Similarity of Weighted Directed Acyclic Graphs

This thesis proposes a weighted DAG (wDAG) similarity algorithm for match-making in e-Business environments. We focus on the metadata representation of buyer and seller agents, as well as a similarity and associated simplicity measure over this information. In order to make the interaction between agents more meaningful and fine-grained, we choose node-labeled, arc-labeled and arc-weighted directed acyclic graphs to represent their products/services. This wDAG representation is more expressive and efficient than the earlier weighted tree representation. The structure-sharing characteristics of wDAGs lead us to use weighted Object-Oriented RuleML to represent them. An association list structure enables the algorithm to reuse the similarity values of shared sub-wDAGs for speed-up. The algorithm finds the similarity between seller and buyer wDAGs efficiently, computing similarity values consistent with our intuitive expectations and properly generalizing an earlier weighted tree algorithm. The applicability and efficiency of that weighted tree similarity algorithm have thus been considerably improved.