs that ensure all-pairs reachability via temporal paths. So far, the best known result is the existence of temporal spanners with 𝒪(nlog n) many edges. We present significant progress towards proving whether linear-size temporal spanners exist in all temporal cliques. We adapt techniques used in previous works and heavily expand and generalize them. This allows us to show that the existence of a linear spanner in cliques and bi-cliques is equivalent and using this, we provide a simpler and more intuitive proof of the 𝒪(nlog n) bound by giving an efficient algorithm for finding linearithmic spanners. Moreover, we use our novel and efficiently computable approach to show that a large class of temporal cliques, called edge-pivotable graphs, admit linear-size temporal spanners. To contrast this, we investigate other classes of temporal cliques that do not belong to the class of edge-pivotable graphs. We introduce two such graph classes and we develop novel algorithmic techniques for establishing the existence of linear temporal spanners in these graph classes as well.
Subject Classification
ACM Subject Classification
- Mathematics of computing → Paths and connectivity problems
Keywords
- Temporal Graphs
- temporal Clique
- temporal Spanner
- Reachability
- Graph Connectivity
- Graph Sparsification
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