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Optimal Probabilistic Ring Exploration by Asynchronous Oblivious Robots [article]

Stéphane Devismes, Franck Petit (LIP, INRIA Rhône-Alpes / LIP Laboratoire de l'Informatique du Parallélisme), Sébastien Tixeuil
2009 arXiv   pre-print
In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the exploration problem of anonymous unoriented rings of any size.  ...  We consider a team of k identical, oblivious, asynchronous mobile robots that are able to sense (i.e., view) their environment, yet are unable to communicate, and evolve on a constrained path.  ...  Theorem 2 There is no exploration protocol (even probabilistic) of a n-size ring with three robots for every n > 3. Proof.  ... 
arXiv:0902.1834v1 fatcat:32xmhg35avgebe26iorsnioazq

Optimal Deterministic Ring Exploration with Oblivious Asynchronous Robots [chapter]

Anissa Lamani, Maria Gradinariu Potop-Butucaru, Sébastien Tixeuil
2010 Lecture Notes in Computer Science  
We consider the problem of exploring an anonymous unoriented ring of size n by k identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment  ...  Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size n is 4.  ...  Four probabilistic robots are proved optimal since the same paper shows that no protocol (probabilistic or deterministic) can explore a ring with three robots. Contribution.  ... 
doi:10.1007/978-3-642-13284-1_15 fatcat:mqo77pcm65b65mkirow2uny3ue

Optimal Probabilistic Ring Exploration by Semi-synchronous Oblivious Robots [chapter]

Stéphane Devismes, Franck Petit, Sébastien Tixeuil
2010 Lecture Notes in Computer Science  
In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the exploration problem of anonymous unoriented rings of any size.  ...  By contrast, we show that four identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive.  ...  Algorithm 1 is a probabilistic exploration protocol for 4 robots in a ring of n > 8 nodes.  ... 
doi:10.1007/978-3-642-11476-2_16 fatcat:xbfxre22hng3zarcpza6fjvwyy

Optimal probabilistic ring exploration by semi-synchronous oblivious robots

Stéphane Devismes, Franck Petit, Sébastien Tixeuil
2013 Theoretical Computer Science  
In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the exploration problem of anonymous unoriented rings of any size.  ...  By contrast, we show that four identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive.  ...  Algorithm 1 is a probabilistic exploration protocol for 4 robots in a ring of n > 8 nodes.  ... 
doi:10.1016/j.tcs.2013.05.031 fatcat:hcd5xezoenggxhxeykuvrt5yim

Oblivious Robots on Graphs: Exploration [chapter]

David Ilcinkas
2019 Lecture Notes in Computer Science  
This chapter focuses on the problem of exploring a graph by a team of mobile robots endowed with vision.  ...  The goal for these robots is to explore the graph in which they are, that is to visit all vertices of the graph.  ...  This more or less explains why exclusive perpetual exploration cannot be solved by more than n − q robots. Algorithmic techniques for oblivious robots in rings and grids.  ... 
doi:10.1007/978-3-030-11072-7_9 fatcat:kipiyqnzybb2fp75dwm3fsdbxe

Optimal Grid Exploration by Asynchronous Oblivious Robots [chapter]

Stéphane Devismes, Anissa Lamani, Franck Petit, Pascal Raymond, Sébastien Tixeuil
2012 Lecture Notes in Computer Science  
We propose optimal (w.r.t. the number of robots) solutions for the deterministic terminating exploration (exploration for short) of a grid-shaped network by a team of k asynchronous oblivious robots in  ...  Then, we propose deterministic algorithms in CORDA to exhibit the optimal number of robots allowing to explore of a given grid.  ...  In this paper, we propose optimal (w.r.t. the number of robots) solutions for the deterministic terminating exploration of a grid-shaped network by a team of k asynchronous oblivious robots in the asynchronous  ... 
doi:10.1007/978-3-642-33536-5_7 fatcat:v6asal3phfcabfe2bgdboscvra

Optimal grid exploration by asynchronous oblivious robots [article]

Stéphane Devismes, Franck Petit , Sébastien Tixeuil
2012 arXiv   pre-print
We propose optimal (w.r.t. the number of robots) solutions for the deterministic terminating exploration of a grid shaped network by a team of k asynchronous oblivious robots in the fully asynchronous  ...  Then, we propose deterministic algorithms in CORDA to exhibit the optimal number of robots allowing to explore of a given grid.  ...  It is shown in [6] that no (probabilistic or deterministic) exploration using less than four oblivious robots is possible for any ring of size at least four in ATOM.  ... 
arXiv:1105.2461v3 fatcat:xova6bxenjfhroyhzld3q6gdzq

On the Self-stabilization of Mobile Oblivious Robots in Uniform Rings [chapter]

Fukuhito Ooshita, Sébastien Tixeuil
2012 Lecture Notes in Computer Science  
We investigate self-stabilizing algorithms for anonymous and oblivious robots in uniform ring networks, that is, we focus on algorithms that can start from any initial configuration (including those with  ...  First, we show that no probabilistic self-stabilizing gathering algorithm exists in the asynchronous (ASYNC) model or if only global-weak and local-strong multiplicity detection is available.  ...  This work is supported in part by JSPS KAKENHI Grant Numbers 24500039, 24650012, 25104516, 26280022, 26330084. This work is supported in part by LINCS.  ... 
doi:10.1007/978-3-642-33536-5_6 fatcat:lirkspzgevespagq6qdbg64ng4

