Sniffing Helps to Meet: Deterministic Rendezvous of Anonymous Agents in the Grid
Younan Gao, Andrzej Pelc

TL;DR
This paper investigates deterministic rendezvous of anonymous agents in an infinite grid, demonstrating how marking nodes enables faster meeting algorithms and establishing complexity bounds across different knowledge scenarios.
Contribution
It introduces a marking-based rendezvous algorithm in grids and provides tight bounds on rendezvous time under various initial knowledge assumptions.
Findings
Rendezvous can be achieved in O(D) time when agents know D or start simultaneously.
No algorithm can do o(D^{√2}) time in the most challenging scenario.
An O(D^2) time algorithm exists for the hardest scenario.
Abstract
Two identical anonymous mobile agents have to meet at a node of the infinite oriented grid whose nodes are unlabeled. This problem is known as rendezvous. The agents execute the same deterministic algorithm. Time is divided into rounds, and in each round each agent can either stay idle at the current node or move to an adjacent node. An adversary places the agents at two nodes of the grid at a distance at most , and wakes them up in possibly different rounds. Each agent starts executing the algorithm in its wakeup round. If agents cannot leave any marks on visited nodes then they can never meet, even if they start simultaneously at adjacent nodes and know it. Hence, we assume that each agent marks any unmarked node it visits, and that an agent can distinguish if a node it visits has been previously marked or not. The time of a rendezvous algorithm is the number of rounds between…
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Taxonomy
TopicsOptimization and Search Problems · Distributed systems and fault tolerance · Cryptography and Data Security
