TY - GEN
T1 - Pebble Guided Rendezvous Despite Fault
AU - Saxena, Ashish
AU - Gorain, Barun
AU - Mandal, Subhrangsu
AU - Mondal, Kaushik
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - We consider the rendezvous problem in an anonymous port-labelled connected simple graph. The objective is for two mobile agents to meet at some node of the graph without prior knowledge of the graph or the other agent’s position. An oracle, that knows the graph and the starting positions of the agents, helps the agents by placing identical pebbles, at most one per node at some of the nodes. We introduce faults by considering the presence of a single faulty node that may remove a pebble that is kept on the node, or may add a pebble where there was no pebble placed by the oracle. The position of the faulty node is unknown to the agents as well as the oracle. Our goal is to find an efficient rendezvous algorithm regardless of the number of pebbles placed by the oracle in the presence of a faulty node. For trees, we present an algorithm that uses O(DlogΔ) pebbles and runs in time O(DlogΔ), where Δ is the maximum node degree and D is the shortest path distance between the initial agent positions. We prove that our algorithm for trees is optimal in terms of time. Additionally, we study the problem in general graphs with the constraint that the initial agent positions are no more than distance three apart. We propose an algorithm using O(logΔ) pebbles with run time O(log3Δ).
AB - We consider the rendezvous problem in an anonymous port-labelled connected simple graph. The objective is for two mobile agents to meet at some node of the graph without prior knowledge of the graph or the other agent’s position. An oracle, that knows the graph and the starting positions of the agents, helps the agents by placing identical pebbles, at most one per node at some of the nodes. We introduce faults by considering the presence of a single faulty node that may remove a pebble that is kept on the node, or may add a pebble where there was no pebble placed by the oracle. The position of the faulty node is unknown to the agents as well as the oracle. Our goal is to find an efficient rendezvous algorithm regardless of the number of pebbles placed by the oracle in the presence of a faulty node. For trees, we present an algorithm that uses O(DlogΔ) pebbles and runs in time O(DlogΔ), where Δ is the maximum node degree and D is the shortest path distance between the initial agent positions. We prove that our algorithm for trees is optimal in terms of time. Additionally, we study the problem in general graphs with the constraint that the initial agent positions are no more than distance three apart. We propose an algorithm using O(logΔ) pebbles with run time O(log3Δ).
KW - Anonymous graphs
KW - Deterministic algorithm
KW - Faults
KW - Mobile agents
KW - Rendezvous
UR - https://www.scopus.com/pages/publications/85207837848
U2 - 10.1007/978-3-031-74498-3_8
DO - 10.1007/978-3-031-74498-3_8
M3 - Conference contribution
AN - SCOPUS:85207837848
SN - 9783031744976
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 121
EP - 125
BT - Stabilization, Safety, and Security of Distributed Systems - 26th International Symposium, SSS 2024, Proceedings
A2 - Masuzawa, Toshimitsu
A2 - Katayama, Yoshiaki
A2 - Kim, Yonghwan
A2 - Kakugawa, Hirotsugu
A2 - Nakamura, Junya
PB - Springer Science and Business Media Deutschland GmbH
T2 - 26th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2024
Y2 - 20 October 2024 through 22 October 2024
ER -