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location: ProblemsDescription / MaximalClique

Maximal Clique

Contents

  1. Maximal Clique
    1. Problem Description
    2. Input format
    3. Output format
    4. Example
    5. Author(s)

Problem Description

This is the problem of finding a maximal clique C in an undirected graph G. I.e., for each other clique C' in G, the number of nodes in C should be larger than the number of nodes in C'.

Input format

As input, a directed graph is given. A solution is the largest clique in the symmetric closure of this input graph. The nodes of the input graph are given by facts of the form node(i). The edges of the graph are given by facts of the form edge(i,j).

The following is an example input: node(1). node(2). node(3). node(4). node(5). node(6). edge(1,2). edge(1,5). edge(2,3). edge(2,5). edge(3,4). edge(4,5). edge(4,6).

Output format

The output should consist of a set of facts of the form clique(i). The set of all 'i' that appear in such a fact, should form a maximal clique in the symmetric closure of the input graph.

For the above example, the only correct output is clique(1). clique(2). clique(5).

Example

Author(s)

Author: Johan Wittocx
Affiliation: Department of Computer Science, K.U.Leuven, Belgium