revolutioner.blogg.se - Algoritma pemrograman parallel graph coloring

Many subjects would have common students (of same batch, some backlog students, etc). We have list different subjects and students enrolled in every subject. Making Schedule or Time Table: Suppose we want to make am exam schedule for a university.

O(V^2 + E) in worst case.(where V is the vertex and E is the edge).

Initialize remaining V-1 vertices as unassignedįor (i = adj.begin() i != adj.end() ++i) Assign the first color to first vertex Assigns colors (starting from 0) to all vertices and prints Prints greedy coloring of the verticesĪdj.push_back(v) // Note: the graph is undirected List *adj // A dynamic array of adjacency lists A class that represents an undirected graph If all previously used colors appear on vertices adjacent to v, assign a new color to it.

That has not been used on any previously colored vertices PseudocodeĬolour it with the lowest numbered colour The nature of the coloring problem depends on the number of colors but not on what they are. In general, one can use any finite set as the "color set". In mathematical and computer representations, it is typical to use the first few positive or non negative integers as the "colors". By planar duality it became coloring the vertices, and in this form it generalizes to all graphs. This was generalized to coloring the faces of a graph embedded in the plane. The convention of using colors originates from coloring the countries of a map, where each face is literally colored. That is partly for perspective, and partly because some problems are best studied in non-vertex form, as for instance is edge coloring. However, non-vertex coloring problems are often stated and studied as is. For example, an edge coloring of a graph is just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. Vertex coloring is the starting point of the subject, and other coloring problems can be transformed into a vertex version. For example, the following can be colored minimum 3 colors. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges share the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.Ĭhromatic Number: The smallest number of colors needed to color a graph G is called its chromatic number. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color this is called a vertex coloring. In graph theory, graph coloring is a special case of graph labeling it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. Reading time: 15 minutes | Coding time: 9 minutes