Canonical Graph Decomposition in Matching
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Date
2009-04-15
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Abstract
In the following thesis, we present our proposed probabilistic approach to the graph isomorphism problem. Through a "divide and conquer" approach, a graph is first decomposed into unique subgraphs, termed atoms, that are used to represent a decomposed graph as a bipartite attributed graph. We propose a modified probabilistic relaxation that simulates belief propagation and operates on the generated bipartite graph, yielding a match matrix that maps together isomorphic atoms from
different graphs. Our proposed approach enforces a two way matching constraint thatguarantees a one-to-one match between isomorphic atoms. On average, the approach converges for isomorphic graphs and diverges for non-isomorphic graphs.
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Keywords
belief propagation, probabilistic relaxation, graph decomposition, graph isomorphism
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Degree
MS
Discipline
Electrical Engineering
