Randomized Rendez-Vous with Limited Memory

We present a tradeoff between the expected time for two identical agents to rendez-vous on a synchronous, anonymous, oriented ring and the memory requirements of the agents. In particular, we show that there exists a 2t state agent, which can achieve rendez-vous on an n node ring in expected time O(n2/2t + 2t) and that any t/2 state agent requires expected time Ω(n2/2t). As a corollary we observe that Θ(log log n) bits of memory are necessary and sufficient to achieve rendezvous in linear time.

[1]  X. Zhang,et al.  Optimal Memory Rendezvous of Anonymous Mobile Agents in a Unidirectional Ring , 2006, SOFSEM.

[2]  Shantanu Das,et al.  Rendezvous of Mobile Agents When Tokens Fail Anytime , 2008, OPODIS.

[3]  Andrzej Pelc,et al.  Asynchronous Deterministic Rendezvous in Graphs , 2005, MFCS.

[4]  Martín Farach-Colton.  LATIN 2004: Theoretical Informatics , 2004, Lecture Notes in Computer Science.

[5]  Dariusz R. Kowalski,et al.  How to Meet in Anonymous Network , 2006, SIROCCO.

[6]  Evangelos Kranakis,et al.  An Algorithmic Theory of Mobile Agents , 2006, TGC.

[7]  Nicola Santoro,et al.  Mobile Agents Rendezvous When Tokens Fail , 2004, SIROCCO.

[8]  Harald Niederreiter,et al.  Probability and computing: randomized algorithms and probabilistic analysis , 2006, Math. Comput..

[9]  Moti Yung,et al.  Agent Rendezvous: A Dynamic Symmetry-Breaking Problem , 1996, ICALP.

[10]  Marcos Kiwi,et al.  LATIN 2006: Theoretical Informatics , 2006, Lecture Notes in Computer Science.

[11]  Sheldon M. Ross,et al.  Probability Models for Computer Science , 2001 .

[12]  Nicola Santoro,et al.  Multiple Mobile Agent Rendezvous in a Ring , 2004, LATIN.

[13]  M. Karonski.  Collisions among Random Walks on a Graph , 1993 .

[14]  Euripides Markou,et al.  Mobile Agent Rendezvous in a Synchronous Torus , 2006, LATIN.

[15]  Evangelos Kranakis,et al.  Mobile Agent Rendezvous: A Survey , 2006, SIROCCO.

[16]  Gregory Dudek,et al.  Collaborative Robot Exploration and Rendezvous: Algorithms, Performance Bounds and Observations , 2001, Auton. Robots.

[17]  Masafumi Yamashita,et al.  Distributed Anonymous Mobile Robots: Formation of Geometric Patterns , 1999, SIAM J. Comput..

[18]  Andrzej Pelc,et al.  Polynomial Deterministic Rendezvous in Arbitrary Graphs , 2004, ISAAC.

[19]  Nicola Santoro,et al.  Multiple Agents RendezVous in a Ring in Spite of a Black Hole , 2003, OPODIS.

[20]  Michel Rigo,et al.  Abstract numeration systems and tilings , 2005 .

[21]  Nicola Santoro,et al.  Mobile agent rendezvous in a ring , 2003, 23rd International Conference on Distributed Computing Systems, 2003. Proceedings..

[22]  V. Baston,et al.  Rendezvous search on a graph , 1999 .

[23]  Andrzej Pelc,et al.  Deterministic Rendezvous in Graphs , 2003 .

[24]  Shmuel Gal,et al.  The theory of search games and rendezvous , 2002, International series in operations research and management science.

[25]  Nicola Santoro,et al.  Design and analysis of distributed algorithms , 2006, Wiley series on parallel and distributed computing.

[26]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[27]  S. Alpern.  The Rendezvous Search Problem , 1995 .