International audienceIn this paper,  we study the problem of gossiping with interference constraint in radio chain networks. Gossiping (or total exchange information) is a protocol where each node in the network has a message and wants to distribute its own message to every other node in the network. The gossiping problem consists in finding the minimum running time (makespan) of a gossiping protocol and efficient algorithms that attain this makespan

Bermond, Jean-Claude

Kodate, Takako

Yu, Joseph

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HAL Id: hal-02316854https://hal.inria.fr/hal-02316854Submitted on 15 Oct 2019HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Gossiping with interference in radio chain networks(upper bound algorithms)Jean-Claude Bermond, Takako Kodate, Joseph YuTo cite this version:Jean-Claude Bermond, Takako Kodate, Joseph Yu. Gossiping with interference in radio chain net-works (upper bound algorithms). JCDCG-3 - 22th Japan Conference on Discrete and ComputationalGeometry, Graphs, and Games, Sep 2019, Tokyo, Japan. ￿hal-02316854￿Gossiping with interference in radio chain networks(upper bound algorithms)Jean-Claude BermondUniversité Côte d’Azur, CNRS, Inria, I3S, France,jean-claude.bermond@inria.frTakako KodateDepartment of Information and Sciences,Tokyo Woman’s Christian University, Japan,kodate@lab.twcu.ac.jpJoseph YuDepartment of Mathematics,University of the Fraser Valley, B.C., Canada,joseph.yu@ufv.caIn this paper, we study the problem of gossiping with interference constraint in radio chainnetworks. Gossiping (or total exchange information) is a protocol where each node in the networkhas a message and wants to distribute its own message to every other node in the network. Thegossiping problem consists in finding the minimum running time (makespan) of a gossiping protocoland efficient algorithms that attain this makespan.Transmission model The radio chain network is modeled as a symmetric dipath Pn, wherethe vertices represent the nodes and the arcs represent the possible communications. A call (s, r)is defined as the transmission from the node s to the node r, in which s is the sender and r isthe receiver and (s, r) is an arc of the dipath. The network is assumed to be synchronous and thetime is slotted into steps. We suppose that each device is equipped with a half duplex interface,and therefore, a node cannot both receive and transmit during a step.Interference model Furthermore, communication is subject to interference constraints. We usea binary asymmetric model of interference based on the distance in the communication digraphlike the ones used in [1, 2, 5]. Let d(s, r) denote the distance, that is the length of a shortestdirected path, from s to r in Pn and dI be a non-negative integer. We assume that when a node stransmits, all nodes v such that d(s, v) ≤ dI are subject to the interference from the transmissionat s. So two calls (s, r) and (s′, r′) do not interfere if d(s, r′) > dI and d(s′, r) > dI . During agiven step only non-interfering (or compatible) calls can be done and we will define a round as aset of such compatible calls. We focus here on the case where dI = 1.Main result Within this model, the problem has been studied in general in [4] where approx-imation results are given in particular for ring and chain networks (see also the survey [3]). Wesolved completely the gossiping problem in radio ring networks (work presented at JCDCG3 2017),and presented partial results for radio chain networks (work presented at JCDCG3 2018).In this talk, we present new gossiping algorithms for chain networks which meet the lowerbounds enabling us to prove the following theorem:Theorem 1 The minimum number R of rounds needed to achieve a gossiping in a chain networkPn (n ≥ 3), with the interference distance dI = 1 isR ={3n− 5 if n ≥ 45 if n = 3References[1] J.C. Bermond, R. Correa and M.L. Yu.: Optimal gathering protocols on paths under interfer-ence constraints, Discrete Mathematics 309: 5574–5587, 2009.[2] J.-C. Bermond, J. Galtier, R. Klasing, N. Morales, and S. Pérennes. Hardness and approx-imation of gathering in static radio networks. Parallel Processing Letters, 16(2): 165–183,2006.[3] L. G ↪asieniec. On efficient gossiping in radio networks. Proc. Int. Conference on Theoreti-cal Computer ScienceColloquium on structural information and communication complexity,SIROCCO 2009, Lectures Notes in Computer science, springer Verlag, vol 5869: 2–14, 2010.[4] L. G ↪asieniec and I. Potapov. Gossiping with unit messages in known radio networks. Proc.2nd IFIP Int. Conference on Theoretical Computer Science: 193–205, 2002.[5] R. Klasing, N. Morales, and S. Pérennes. On the complexity of bandwidth allocation in radionetworks. Theoretical Computer Science, 406(3): 225–239, 2008.

Gossiping with interference in radio chain networks (upper bound algorithms)

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Gossiping with interference in radio chain networks (upper bound algorithms)

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