Learning a Go Heuristic with TILDE
CG '00 Revised Papers from the Second International Conference on Computers and Games
The subgraph homeomorphism problem
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Exact Formulae for the Lovász Theta Function of Sparse Circulant Graphs
SIAM Journal on Discrete Mathematics
Finding Frequent Patterns in a Large Sparse Graph*
Data Mining and Knowledge Discovery
Support measures for graph data*
Data Mining and Knowledge Discovery
Fast best-effort pattern matching in large attributed graphs
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Approximately Counting Embeddings into Random Graphs
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Efficient Algorithms for Mining Significant Substructures in Graphs with Quality Guarantees
ICDM '07 Proceedings of the 2007 Seventh IEEE International Conference on Data Mining
The levelwise version space algorithm and its application to molecular fragment finding
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 2
An efficiently computable support measure for frequent subgraph pattern mining
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Nearly exact mining of frequent trees in large networks
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
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In graph mining, a frequency measure for graphs is anti-monotonic if the frequency of a pattern never exceeds the frequency of a subpattern. The efficiency and correctness of most graph pattern miners relies critically on this property. We study the case where frequent subgraphs have to be found in one graph. Vanetik et al. (Data Min Knowl Disc 13(2):243---260, 2006) already gave sufficient and necessary conditions for anti-monotonicity of graph measures depending only on the edge-overlaps between the instances of the pattern in a labeled graph. We extend these results to homomorphisms, isomorphisms and homeomorphisms on both labeled and unlabeled, directed and undirected graphs, for vertex- and edge-overlap. We show a set of reductions between the different morphisms that preserve overlap. As a secondary contribution, we prove that the popular maximum independent set measure assigns the minimal possible normalized frequency and we introduce a new measure based on the minimum clique partition that assigns the maximum possible normalized frequency. In that way, we obtain that all normalized anti-monotonic overlap graph measures are bounded from above and below. We also introduce a new measure sandwiched between the former two based on the polynomial time computable Lovász 驴-function.