Gathering of Robots in a Ring with Mobile Faults

The gathering of two or more agents in a graph is an important problem in the area of distributed computing and has been extensively studied especially for the fault free scenario. In this paper we consider the mobile agents gathering problem in the presence of an adversarial malicious agent which by occupying an empty node might prevent honest agents from entering this node. The honest agents move in synchronous rounds and at each round an agent can move to an adjacent node only if this node is not occupied by the malicious agent. We model the honest agents as identical finite state automata moving in an anonymous oriented grid topology and having no information about the size of the graph, while the malicious agent is assumed to be arbitrarily fast and to have full knowledge of the locations and the strategy of the honest agents at all times. The agents cannot leave messages at nodes or communicate with each-other unless they meet at a node. Previous studies consider the problem for ring networks and for asynchronous grids, where rendezvous was solved only for the special case of agents starting already in connected configurations. In this paper, we study the problem for synchronous agents in anonymous oriented grid networks for any number of agents starting in distinct locations. We first show that rendezvous is impossible for 2 agents even when the agents can see the locations of each-other at all times, while 3 agents can gather if they have global visibility. We then present a universal deterministic algorithm that solves the problem for 4 or more agents having only local visibility and constant memory, in any oriented grid with a malicious mobile adversary.

[1]  Andrzej Pelc,et al.  Rendezvous in networks in spite of delay faults , 2015, Distributed Computing.

[2]  Nicola Santoro,et al.  Mobile Search for a Black Hole in an Anonymous Ring , 2007, Algorithmica.

[3]  Attila Pásztor,et al.  Simulacija grupiranja stvarne skupine robota , 2014 .

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

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

[6]  Euripides Markou,et al.  Improved periodic data retrieval in asynchronous rings with a faulty host , 2015, Theor. Comput. Sci..

[7]  Euripides Markou,et al.  Hardness and Approximation Results for Black Hole Search in Arbitrary Graphs , 2005, SIROCCO.

[8]  Maria Gradinariu Potop-Butucaru,et al.  Gathering fat mobile robots with slim omnidirectional cameras , 2014, Theor. Comput. Sci..

[9]  Lali Barrière,et al.  Connected graph searching , 2012, Inf. Comput..

[10]  Paola Flocchini,et al.  Decontamination of chordal rings and tori , 2006, Proceedings 20th IEEE International Parallel & Distributed Processing Symposium.

[11]  Jurek Czyzowicz,et al.  Rendezvous on a Line by Location-Aware Robots Despite the Presence of Byzantine Faults , 2017, ALGOSENSORS.

[12]  Nicola Santoro,et al.  Gathering in Dynamic Rings , 2017, SIROCCO.

[13]  Euripides Markou,et al.  Tight bounds for black hole search with scattered agents in synchronous rings , 2013, Theor. Comput. Sci..

[14]  Nicola Santoro,et al.  Distributed Computing by Oblivious Mobile Robots , 2012, Synthesis Lectures on Distributed Computing Theory.

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

[16]  Euripides Markou,et al.  Deterministic symmetric rendezvous with tokens in a synchronous torus , 2011, Discret. Appl. Math..

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

[18]  Mattia D'Emidio,et al.  Explore and repair graphs with black holes using mobile entities , 2015, Theor. Comput. Sci..

[19]  Flaminia L. Luccio.  Contiguous Search Problem in Sierpiński Graphs , 2008, Theory of Computing Systems.

[20]  Alfredo Navarra,et al.  Optimal gathering of oblivious robots in anonymous graphs and its application on trees and rings , 2016, Distributed Computing.

[21]  Jurek Czyzowicz,et al.  The Power of Tokens: Rendezvous and Symmetry Detection for Two Mobile Agents in a Ring , 2008, SOFSEM.

[22]  Jurek Czyzowicz,et al.  Gathering in the Plane of Location-Aware Robots in the Presence of Spies , 2017, SIROCCO.

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

[24]  Yukiko Yamauchi,et al.  Mobile Agent Rendezvous on a Probabilistic Edge Evolving Ring , 2012, 2012 Third International Conference on Networking and Computing.

[25]  Attila Pásztor,et al.  GATHERING SIMULATION OF REAL ROBOT SWARM , 2014 .

[26]  Euripides Markou,et al.  Mobile Agents Rendezvous in Spite of a Malicious Agent , 2015, ALGOSENSORS.

[27]  Nicola Santoro,et al.  Distributed Security Algorithms by Mobile Agents , 2006, ICDCN.

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

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

[30]  Steve Alpern,et al.  Searching for an Agent Who May OR May Not Want to be Found , 2002, Oper. Res..

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

[32]  Brian D. O. Anderson,et al.  The Multi-Agent Rendezvous Problem. An Extended Summary , 2005 .

[33]  Sébastien Tixeuil,et al.  Gathering of Mobile Robots Tolerating Multiple Crash Faults , 2013, 2013 IEEE 33rd International Conference on Distributed Computing Systems.

[34]  Paola Flocchini,et al.  Decontamination of hypercubes by mobile agents , 2008, Networks.

[35]  Euripides Markou,et al.  The Mobile Agent Rendezvous Problem in the Ring , 2010, Synthesis Lectures on Distributed Computing Theory.

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

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

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

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

[40]  Colin Cooper,et al.  Locating and Repairing Faults in a Network with Mobile Agents , 2008, SIROCCO.

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

[42]  Nicola Santoro,et al.  Rendezvous of Mobile Agents in Unknown Graphs with Faulty Links , 2007, DISC.

[43]  Euripides Markou,et al.  Hardness and approximation results for Black Hole Search in arbitrary networks , 2007, Theor. Comput. Sci..

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