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| * Input Predicates: node/1, link/2, colour/1 * Output Predicates: chosenColour/2 |
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| == Predicates == | |
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| == Input == | * '''Input''': {{{node/1, link/2, colour/1}}} * '''Output''': {{{chosenColour/2}}} == Input format == |
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| A number of link facts which say which nodes are linked. Note that if link(N1,N2). is included then so will link(N2,N1). | A number of link facts which say which nodes are linked. Note that if {{{link(N1,N2)}}}. is included then so will {{{link(N2,N1)}}}. |
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node(1). node(2). node(3). link(1,2). link(2,1). link(2,3). link(3,2). link(3,1). link(1,3). colour(red). colour(green). colour(blue). |
{{{ node(1). node(2). node(3). link(1,2). link(2,1). link(2,3). link(3,2). link(3,1). link(1,3). colour(red). colour(green). colour(blue). }}} |
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chosenColour(1,red). chosenColour(2,green). chosenColour(3,blue). |
{{{ chosenColour(1,red). chosenColour(2,green). chosenColour(3,blue). }}} |
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| The Two Possible Values of the Chromatic Number of a Random Graph (with A. Naor) Annals of Mathematics, 162 (3), (2005), 1333-1349. http://www.cs.ucsc.edu/~optas/papers/kcol.pdf |
The Two Possible Values of the Chromatic Number of a Random Graph (with A. Naor) <<BR>> Annals of Mathematics, 162 (3), (2005), 1333-1349. <<BR>> http://www.cs.ucsc.edu/~optas/papers/kcol.pdf <<BR>> |
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| {{{ ./graphGenerator.pl --nodes=$N --density=$D --colours=$C }}} == Example(s) == |
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| ./graphGenerator.pl --nodes=$N --density=$D --colours=$C | == Comment == This problem was part of the Second ASP Competition and was proposed by Martin Brain. == Author(s) == * Author: Yuliya Lierler * Affiliation: University of Kentucky, USA * Author: Marcello Balduccini * Affiliation: Kodak Research Labs, USA |
Graph Colouring
Contents
Problem Description
A graph is a set of nodes and a symmetric, binary link relation on nodes. Given a set of N colours, a graph is colourable if each node can be assigned a colour in such a way that any two nodes that are linked together cannot have the same colour.
Predicates
Input: node/1, link/2, colour/1
Output: chosenColour/2
Input format
A number of node facts which give the names of the nodes. Node names are consecutive, ascending integers starting from 1.
A number of colour facts which give the names of the colours. Colour names start with the sequence "red", "green", "blue".
A number of link facts which say which nodes are linked. Note that if link(N1,N2). is included then so will link(N2,N1).
For example:
node(1). node(2). node(3). link(1,2). link(2,1). link(2,3). link(3,2). link(3,1). link(1,3). colour(red). colour(green). colour(blue).
Output format
The initial facts and a set of choosenColour predicates, one for each node, specifying the node's colour. Continuing the example:
chosenColour(1,red). chosenColour(2,green). chosenColour(3,blue).
Calibration
The Two Possible Values of the Chromatic Number of a Random Graph (with A. Naor)
Annals of Mathematics, 162 (3), (2005), 1333-1349.
http://www.cs.ucsc.edu/~optas/papers/kcol.pdf
Suggests that given a random graph with n nodes and a density of (d/n) then the chromatic number is either k or k+1 where k is the smallest number such that d < 2k log(k).
Thus settings with around 125-150 nodes (135 is good), link density of 0.1 (d = 12-15) and 5 colours gives difficult programs.
./graphGenerator.pl --nodes=$N --density=$D --colours=$C
Example(s)
Comment
This problem was part of the Second ASP Competition and was proposed by Martin Brain.
Author(s)
- Author: Yuliya Lierler
- Affiliation: University of Kentucky, USA
- Author: Marcello Balduccini
- Affiliation: Kodak Research Labs, USA