Optimal Torus Exploration by Oblivious Robots [chapter]

Stéphane Devismes, Anissa Lamani, Franck Petit, Sébastien Tixeuil
2015 Lecture Notes in Computer Science  
We propose an optimal (w.r.t. the number of robots) solution for the terminating exploration of a torus-shaped network by a team of k such robots.  ...  In this paper, we propose an optimal (w.r.t. the number of robots) solution for the terminating exploration of a torus-shaped network by a team of k such robots.  ...  Going higher dimension (from a ring to a torus) did not increase the robot number complexity of the exploration problem. The issue of the d-dimensional tori (for d > 2) remains open.  ... 
doi:10.1007/978-3-319-26850-7_13 fatcat:lmm3zcncivgdfomcoxlvoarslm

Ring Exploration with Oblivious Myopic Robots [article]

Ajoy K. Datta, Anissa Lamani, Lawrence L. Larmore, Franck Petit
2012 arXiv   pre-print
In this paper, we consider deterministic exploration in an anonymous, unoriented ring using asynchronous, oblivious, and myopic robots.  ...  The exploration problem in the discrete universe, using identical oblivious asynchronous robots without direct communication, has been well investigated.  ...  In the same paper, the authors give a probabilistic algorithm that solves the problem on a ring of size n > 8 that is optimal for the number of robots.  ... 
arXiv:1205.5003v1 fatcat:bmgotnjqwzeotkq24gvflqxtqq

Computing by Mobile Robotic Sensors [chapter]

Paola Flocchini, Giuseppe Prencipe, Nicola Santoro
2010 Monographs in Theoretical Computer Science  
The research areas of mobile robotic sensors lie in the intersection of two major fields of investigations carried out by quite distinct communities of researchers: autonomous robots and mobile sensor  ...  This means that synchronization, interaction, and communication of information among the robotic sensors can be achieved solely by means of their sensing capability, usually called vision.  ...  With respect to gathering, the outstanding open problem is whether it is possible to gather when the robotic sensors are asynchronous, oblivious and without common orientation.  ... 
doi:10.1007/978-3-642-14849-1_21 dblp:series/eatcs/FlocchiniPS11 fatcat:moittdti4vh6viqtuzlppiyyk4

Stabilizing Tiny Interaction Protocols [article]

Davide Canepa, Maria Gradinariu Potop-Butucaru
2010 arXiv   pre-print
In this work we only explore the power of oblivious stateless agents.  ...  Interestingly, our work proposes for the first time a model that unifies the recent studies in mobile robots(agents) that evolve in a discrete space and the already established population protocols paradigm  ...  , nodes and agents are oblivious, anonymous and uniform.  ... 
arXiv:0806.3471v2 fatcat:odfdkntoifb5dmcfol4t2rucre

Asynchronous Deterministic Rendezvous in Graphs [chapter]

Gianluca De Marco, Luisa Gargano, Evangelos Kranakis, Danny Krizanc, Andrzej Pelc, Ugo Vaccaro
2005 Lecture Notes in Computer Science  
These results still hold for the case of the ring of unknown size but then we also give an optimal algorithm of cost O(n|L min |), if the size n of the ring is known, and of cost O(n|L max |), if it is  ...  Since in the asynchronous setting meeting at a node, which is normally required in rendezvous, is in general impossible, we relax the demand by allowing meeting of the agents inside an edge as well.  ...  Optimal rendezvous in the ring Our results for the infinite line carry over to the case when agents are situated in a ring of unknown size n.  ... 
doi:10.1007/11549345_24 fatcat:evp7jkhjxvf6hiy37amaf3m4xi

Asynchronous deterministic rendezvous in graphs

Gianluca De Marco, Luisa Gargano, Evangelos Kranakis, Danny Krizanc, Andrzej Pelc, Ugo Vaccaro
2006 Theoretical Computer Science  
These results still hold for the case of the ring of unknown size, but then we also give an optimal algorithm of cost O(n|L min |), if the size n of the ring is known, and of cost O(n|L max |), if it is  ...  Since in the asynchronous setting, meeting at a node, which is normally required in rendezvous, is in general impossible, we relax the demand by allowing meeting of the agents inside an edge as well.  ...  Moreover, if the size n of the ring is known to the agents, then Algorithm Rendezvous-in-Ring can be modified to have cost O(n|L min |), which is optimal. ). Suppose they do not meet by this time.  ... 
doi:10.1016/j.tcs.2005.12.016 fatcat:nnwwybsqc5bmlcmrjp4datyveq

Cooperating Mobile Agents [chapter]

Sukumar Ghosh, Anurag Dasgupta
2012 Mobile Agents in Networking and Distributed Computing  
Each hop by an agent is completed in zero time. The agent computation is superimposed on the underlying distributed computation executed by the network of processes.  ...  An action by a process involves several steps, these include: receiving a message, updating its own state, and sending a message.  ...  In case of exploration without communication, the agents are oblivious of one another.  ... 
doi:10.1002/9781118135617.ch5 fatcat:wifipc6og5hh3oqcenhemqmrfq
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