Time and Space Efficient Discovery of Maximal Geometric Graphs View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2007

AUTHORS

Hiroki Arimura , Takeaki Uno , Shinichi Shimozono

ABSTRACT

A geometric graph is a labeled graph whose vertices are points in the 2D plane with an isomorphism invariant under geometric transformations such as translation, rotation, and scaling. While Kuramochi and Karypis (ICDM2002) extensively studied the frequent pattern mining problem for geometric subgraphs, the maximal graph mining has not been considered so far. In this paper, we study the maximal (or closed) graph mining problem for the general class of geometric graphs in the 2D plane by extending the framework of Kuramochi and Karypis. Combining techniques of canonical encoding and a depth-first search tree for the class of maximal patterns, we present a polynomial delay and polynomial space algorithm, MaxGeo, that enumerates all maximal subgraphs in a given input geometric graph without duplicates. This is the first result establishing the output-sensitive complexity of closed graph mining for geometric graphs. We also show that the frequent graph mining problem is also solvable in polynomial delay and polynomial time. More... »

PAGES

42-55

Book

TITLE

Discovery Science

ISBN

978-3-540-75487-9

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-75488-6_6

DOI

http://dx.doi.org/10.1007/978-3-540-75488-6_6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1001317711


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