A self-stabilizing memory efficient algorithm for the minimum diameter spanning tree under an omnipotent daemon

Blin, Lélia; Boubekeur, Fadwa; Dubois, Swan

doi:10.1016/j.jpdc.2018.02.007

Cited by 6 publications

(3 citation statements)

References 41 publications

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“…On the other hand, growing and merging trees is the main technique for designing self-stabilizing leader election algorithms in networks, as the leader is often the root of an inward tree [3,4,2,9]. To the best of our knowledge, all algorithms that do not assume a pre-existing leader [3,4,2,8] for tree-construction use Ωplog nq bits per node. This high space-complexity is due to the implementation of two main techniques, used by all algorithms, and recalled below.…”

Section: Introductionmentioning

confidence: 99%

Compact Self-Stabilizing Leader Election for General Networks

Blin

Tixeuil²

2018

Lecture Notes in Computer Science

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We present a self-stabilizing leader election algorithm for arbitrary networks, with spacecomplexity Opmaxtlog ∆, log log nuq bits per node in n-node networks with maximum degree ∆. This space complexity is sub-logarithmic in n as long as ∆ " n op1q . The best space-complexity known so far for arbitrary networks was Oplog nq bits per node, and algorithms with sublogarithmic space-complexities were known for the ring only. To our knowledge, our algorithm is the first algorithm for self-stabilizing leader election to break the Ωplog nq bound for silent algorithms in arbitrary networks. Breaking this bound was obtained via the design of a (nonsilent) self-stabilizing algorithm using sophisticated tools such as solving the distance-2 coloring problem in a silent self-stabilizing manner, with space-complexity Opmaxtlog ∆, log log nuq bits per node. Solving this latter coloring problem allows us to implement a sub-logarithmic encoding of spanning trees -storing the IDs of the neighbors requires Ωplog nq bits per node, while we encode spanning trees using Opmaxtlog ∆, log log nuq bits per node. Moreover, we show how to construct such compactly encoded spanning trees without relying on variables encoding distances or number of nodes, as these two types of variables would also require Ωplog nq bits per node. * Sorbonne Universités, UPMC Univ Paris 06, CNRS, Université d'Evry-Val-d'Essonne, LIP6 UMR 7606, 4 place Jussieu 75005, Paris. † Sorbonne Universités, UPMC Univ Paris 06, CNRS, LIP6 UMR 7606, 4 place Jussieu 75005, Paris.

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Section: Introductionmentioning

confidence: 99%

Compact Self-Stabilizing Leader Election for General Networks

Blin

Tixeuil²

2018

Lecture Notes in Computer Science

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“…To make the token visit all the nodes we need to build a spanning tree beforehand, and we make the token traverse the tree. We use the same spanning tree construction and token circulation as in [5], inspired by the tree algorithm of [8] and the token algorithm of [17]. Indeed, these algorithms ensure to stabilize to a token circulation on a spanning tree in O(n) rounds using only O(log n) bits under our settings.…”

Section: Mst Construction Algorithmmentioning

confidence: 99%

Silent MST approximation for tiny memory

Blin¹,

Dubois²,

Feuilloley³

2019

Preprint

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In network distributed computing, minimum spanning tree (MST) is one of the key problems, and silent self-stabilization one of the most demanding fault-tolerance properties. For this problem and this model, a polynomial-time algorithm with O(log 2 n) memory is known for the state model. This is memory optimal for weights in the classic [1, poly(n)] range (where n is the size of the network). In this paper, we go below this O(log 2 n) memory, using approximation and parametrized complexity.More specifically, our contributions are two-fold. We introduce a second parameter s, which is the space needed to encode a weight, and we design a silent polynomial-time self-stabilizing algorithm, with space O(log n • s). In turn, this allows us to get an approximation algorithm for the problem, with a trade-off between the approximation ratio of the solution and the space used. For polynomial weights, this trade-off goes smoothly from memory O(log n) for an n-approximation, to memory O(log 2 n) for exact solutions, with for example memory O(log n log log n) for a 2-approximation.

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“…In S, this assumption makes the design of algorithms much more challenging, which often require the use of node identifiers or the construction of an underlying vertex coloring. Token circulation algorithms for S are proposed in [2,1,4]. All these algorithms work over tree topologies and use Θ(log n) bits of memory per node.…”

Section: Introductionmentioning

confidence: 99%

Optimal Memory Requirement for Self-stabilizing Token Circulation

Blin,

Le Bouder,

Petit

2024

Lecture Notes in Computer Science

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In this paper, we consider networks where every transmitted message is received by all of the transmitter's neighbors. Typical such networks are wireless networks, in which to dedicate a message to a specific neighbor, the sender must specify who the recipient is by specifying the recipient's ID. Adding an identifier has a non-negligible cost, more precisely O(log n) bits in an n-node graph. Token Circulation (TC) is a fundamental problem that consists in guaranteeing that a single token circulates from one node to another, the token fairly visiting every node infinitely often. TC inherently requires that the token holder selects a unique neighboring node to which to pass the token. This paper proposes a solution that overcomes the communication of identifiers. It achieves optimal space complexity for the token circulation problem.The contribution of this paper is fourfold. First, we present the first deterministic depthfirst token circulation algorithm for rooted wireless networks that uses only O(log log n) bits of memory per node. This is an exponential improvement compared to the classical addressing. Our algorithm assumes a Destination-Oriented Directed Acyclic Graph (DODAG) spanning the network. Less popular than spanning trees, DODAGs are nonetheless more general and adaptable spanning structures, since they do not need to distinguish one neighboring node as unique parent. Second, our algorithm has the very desirable property of being self-stabilizing. This means that starting from a configuration where zero or more than one token circulate in the network, the system is guaranteed to eventually work correctly, i.e., a single token eventually fairly visits every node infinitely often, following a depth-first order. Third, it works under the unfair scheduler, that is the most challenging scheduling assumption of the model. Finally, we show that our algorithm is optimal in terms of space complexity. Meaning that, for every n-node network, no TC algorithm can use less than Ω(log log n) bits of memory per node, even given a rooted spanning tree and even without considering self-stabilization.

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A self-stabilizing memory efficient algorithm for the minimum diameter spanning tree under an omnipotent daemon

Cited by 6 publications

References 41 publications

Compact Self-Stabilizing Leader Election for General Networks

Compact Self-Stabilizing Leader Election for General Networks

Silent MST approximation for tiny memory

Optimal Memory Requirement for Self-stabilizing Token Circulation

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