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Title: Canonical Graph Decomposition in Matching
Authors: Yaghi, Haytham H
Advisors: Dr. Huaiyu Dai, Committee Member
Dr. Carla Savage, Committee Member
Dr. Hamid Krim, Committee Chair
Keywords: belief propagation
probabilistic relaxation
graph decomposition
graph isomorphism
Issue Date: 15-Apr-2009
Degree: MS
Discipline: Electrical Engineering
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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