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