Asynchronous deterministic rendezvous in bounded terrains

Jurek Czyzowicz 1 David Ilcinkas 2, 3 Arnaud Labourel 4 Andrzej Pelc 1
3 CEPAGE - Algorithmics for computationally intensive applications over wide scale distributed platforms
Université Sciences et Technologies - Bordeaux 1, Inria Bordeaux - Sud-Ouest, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
Abstract : Two mobile agents (robots) have to meet in an a priori unknown bounded terrain modeled as a polygon, possibly with polygonal obstacles. Robots are modeled as points, and each of them is equipped with a compass. Compasses of robots may be incoherent. Robots construct their routes, but the actual walk of each robot is decided by the adversary that may, e.g., speed up or slow down the robot. We consider several scenarios, depending on three factors: (1) obstacles in the terrain are present, or not, (2) compasses of both robots agree, or not, (3) robots have or do not have a map of the terrain with their positions marked. The cost of a rendezvous algorithm is the worst-case sum of lengths of the robots' trajectories until they meet. For each scenario we design a deterministic rendezvous algorithm and analyze its cost. We also prove lower bounds on the cost of any deterministic rendezvous algorithm in each case. For all scenarios these bounds are tight.
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Submitted on : Tuesday, November 22, 2011 - 3:40:04 PM
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Jurek Czyzowicz, David Ilcinkas, Arnaud Labourel, Andrzej Pelc. Asynchronous deterministic rendezvous in bounded terrains. Theoretical Computer Science, Elsevier, 2011, 412 (50), pp.6926-6937. ⟨10.1016/j.tcs.2011.09.002⟩. ⟨hal-00643686⟩



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