Deterministic local algorithms, unique identifiers, and fractional graph colouring
نویسندگان
چکیده
منابع مشابه
Deterministic Local Algorithms, Unique Identifiers, and Fractional Graph Colouring
In the fractional graph colouring problem, the task is to schedule the activities of the nodes so that each node is active for 1 time unit in total, and at each point of time the set of active nodes forms an independent set. We show that for any α > 1 there exists a deterministic distributed algorithm that finds a fractional graph colouring of length at most α(∆ + 1) in any graph in one synchro...
متن کاملGraph colouring algorithms
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available techniques and is organized by algorithmic paradigm.
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Article history: Received 14 April 2010 Revised 20 June 2010 Available online 1 August 2010
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The paper investigates the application of the Mean Field Annealing (MFA) approach to graph colouring using the Petford and Welsh algorithm as a Generalised Boltzmann Machine. The operation of the MFA algorithm for a Generalised Boltzmann Machine is characterised by the deenition of an appropriate energy function which the algorithm attempts to minimise. In the case of graph colouring a relation...
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We present a deterministic algorithm producing the number of k-colourings of a graph on n vertices in time 2nnO(1). We also show that the chromatic number can be found by a polynomial space algorithm running in time O(2.2461). Finally, we present a family of polynomial space approximation algorithms that find a number between χ(G) and (1 + )χ(G) in time O(1.2209 + 2.2461 − ).
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2016
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2014.06.044