Locality based graph coloring

Szegedy, Márió; Vishwanathan, Sundar

doi:10.1145/167088.167156

Cited by 72 publications

(88 citation statements)

References 9 publications

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“…This problem is closely related to the MIS problem, and similarly to the latter problem, the coloring problem is one of the most central and most intensively studied problems in Distributed Algorithms [10,11,17,16,24]. The goal of the coloring problem is to assign colors to vertices so that for each edge e, the endpoints of e are assigned distinct colors.…”

Section: Coloringmentioning

confidence: 99%

Sublogarithmic distributed MIS algorithm for sparse graphs using nash-williams decomposition

Barenboim

Elkin

2008

Proceedings of the Twenty-Seventh ACM Symposium on Principles of Distributed Computing

103

287

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We study the distributed maximal independent set (henceforth, MIS) problem on sparse graphs. Currently, there are known algorithms with a sublogarithmic running time for this problem on oriented trees and graphs of bounded degrees. We devise the first sublogarithmic algorithm for computing MIS on graphs of bounded arboricity. This is a large family of graphs that includes graphs of bounded degree, planar graphs, graphs of bounded genus, graphs of bounded treewidth, graphs that exclude a fixed minor, and many other graphs. We also devise efficient algorithms for coloring graphs from these families.These results are achieved by the following technique that may be of independent interest. Our algorithm starts with computing a certain graph-theoretic structure, called NashWilliams forests-decomposition. Then this structure is used to compute the MIS or coloring. Our results demonstrate that this methodology is very powerful.Finally, we show nearly-tight lower bounds on the running time of any distributed algorithm for computing a forestsdecomposition.

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Section: Coloringmentioning

confidence: 99%

Sublogarithmic distributed MIS algorithm for sparse graphs using nash-williams decomposition

Barenboim

Elkin

2008

Proceedings of the Twenty-Seventh ACM Symposium on Principles of Distributed Computing

103

287

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“…At implementation level, this means that each node needs to periodically estimate with a sufficient level of confidence which nodes of the network are potential conflicting neighbours. The majority of decentralised schemes require that each serving node needs local knowledge of the local neighbourhood [3][4][5][6], and any attempt to relax this hypothesis comes at the expense of performance, as shown in Section 2.…”

Section: Wireless Communications and Mobile Computingmentioning

confidence: 99%

“…The characterisation of the first time to FK generally depends on the realisation of a sequence of user reports; this means that is a random variable. More precisely, by (6), is a stopping time; see, for example, [27].…”

Section: Definition 1 (Full Knowledge)mentioning

confidence: 99%

Updating Neighbour Cell List via Crowdsourced User Reports: A Framework for Measuring Time Performance

Checco

Lancia

Leith

2018

Wireless Communications and Mobile Computing

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In modern wireless networks deployments, each serving node needs to keep its Neighbour Cell List (NCL) constantly up to date to keep track of network changes. The time needed by each serving node to update its NCL is an important parameter of the network's reliability and performance. An adequate estimate of such parameter enables a significant improvement of self-configuration functionalities. This paper focuses on the update time of NCLs when an approach of crowdsourced user reports is adopted. In this setting, each user periodically reports to the serving node information about the set of nodes sensed by the user itself. We show that, by mapping the local topological structure of the network onto states of increasing knowledge, a crisp mathematical framework can be obtained, which allows in turn for the use of a variety of user mobility models. Further, using a simplified mobility model we show how to obtain useful upper bounds on the expected time for a serving node to gain Full Knowledge of its local neighbourhood.

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“…Linial [27] proved that O(∆ 2 )-coloring can be computed deterministically in O(log * n) time, independent of ∆. Szegedy and Vishwanathan [38] later improved the running time of this algorithm to √ log n) time [32] or O(∆ + log * n) time [8]. Even if the palette size is enlarged to O(∆), the Panconesi-Srinivasan [32] algorithm remains the fastest, when time is expressed as a function of n. However, Barenboim and Elkin [6] gave an O(min{λ log n, λ + log 1+ n})-time algorithm for O(λ)-coloring, and an O(log λ log n)-time algorithm for λ 1+ -coloring.…”

Section: Deterministic Mis the Fastest Deterministic Mis Algorithms Fmentioning

confidence: 99%

“…The coloring algorithms of [27,38] take O(log * β) time steps in H [1,α−1] , each of which can be simulated with α − 1 time steps in H. By Theorem 2.4,…”

Section: Proofmentioning

confidence: 99%

The Locality of Distributed Symmetry Breaking

Barenboim

Elkin

Pettie

et al. 2016

J. ACM

132

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Symmetry breaking problems are among the most well studied in the field of distributed computing and yet the most fundamental questions about their complexity remain open. In this paper we work in the LOCAL model (where the input graph and underlying distributed network are identical) and study the randomized complexity of four fundamental symmetry breaking problems on graphs: computing MISs (maximal independent sets), maximal matchings, vertex colorings, and ruling sets. A small sample of our results includes

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Locality based graph coloring

Cited by 72 publications

References 9 publications

Sublogarithmic distributed MIS algorithm for sparse graphs using nash-williams decomposition

Sublogarithmic distributed MIS algorithm for sparse graphs using nash-williams decomposition

Updating Neighbour Cell List via Crowdsourced User Reports: A Framework for Measuring Time Performance

The Locality of Distributed Symmetry Breaking

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