welcome: please sign in
location: Diff for "FinalProblemDescriptions/GraphColouring"
Differences between revisions 4 and 5
⇤ ← Revision 4 as of 2011-01-20 14:37:06 →
Size: 2161
Editor: CarmenSantoro
Comment:
← Revision 5 as of 2011-02-02 19:11:33 → ⇥
Size: 1491
Editor: MarioAlviano
Comment:
Deletions are marked like this. Additions are marked like this.
Line 23: Line 23:
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).
}}}
Line 40: Line 25:
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 ==		 A set of choosenColour predicates, one for each node, specifying the node's colour.
Line 48: Line 27:
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>>		 == Example(s) ==
Line 52: Line 29:
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). Input: {{{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).}}}
Line 54: Line 31:
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) ==		 Output: {{{chosenColour(1,red). chosenColour(2,green). chosenColour(3,blue).}}}

Graph Colouring

Contents

  1. Graph Colouring
    1. Problem Description
    2. Predicates
    3. Input format
    4. Output format
    5. Example(s)
    6. Comment
    7. Author(s)

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).

Output format

A set of choosenColour predicates, one for each node, specifying the node's colour.

Example(s)

Input: 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: chosenColour(1,red). chosenColour(2,green). chosenColour(3,blue).

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

ASP Competition 2011: FinalProblemDescriptions/GraphColouring (last edited 2011-02-02 19:11:33 by MarioAlviano)