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On the Time and the Bit Complexity of Distributed Randomised Anonymous Ring Colouring

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Τίτλος: On the Time and the Bit Complexity of Distributed Randomised Anonymous Ring Colouring
Συγγραφείς: Métivier, Yves, Robson, J.M., Saheb-Djahromi, Nasser, Zemmari, Akka
Συνεισφορές: Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CPU
Πηγή: ISSN: 1879-2294.
Στοιχεία εκδότη: HAL CCSD
Elsevier
Έτος έκδοσης: 2013
Συλλογή: Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe)
Θεματικοί όροι: Colouring, Mellin Transform, Probabilistic Analysis, Randomised Distributed Graph Algorithm, Ring, Time Complexity, bit complexity, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC]
Περιγραφή: International audience ; We present and analyse a very simple randomised distributed vertex colouring algorithm for ring graphs. Its time complexity is ${\log_2 n} + o(\log n)$ on average and $2{\log_2 n}+ o(\log n)$ with probability $1- o(n^{-1}).$ Each message containing $1$ bit we deduce the same values for its bit complexity. Then we compose this algorithm with another and we obtain a $3$-colouring algorithm for ring graphs. Thanks to an overlapping, we obtain once more the same values for the time complexities on average and with probability $1- o(n^{-1}).$ The same results hold for the bit complexity. These results are obtained using the Mellin transform. We establish lower bounds (on average and with probability $1- o(n^{-1})$) for the distributed randomised anonymous ring colouring problem. We prove that our algorithms match these lower bounds modulo a negligible additive function (negligible with respect to $\log_2 n$). We assume that the ring is anonymous: unique identities are not available to distinguish the processes; we only assume that each vertex distinguishes between its neighbours. Furthermore we do not assume that the size (or an upper bound on the size) of the ring is known.
Τύπος εγγράφου: article in journal/newspaper
Γλώσσα: English
Relation: hal-00695983; https://hal.archives-ouvertes.fr/hal-00695983
Διαθεσιμότητα: https://hal.archives-ouvertes.fr/hal-00695983
Αριθμός Καταχώρησης: edsbas.E4F42AF1
Βάση Δεδομένων: BASE
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  – Url: https://hal.archives-ouvertes.fr/hal-00695983#
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  Data: On the Time and the Bit Complexity of Distributed Randomised Anonymous Ring Colouring
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  Data: <searchLink fieldCode="AR" term="%22Métivier%2C+Yves%22">Métivier, Yves</searchLink><br /><searchLink fieldCode="AR" term="%22Robson%2C+J%2EM%2E%22">Robson, J.M.</searchLink><br /><searchLink fieldCode="AR" term="%22Saheb-Djahromi%2C+Nasser%22">Saheb-Djahromi, Nasser</searchLink><br /><searchLink fieldCode="AR" term="%22Zemmari%2C+Akka%22">Zemmari, Akka</searchLink>
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  Data: Laboratoire Bordelais de Recherche en Informatique (LaBRI)<br />Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)<br />CPU
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  Data: <i>ISSN: 1879-2294</i>.
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  Data: HAL CCSD<br />Elsevier
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  Data: 2013
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  Data: <searchLink fieldCode="DE" term="%22Colouring%22">Colouring</searchLink><br /><searchLink fieldCode="DE" term="%22Mellin+Transform%22">Mellin Transform</searchLink><br /><searchLink fieldCode="DE" term="%22Probabilistic+Analysis%22">Probabilistic Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Randomised+Distributed+Graph+Algorithm%22">Randomised Distributed Graph Algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22Ring%22">Ring</searchLink><br /><searchLink fieldCode="DE" term="%22Time+Complexity%22">Time Complexity</searchLink><br /><searchLink fieldCode="DE" term="%22bit+complexity%22">bit complexity</searchLink><br /><searchLink fieldCode="DE" term="%22[INFO%2EINFO-DC]Computer+Science+[cs]%2FDistributed%22">[INFO.INFO-DC]Computer Science [cs]/Distributed</searchLink><br /><searchLink fieldCode="DE" term="%22Parallel%22">Parallel</searchLink><br /><searchLink fieldCode="DE" term="%22and+Cluster+Computing+[cs%2EDC]%22">and Cluster Computing [cs.DC]</searchLink>
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  Data: International audience ; We present and analyse a very simple randomised distributed vertex colouring algorithm for ring graphs. Its time complexity is ${\log_2 n} + o(\log n)$ on average and $2{\log_2 n}+ o(\log n)$ with probability $1- o(n^{-1}).$ Each message containing $1$ bit we deduce the same values for its bit complexity. Then we compose this algorithm with another and we obtain a $3$-colouring algorithm for ring graphs. Thanks to an overlapping, we obtain once more the same values for the time complexities on average and with probability $1- o(n^{-1}).$ The same results hold for the bit complexity. These results are obtained using the Mellin transform. We establish lower bounds (on average and with probability $1- o(n^{-1})$) for the distributed randomised anonymous ring colouring problem. We prove that our algorithms match these lower bounds modulo a negligible additive function (negligible with respect to $\log_2 n$). We assume that the ring is anonymous: unique identities are not available to distinguish the processes; we only assume that each vertex distinguishes between its neighbours. Furthermore we do not assume that the size (or an upper bound on the size) of the ring is known.
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  Data: article in journal/newspaper
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Colouring
        Type: general
      – SubjectFull: Mellin Transform
        Type: general
      – SubjectFull: Probabilistic Analysis
        Type: general
      – SubjectFull: Randomised Distributed Graph Algorithm
        Type: general
      – SubjectFull: Ring
        Type: general
      – SubjectFull: Time Complexity
        Type: general
      – SubjectFull: bit complexity
        Type: general
      – SubjectFull: [INFO.INFO-DC]Computer Science [cs]/Distributed
        Type: general
      – SubjectFull: Parallel
        Type: general
      – SubjectFull: and Cluster Computing [cs.DC]
        Type: general
    Titles:
      – TitleFull: On the Time and the Bit Complexity of Distributed Randomised Anonymous Ring Colouring
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            NameFull: Métivier, Yves
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            NameFull: Robson, J.M.
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            NameFull: Saheb-Djahromi, Nasser
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            NameFull: Zemmari, Akka
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          Dates:
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              M: 01
              Type: published
              Y: 2013
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            – TitleFull: ISSN: 1879-2294
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