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Abstract

Discovery of knowledge from geometric graph databases is of particular importance in chemistry and
biology, because chemical compounds and proteins are represented as graphs with 3D geometric coordinates. In
such applications, scientists are not interested in the statistics of the whole database. Instead they need information
about a novel drug candidate or protein at hand, represented as a query graph. We propose a polynomial-delay
algorithm for geometric frequent subgraph retrieval. It enumerates all subgraphs of a single given query graph
which are frequent geometric epsilon-subgraphs under the entire class of rigid geometric transformations in a database.
By using geometric epsilon-subgraphs, we achieve tolerance against variations in geometry. We compare the proposed
algorithm to gSpan on chemical compound data, and we show that for a given minimum support the total number
of frequent patterns is substantially limited by requiring geometric matching. Although the computation time per
pattern is larger than for non-geometric graph mining, the total time is within a reasonable level even for small
minimum support.