How to meet asynchronously at polynomial cost

Two mobile agents starting at different nodes of an unknown network have to meet. This task is known in the literature as rendezvous. Each agent has a different label which is a positive integer known to it but unknown to the other agent. Agents move in an asynchronous way: the speed of agents may vary and is controlled by an adversary. The cost of a rendezvous algorithm is the total number of edge traversals by both agents until their meeting. The only previous deterministic algorithm solving this problem has cost exponential in the size of the graph and in the larger label. In this paper we present a deterministic rendezvous algorithm with cost polynomial in the size of the graph and in the length of the smaller label. Hence, we decrease the cost exponentially in the size of the graph and doubly exponentially in the labels of agents. As an application of our rendezvous algorithm we solve several fundamental problems involving teams of unknown size larger than 1 of labeled agents moving asynchronously in...

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

[2]  Pat Morin,et al.  Randomized Rendez-Vous with Limited Memory , 2008, LATIN.

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

[4]  Nicola Santoro,et al.  Gathering of Asynchronous Oblivious Robots with Limited Visibility , 2001, STACS.

[5]  Andrzej Pelc,et al.  How to meet asynchronously (almost) everywhere , 2010, SODA '10.

[6]  Sándor P. Fekete,et al.  Asymmetric rendezvous on the plane , 1998, SCG '98.

[7]  Hagit Attiya,et al.  Renaming in an asynchronous environment , 1990, JACM.

[8]  Adrian Kosowski,et al.  Constructing a Map of an Anonymous Graph: Applications of Universal Sequences , 2010, OPODIS.

[9]  Andrzej Pelc,et al.  Deterministic Rendezvous in Trees with Little Memory , 2008, DISC.

[10]  Reuven Cohen,et al.  Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems , 2005, SIAM J. Comput..

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

[12]  Steve Alpern.  Rendezvous Search on Labelled Networks , 2000 .

[13]  Jurek Czyzowicz,et al.  Tell Me Where I Am So I Can Meet You Sooner , 2010, ICALP.

[14]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[15]  S. Gal,et al.  Rendezvous search when marks are left at the starting points , 2001 .

[16]  Andrzej Pelc,et al.  Decidability classes for mobile agents computing , 2010, J. Parallel Distributed Comput..

[17]  Nicola Santoro,et al.  Solving the Robots Gathering Problem , 2003, ICALP.

[18]  Jurek Czyzowicz,et al.  Almost Optimal Asynchronous Rendezvous in Infinite Multidimensional Grids , 2010, DISC.

[19]  Andrzej Pelc,et al.  Gathering Despite Mischief , 2012, SODA.

[20]  S. Alpern,et al.  Minimax Rendezvous on the Line , 1996 .

[21]  Sándor P. Fekete,et al.  Two Dimensional Rendezvous Search , 2001, Oper. Res..

[22]  Andrzej Pelc,et al.  Delays Induce an Exponential Memory Gap for Rendezvous in Trees , 2011, TALG.

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

[24]  Andrzej Pelc,et al.  Asynchronous Rendezvous of Anonymous Agents in Arbitrary Graphs , 2011, OPODIS.

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

[26]  Andrzej Pelc,et al.  How to meet when you forget: log-space rendezvous in arbitrary graphs , 2010, Distributed Computing.

[27]  Andrzej Pelc,et al.  Deterministic rendezvous in networks: A comprehensive survey , 2012, Networks.

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

[29]  Omer Reingold,et al.  Undirected connectivity in log-space , 2008, JACM.

[30]  Noa Agmon,et al.  Fault-tolerant gathering algorithms for autonomous mobile robots , 2004, SODA '04.

[31]  Richard Weber,et al.  The rendezvous problem on discrete locations , 1990, Journal of Applied Probability.

[32]  Uri Zwick,et al.  Deterministic rendezvous, treasure hunts and strongly universal exploration sequences , 2007, SODA '07.

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

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

[35]  Pierre Fraigniaud,et al.  Methods and problems of communication in usual networks , 1994, Discret. Appl. Math..

[36]  Reuven Cohen,et al.  Convergence of Autonomous Mobile Robots with Inaccurate Sensors and Movements , 2006, SIAM J. Comput..

[37]  Andrzej Pelc,et al.  Anonymous Meeting in Networks , 2013, SODA.