TY - GEN
T1 - Romeo and Juliet Is EXPTIME-Complete
AU - Gahlawat, Harmender
AU - Křišťan, Jan Matyáš
AU - Valla, Tomáš
N1 - Publisher Copyright:
© Harmender Gahlawat, Jan Matyáš Křišťan, and Tomáš Valla.
PY - 2024/8/1
Y1 - 2024/8/1
N2 - 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.
AB - 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.
KW - Dynamic Separators
KW - EXPTIME-completeness
KW - Rendezvous Games on graphs
UR - https://www.scopus.com/pages/publications/85203348327
U2 - 10.4230/LIPIcs.MFCS.2024.54
DO - 10.4230/LIPIcs.MFCS.2024.54
M3 - Conference contribution
AN - SCOPUS:85203348327
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 49th International Symposium on Mathematical Foundations of Computer Science, MFCS 2024
A2 - Kralovic, Rastislav
A2 - Kucera, Antonin
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 49th International Symposium on Mathematical Foundations of Computer Science, MFCS 2024
Y2 - 26 August 2024 through 30 August 2024
ER -