The topology of look-compute-move robot wait-free algorithms with hard termination

Alcántara, Manuel; Castañeda, Armando; Flores-Peñaloza, David; Rajsbaum, Sergio

doi:10.1007/s00446-018-0345-3

Cited by 12 publications

(21 citation statements)

References 37 publications

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“…Indeed, exact consensus requires quite strong assumptions on the underlying network [31,54]. Fortunately, exact consensus is an unnecessarily strong requirement for several applications that require agreement: both the asymptotic and the approximate consensus problems have not only a variety of applications in the design of human-made control systems like sensor fusion [6], clock synchronization [42], formation control [26], rendezvous in space [43] and robot gathering [2,13,21], or load balancing [23] but also for analyzing natural systems like bird flocking [56], firefly synchronization [46], or opinion dynamics [36]. These problems often have to be solved under harsh environmental restrictions in which exact consensus is not achievable, or too costly to achieve: with limited computational power and local storage, under restricted communication abilities, and in presence of communication uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Tight Bounds for Asymptotic and Approximate Consensus

Függer

Nowak

Schwarz

2021

J. ACM

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Agreeing on a common value among a set of agents is a fundamental problem in distributed computing, which occurs in several variants: In contrast to exact consensus, approximate variants are studied in systems where exact agreement is not possible or required, e.g., in human-made distributed control systems and in the analysis of natural distributed systems, such as bird flocking and opinion dynamics. We study the time complexity of two classical agreement problems: non-terminating asymptotic consensus and terminating approximate consensus. Asymptotic consensus, requires agents to repeatedly set their outputs such that the outputs converge to a common value within the convex hull of initial values; approximate consensus requires agents to eventually stop setting their outputs, which must then lie within a predefined distance of each other. We prove tight lower bounds on the contraction ratios of asymptotic consensus algorithms subject to oblivious message adversaries, from which we deduce bounds on the time complexity of approximate consensus algorithms. In particular, the obtained bounds show optimality of asymptotic and approximate consensus algorithms presented by Charron-Bost et al. (ICALP’16) for certain systems, including the strongest oblivious message adversary in which asymptotic and approximate consensus are solvable. As a corollary we also obtain asymptotically tight bounds for asymptotic consensus in the classical asynchronous model with crashes. Central to the lower-bound proofs is an extended notion of valency, the set of reachable limits of an asymptotic consensus algorithm starting from a given configuration. We further relate topological properties of valencies to the solvability of exact consensus, shedding some light on the relation of these three fundamental problems in dynamic networks.

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Section: Introductionmentioning

confidence: 99%

Tight Bounds for Asymptotic and Approximate Consensus

Függer

Nowak

Schwarz

2021

J. ACM

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“…Figure 1(a) gives an example of graphical approximate on a tree. Prior work has mostly focused on the cases when G is a path [7,18,22,23,38], a graph whose clique graph is a tree [3], or a chordal graph [35], i.e., a graph that contains no induced cycle of length greater than three.…”

Section: Graphical Approximate Agreementmentioning

confidence: 99%

“…Approximate gathering on graphs. Alcántara, Castañeda, Flores-Peñaloza, and Rajsbaum [3] investigated approximate agreement with the following weaker clique gathering validity condition: if all inputs values are adjacent, then each output value has to be one of the input values. Their validity condition arises from considering an approximate gathering problem for robots on a graph.…”

Section: Graphical Approximate Agreementmentioning

confidence: 99%

Wait-free approximate agreement on graphs

Alistarh

Ellen

Rybicki

2021

Preprint

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Approximate agreement is one of the few variants of consensus that can be solved in a wait-free manner in asynchronous systems where processes communicate by reading and writing to shared memory. In this work, we consider a natural generalisation of approximate agreement on arbitrary undirected connected graphs. Each process is given a vertex of the graph as input and, if non-faulty, must output a vertex such that -all the outputs are within distance 1 of one another, and -each output value lies on a shortest path between two input values.From prior work, it is known that there is no wait-free algorithm among n ≥ 3 processes for this problem on any cycle of length c ≥ 4, by reduction from 2-set agreement (Castañeda et al., 2018).In this work, we investigate the solvability and complexity of this task on general graphs. We give a new, direct proof of the impossibility of approximate agreement on cycles of length c ≥ 4, via a generalisation of Sperner's Lemma to convex polygons. We also extend the reduction from 2-set agreement to a larger class of graphs, showing that approximate agreement on on these graphs is unsolvable. Furthermore, we show that combinatorial arguments, used by both existing proofs, are necessary, by showing that the impossibility of a wait-free algorithm in the nonuniform iterated snapshot model cannot be proved via an extension-based proof. On the positive side, we present a wait-free algorithm for a class of graphs that properly contains the class of chordal graphs.

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“…Furthermore, since robots in OBLOT are luminous robots with k = 1 color, this result implies that asynchronous luminous robots are at least as powerful as semi-synchronous traditional robots. Since their introduction, a large amount of work has been done on luminous robots ( [1], [2], [4], [8], [10], [17], [21], [23]- [26], [30]; see [11] for a recent review). In this paper we continue the investigation on the computational impact of lights, and examine the problem of forming a sequence of geometric patterns.…”

Section: A Frameworkmentioning

confidence: 99%

Forming Sequences of Patterns With Luminous Robots

et al. 2020

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The extensive studies on computing by a team of identical mobile robots operating in the plane in Look-Compute-Move cycles have been carried out mainly in the traditional OBLOT model, where the robots are silent (have no communication capabilities) and oblivious (in a cycle, they have no memory previous cycles). To partially overcome the limits of obliviousness and silence while maintaining some of their advantages, the stronger model of luminous robots, LUMI, has been introduced where the robots, otherwise oblivious and silent, carry a visible light that can take a number of different colors; a color can be seen by observing robots, and persists from a cycle to the next. In the study of the computational impact of lights, an immediate concern has been to understand and determine the additional computational strength of LUMI over OBLOT. Within this line of investigation, we examine the problem of forming a sequence of geometric patterns, PATTERNSEQUENCEFORMATION. A complete characterization of the sequences of patterns formable from a given starting configuration has been determined in the OBLOT model. In this paper, we study the formation of sequences of patterns in the LUMI model and provide a complete characterization. The characterization is constructive: our universal protocol forms all formable sequences, and it does so asynchronously and without rigidity. This characterization explicitly and clearly identifies the computational strength of LUMI over OBLOT with respect to the PATTERNSEQUENCEFORMATION problem. INDEX TERMS Autonomous mobile robots, distributed computing, oblivious, pattern formation, sequence of patterns, visible lights.

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The topology of look-compute-move robot wait-free algorithms with hard termination

Cited by 12 publications

References 37 publications

Tight Bounds for Asymptotic and Approximate Consensus

Tight Bounds for Asymptotic and Approximate Consensus

Wait-free approximate agreement on graphs

Forming Sequences of Patterns With Luminous Robots

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