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Romeo and Juliet Is EXPTIME-Complete

Authors Harmender Gahlawat , Jan Matyáš Křišťan, Tomáš Valla

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Rendezvous Games on graphs
  • EXPTIME-completeness
  • Dynamic Separators

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Abstract

Romeo and Juliet is a two player Rendezvous game played on graphs where one player controls two agents, Romeo (ℛ) and Juliet (𝒥) who aim to meet at a vertex against k adversaries, called dividers, controlled by the other player. The optimization in this game lies at deciding the minimum number of dividers sufficient to restrict ℛ and 𝒥 from meeting in a graph, called the dynamic separation number. We establish that Romeo and Juliet is EXPTIME-complete, settling a conjecture of Fomin, Golovach, and Thilikos [Inf. and Comp., 2023] positively. We also consider the game for directed graphs and establish that although the game is EXPTIME-complete for general directed graphs, it is PSPACE-complete and co-W[2]-hard for directed acyclic graphs.

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Harmender Gahlawat, Jan Matyáš Křišťan, and Tomáš Valla. Romeo and Juliet Is EXPTIME-Complete. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.54

Author Details

Harmender Gahlawat
  • G-SCOP, Grenoble-INP, France
Jan Matyáš Křišťan
  • Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Tomáš Valla
  • Faculty of Information Technology, Czech Technical University in Prague, Czech Republic

Funding

This work was supported by the Czech Science Foundation Grant no. 24-12046S. This work was supported by the Grant Agency of the Czech Technical University in Prague, grant No. SGS23/205/OHK3/3T/18.

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