Safe Haskell	Safe-Infered

Ganeti.HTools.Graph

Contents

Type declarations
Vertices characteristics
Coloring

Description

Algorithms on Graphs.

This module contains a few graph algorithms and the transoformations needed for them to be used on nodes.

For more information about Graph Coloring see: http://en.wikipedia.org/wiki/Graph_coloring http://en.wikipedia.org/wiki/Greedy_coloring

LF-coloring is described in: Welsh, D. J. A.; Powell, M. B. (1967), An upper bound for the chromatic number of a graph and its application to timetabling problems, The Computer Journal 10 (1): 85-86, doi:10.1093comjnl10.1.85 http://comjnl.oxfordjournals.org/content/10/1/85

DSatur is described in: Brelaz, D. (1979), New methods to color the vertices of a graph, Communications of the ACM 22 (4): 251-256, doi:10.1145/359094.359101 http://dx.doi.org/10.1145%2F359094.359101

Also interesting: Klotz, W. (2002). Graph coloring algorithms. Mathematics Report, Technical University Clausthal, 1-9. <http:www.math.tu-clausthal.deArbeitsgruppenDiskrete-Optimierung publications2002/gca.pdf>

Synopsis

Type declarations

type Color = IntSource

Node colors.

type Satur = IntSource

type VertColorMap = IntMap Color Source

Vertex to Color association.

type ColorVertMap = IntMap [Int]Source

Color to Vertex association.

Vertices characteristics

verticesDegree :: Graph -> [(Vertex, Int)]Source

verticesByDegreeDesc :: Graph -> [Vertex]Source

vertices of a graph, sorted by ascending degree.

verticesByDegreeAsc :: Graph -> [Vertex]Source

vertices of a graph, sorted by descending degree.

neighbors :: Graph -> Vertex -> [Vertex]Source

Get the neighbors of a vertex.

hasLoop :: Graph -> BoolSource

Check whether a graph has no loops. (vertices connected to themselves)

isUndirected :: Graph -> BoolSource

Check whether a graph is undirected

Coloring

emptyVertColorMap :: VertColorMap Source

Empty color map.

isColorable :: Graph -> BoolSource

Check whether a graph is colorable.

verticesColors :: VertColorMap -> [Vertex] -> [Color]Source

verticesColorSet :: VertColorMap -> [Vertex] -> IntSetSource

neighColors :: Graph -> VertColorMap -> Vertex -> [Color]Source

colorNode :: Graph -> VertColorMap -> Vertex -> Color Source

colorNodeInMap :: Graph -> Vertex -> VertColorMap -> VertColorMap Source

colorInOrder :: Graph -> [Vertex] -> VertColorMap Source

Color greedily all nodes in the given order.

colorLF :: Graph -> VertColorMap Source

Color greedily all nodes, larger first.

vertexSaturation :: Graph -> VertColorMap -> Vertex -> (Vertex, (Satur, Int))Source

vertexColorDegree :: Graph -> VertColorMap -> Vertex -> (Vertex, (Int, Int))Source

colorDynamicOrder :: Ord a => (Graph -> VertColorMap -> Vertex -> (Vertex, a)) -> Graph -> VertColorMap -> [Vertex] -> VertColorMap Source

colorDcolor :: Graph -> VertColorMap Source

Color greedily all nodes, highest number of colored neighbors, then highest degree. This is slower than colorLF as we must dynamically recalculate which node to color next among all remaining ones but produces better results.

colorDsatur :: Graph -> VertColorMap Source

Color greedily all nodes, highest saturation, then highest degree. This is slower than colorLF as we must dynamically recalculate which node to color next among all remaining ones but produces better results.

colorVertMap :: VertColorMap -> ColorVertMap Source

ColorVertMap from VertColorMap.