Coloring Problems
DIMACS Graph Format

Last revision: May 08, 1993
Abbreviated: Bart Massey March 02, 2001

Introduction

One purpose of the DIMACS Challenge is to ease the effort required to test and compare algorithms and heuristics by providing a common testbed of instances and analysis tools. To facilitate this effort, a standard format must be chosen for the problems addressed. This document outlines a format for graphs that is suitable for those looking at graph coloring. This format extends to a flexible format suitable for many types of graph and network problems. This format was also the format chosen for the First Computational Challenge on network flows and matchings.

Input Files

An input file contains all the information about a graph needed to define a coloring problem.

In this format, nodes are numbered from 1 up to n edges in the graph.

Files are assumed to be well-formed and internally consistent: node identifier values are valid, nodes are defined uniquely, exactly m edges are defined, and so forth.

Comments. Comment lines give human-readable information about the file and are ignored by programs. Comment lines can appear anywhere in the file. Each comment line begins with a lower-case character c.
```
 
c This is an example of a comment line.
```
Problem line. There is one problem line per input file. The problem line must appear before any node or arc descriptor lines. For network instances, the problem line has the following format.
```
p FORMAT NODES EDGES
```
The lower-case character p signifies that this is the problem line. The FORMAT field is for consistency with the previous Challenge, and should contain the word ``edge''. The NODES field contains an integer value specifying n, the number of nodes in the graph. The EDGES field contains an integer value specifying m, the number of edges in the graph.
Edge Descriptors. There is one edge descriptor line for each edge the graph, each with the following format. Each edge (v,w) appears exactly once in the input file and is not repeated as (w,v).
```
e W V
```
The lower-case character e signifies that this is an edge descriptor line. For an edge (w,v) the fields W and V specify its endpoints.

Output Files

Every algorithm or heuristic should create an output file. This output file should consist of one or more of the following lines, depending on the type of algorithm and problem being solved.

Solution Line
```
s TYPE SOLUTION
```
The lower-case character s signifies that this is a solution line. The TYPE field denotes the type of solution contained in the file. This should be the string ``col'' denoting a graph coloring.
The SOLUTION field contains an integer corresponding to the solution value. This is the number of colors used for graph coloring.
Bound Line
```
b BOUND
```
The lower-case character b signifies that this is a bound on the the solution. The BOUND field contains an integer value that gives a bound on the solution value. This bound is a lower bound on the number of colors needed for coloring the graph.
Label Line
```
l V N
```
The lower-case character l signifies that this is a label line, used for graph coloring. The V field gives the node number for the node in the clique while the N field gives the corresponding label. There will be one label line for each node in the graph.

DIMACS Project: Rutgers University
Bart Massey

Coloring Problems DIMACS Graph Format

Introduction

Input Files

Output Files

Coloring Problems
DIMACS Graph Format