Sub-Graph Isomorphism

Problem Statement

• There are two directed graphs G and G’. The graphs do not have self-edges.
• The task is to find a one-one mapping M from nodes in G to nodes in G’ such that there is an edge from v1 to v2 in G if and only if there is an edge from M(v1) to M(v2) in G'.
• We use miniSAT, a complete SAT solver for this problem.
• The code reads two graphs in the given input format and converts the mapping problem into a CNF SAT formula.
• The SAT formula will is input to miniSAT, which returns a variable assignment that satisfies the formula (or an answer "no", signifying that the problem is unsatisfiable).
• The SAT assignment is then converted into a mapping from nodes of G to nodes of G' and output in the given output format.

Input format

• Nodes are represented by positive integers starting from 1. Each line represents an edge from the first node to the second.
• Both graphs are presented in the single file, the larger first.
• The line with "0 0" is the boundary between the two.
• Sample input:

1 2
1 3
1 4
2 4
3 4
0 0
1 2
3 2

Output format

• The mapping should map each node of G into a node id for G’.
• The first numbers on each line represent a node as numbered in the smaller graph G, and the second number represents the node of the larger graph G’ to which it is mapped.
• Output for the sample input:

1 2
2 4
3 3

• If the problem is unsatisfiable output a 0.