Indexing a dictionary for subset matching queries
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
Indexing a dictionary for subset matching queries
Algorithms and Applications
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Using the notions of Q-heaps and fusion trees developed by Fredman and Willard, we develop general transformation techniques to reduce a number of computational geometry problems to their special versions in partially ranked spaces. In particular, we develop a fast fractional cascading technique, which uses linear space and enables sublogarithmic iterative search on catalog trees in the case when the degree of each node is bounded by $O(\log^{\epsilon}n)$ for some constant $\epsilon 0$, where $n$ is the total size of all the lists stored in the tree. We apply the fast fractional cascading technique in combination with the other techniques to derive the first linear-space sublogarithmic time algorithms for two fundamental geometric retrieval problems: orthogonal segment intersection and rectangular point enclosure.