Convergence and covering on graphs for wait-free robots

Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article,...
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Autor*in:	Castañeda, Armando [verfasserIn] Rajsbaum, Sergio Roy, Matthieu

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	Robot gathering Agreement Symmetry breaking Shared memory Wait-freedom Combinatorial topology

Anmerkung:	© The Author(s) 2017

Übergeordnetes Werk:	Enthalten in: Journal of the Brazilian Computer Society - London : Springer, 1996, 24(2018), 1 vom: 08. Jan.
Übergeordnetes Werk:	volume:24 ; year:2018 ; number:1 ; day:08 ; month:01

Links:	Volltext

DOI / URN:	10.1186/s13173-017-0065-8

Katalog-ID:	SPR03074444X

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520			\|a Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results.
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allfields	10.1186/s13173-017-0065-8 doi (DE-627)SPR03074444X (SPR)s13173-017-0065-8-e DE-627 ger DE-627 rakwb eng Castañeda, Armando verfasserin aut Convergence and covering on graphs for wait-free robots 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results. Robot gathering (dpeaa)DE-He213 Agreement (dpeaa)DE-He213 Symmetry breaking (dpeaa)DE-He213 Shared memory (dpeaa)DE-He213 Wait-freedom (dpeaa)DE-He213 Combinatorial topology (dpeaa)DE-He213 Rajsbaum, Sergio aut Roy, Matthieu aut Enthalten in Journal of the Brazilian Computer Society London : Springer, 1996 24(2018), 1 vom: 08. Jan. (DE-627)324613377 (DE-600)2028746-X 1678-4804 nnns volume:24 year:2018 number:1 day:08 month:01 https://dx.doi.org/10.1186/s13173-017-0065-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 08 01
spelling	10.1186/s13173-017-0065-8 doi (DE-627)SPR03074444X (SPR)s13173-017-0065-8-e DE-627 ger DE-627 rakwb eng Castañeda, Armando verfasserin aut Convergence and covering on graphs for wait-free robots 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results. Robot gathering (dpeaa)DE-He213 Agreement (dpeaa)DE-He213 Symmetry breaking (dpeaa)DE-He213 Shared memory (dpeaa)DE-He213 Wait-freedom (dpeaa)DE-He213 Combinatorial topology (dpeaa)DE-He213 Rajsbaum, Sergio aut Roy, Matthieu aut Enthalten in Journal of the Brazilian Computer Society London : Springer, 1996 24(2018), 1 vom: 08. Jan. (DE-627)324613377 (DE-600)2028746-X 1678-4804 nnns volume:24 year:2018 number:1 day:08 month:01 https://dx.doi.org/10.1186/s13173-017-0065-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 08 01
allfields_unstemmed	10.1186/s13173-017-0065-8 doi (DE-627)SPR03074444X (SPR)s13173-017-0065-8-e DE-627 ger DE-627 rakwb eng Castañeda, Armando verfasserin aut Convergence and covering on graphs for wait-free robots 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results. Robot gathering (dpeaa)DE-He213 Agreement (dpeaa)DE-He213 Symmetry breaking (dpeaa)DE-He213 Shared memory (dpeaa)DE-He213 Wait-freedom (dpeaa)DE-He213 Combinatorial topology (dpeaa)DE-He213 Rajsbaum, Sergio aut Roy, Matthieu aut Enthalten in Journal of the Brazilian Computer Society London : Springer, 1996 24(2018), 1 vom: 08. Jan. (DE-627)324613377 (DE-600)2028746-X 1678-4804 nnns volume:24 year:2018 number:1 day:08 month:01 https://dx.doi.org/10.1186/s13173-017-0065-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 08 01
allfieldsGer	10.1186/s13173-017-0065-8 doi (DE-627)SPR03074444X (SPR)s13173-017-0065-8-e DE-627 ger DE-627 rakwb eng Castañeda, Armando verfasserin aut Convergence and covering on graphs for wait-free robots 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results. Robot gathering (dpeaa)DE-He213 Agreement (dpeaa)DE-He213 Symmetry breaking (dpeaa)DE-He213 Shared memory (dpeaa)DE-He213 Wait-freedom (dpeaa)DE-He213 Combinatorial topology (dpeaa)DE-He213 Rajsbaum, Sergio aut Roy, Matthieu aut Enthalten in Journal of the Brazilian Computer Society London : Springer, 1996 24(2018), 1 vom: 08. Jan. (DE-627)324613377 (DE-600)2028746-X 1678-4804 nnns volume:24 year:2018 number:1 day:08 month:01 https://dx.doi.org/10.1186/s13173-017-0065-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 08 01
allfieldsSound	10.1186/s13173-017-0065-8 doi (DE-627)SPR03074444X (SPR)s13173-017-0065-8-e DE-627 ger DE-627 rakwb eng Castañeda, Armando verfasserin aut Convergence and covering on graphs for wait-free robots 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2017 Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results. Robot gathering (dpeaa)DE-He213 Agreement (dpeaa)DE-He213 Symmetry breaking (dpeaa)DE-He213 Shared memory (dpeaa)DE-He213 Wait-freedom (dpeaa)DE-He213 Combinatorial topology (dpeaa)DE-He213 Rajsbaum, Sergio aut Roy, Matthieu aut Enthalten in Journal of the Brazilian Computer Society London : Springer, 1996 24(2018), 1 vom: 08. Jan. (DE-627)324613377 (DE-600)2028746-X 1678-4804 nnns volume:24 year:2018 number:1 day:08 month:01 https://dx.doi.org/10.1186/s13173-017-0065-8 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2018 1 08 01
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author	Castañeda, Armando
spellingShingle	Castañeda, Armando misc Robot gathering misc Agreement misc Symmetry breaking misc Shared memory misc Wait-freedom misc Combinatorial topology Convergence and covering on graphs for wait-free robots
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topic_title	Convergence and covering on graphs for wait-free robots Robot gathering (dpeaa)DE-He213 Agreement (dpeaa)DE-He213 Symmetry breaking (dpeaa)DE-He213 Shared memory (dpeaa)DE-He213 Wait-freedom (dpeaa)DE-He213 Combinatorial topology (dpeaa)DE-He213
topic	misc Robot gathering misc Agreement misc Symmetry breaking misc Shared memory misc Wait-freedom misc Combinatorial topology
topic_unstemmed	misc Robot gathering misc Agreement misc Symmetry breaking misc Shared memory misc Wait-freedom misc Combinatorial topology
topic_browse	misc Robot gathering misc Agreement misc Symmetry breaking misc Shared memory misc Wait-freedom misc Combinatorial topology
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title	Convergence and covering on graphs for wait-free robots
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title_full	Convergence and covering on graphs for wait-free robots
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title_sort	convergence and covering on graphs for wait-free robots
title_auth	Convergence and covering on graphs for wait-free robots
abstract	Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results. © The Author(s) 2017
abstractGer	Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results. © The Author(s) 2017
abstract_unstemmed	Abstract The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results. © The Author(s) 2017
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title_short	Convergence and covering on graphs for wait-free robots
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