A Topological Perspective on Distributed Network Algorithms

Castañeda, Armando; Fraigniaud, Pierre; Paz, Ami; Rajsbaum, Sergio; Roy, Matthieu; Travers, Corentin

doi:10.1007/978-3-030-24922-9_1

Cited by 6 publications

(19 citation statements)

References 44 publications

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“…We now state the main technical result of the section. It extends the result from Castañeda et al [6] and adapts it to the interpretation of complexes we need here. While Castañeda et al studied the complex given by the interpretation of a single graph (to capture models like LOCAL and CON GEST [25]), we care about the complex resulting of the interpretation of a set of graphs.…”

Section: A Powerful Toolsupporting

confidence: 86%

“…As before, we start with the simple closed-above case, where the model is the closure of a single graph. In this case the tight lower bound follows from Castañeda et al [6,Thm 5.1], as mentionned above.…”

Section: One Round Lower Bounds For One Round: a Touch Of Topologymentioning

confidence: 71%

“…These models capture some safety properties, where we require some underlying structure in communication, like having an underlying star, ring or tree. This is a strict generalization of the models with a fixed communication graph considered by Castañeda et al [6].…”

Section: Introduction 1motivationmentioning

confidence: 96%

“…From Castañeda et al [6,Thm 5.1], we know this bound is tight: the oblivious model with a single graph cannot solve -set agreement in one round for < ( ). Hence the weaker simple closedabove model generated by cannot solve -set agreement in one round for < ( ).…”

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confidence: 99%

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K-set agreement bounds in round-based models through combinatorial topology

Shimi

Castañeda²

2020

Proceedings of the 39th Symposium on Principles of Distributed Computing

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Round-based models are very common message-passing models; combinatorial topology applied to distributed computing provides sweeping results like general lower bounds. We combine both to study the computability of-set agreement. Among all the possible round-based models, we consider oblivious ones, where the constraints are given only round per round by a set of allowed graphs. And among oblivious models, we focus on closed-above ones, that is models where the set of possible graphs contains all graphs with more edges than some starting graphs. These capture intuitively the underlying structure required by some communication model, like containing a ring. We then derive lower bounds and upper bounds in one round for-set agreement, such that these bounds are proved using combinatorial topology but stated only in terms of graph properties. These bounds extend to multiple rounds when limiting our algorithms to be oblivious-recalling only pairs of processes and initial value, not who send what and when.

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Section: A Powerful Toolsupporting

confidence: 86%

Section: One Round Lower Bounds For One Round: a Touch Of Topologymentioning

confidence: 71%

Section: Introduction 1motivationmentioning

confidence: 96%

mentioning

confidence: 99%

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K-set agreement bounds in round-based models through combinatorial topology

Shimi

Castañeda²

2020

Proceedings of the 39th Symposium on Principles of Distributed Computing

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“…We now state the main technical result of the section. It extends the result from Castañeda et al [5] and adapts it to the interpretation of complexes we need here. While Castañeda et al studied the complex given by the interpretation of a single graph (to capture models like LOCAL and CONGEST), we care about the complex resulting of the interpretation of a set of graphs.…”

Section: 15 ([H ])supporting

confidence: 86%

K set-agreement bounds in round-based models through combinatorial topology

Shimi¹,

Castañeda²

2020

Preprint

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Round-based models are the main message-passing models; combinatorial topology applied to distributed computing provide sweeping results like general lower bounds. We combine both to study the computability of k set-agreement. Among all the possible round-based models, we consider oblivious ones, where the constraints are given only round per round by a set of allowed graphs. And among oblivious models, we focus on closed-above ones, that is models where the set of possible graphs is a union of above-closure of graphs. These capture intuitively the underlying structure required by some communication model, like containing a ring.We then derive lower bounds and upper bounds in one round for k set-agreement, such that these bounds are proved using combinatorial topology but stated only in terms of graph properties. These bounds extend to multiple rounds when limiting our algorithms to oblivious ones, that is ones that recall only pairs of process and initial value.CCS Concepts: • Theory of computation → Design and analysis of algorithms; Distributed algorithms;

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Synchronous t-Resilient Consensus in Arbitrary Graphs

Castañeda¹,

Fraigniaud

Paz

et al. 2019

Lecture Notes in Computer Science

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We study the number of rounds needed to solve consensus in a synchronous network G where at most t nodes may fail by crashing. This problem has been thoroughly studied when G is a complete graph, but very little is known when G is arbitrary. We define a notion of radius(G, t), that extends the standard graph theoretical notion of radius, for considering all the ways in which t nodes may crash, and we present an algorithm that solves consensus in radius(G, t) rounds. Then we derive a lower bound showing that, among oblivious algorithms, our algorithm is optimal for a large family of graphs including all vertex-transitive graphs.

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A Topological Perspective on Distributed Network Algorithms

Cited by 6 publications

References 44 publications

K-set agreement bounds in round-based models through combinatorial topology

K-set agreement bounds in round-based models through combinatorial topology

K set-agreement bounds in round-based models through combinatorial topology

Synchronous t-Resilient Consensus in Arbitrary Graphs

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