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Abstract: Two mobile agents robots have to meet in an a priori unknown boundedterrain modeled as a polygon, possibly with polygonal obstacles. Agents aremodeled as points, and each of them is equipped with a compass. Compasses ofagents may be incoherent. Agents construct their routes, but the actual walk ofeach agent is decided by the adversary: the movement of the agent can be atarbitrary speed, the agent may sometimes stop or go back and forth, as long asthe walk of the agent in each segment of its route is continuous, does notleave it and covers all of it. We consider several scenarios, depending onthree factors: 1 obstacles in the terrain are present, or not, 2 compassesof both agents agree, or not, 3 agents have or do not have a map of theterrain with their positions marked. The cost of a rendezvous algorithm is theworst-case sum of lengths of the agents- trajectories until their meeting. Foreach scenario we design a deterministic rendezvous algorithm and analyze itscost. We also prove lower bounds on the cost of any deterministic rendezvousalgorithm in each case. For all scenarios these bounds are tight.



Author: Jurek Czyzowicz, David Ilcinkas LaBRI, INRIA Bordeaux - Sud-Ouest, Arnaud Labourel LaBRI, Andrzej Pelc

Source: https://arxiv.org/







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