Dynamic Tree Cross Products

15 years 10 months ago

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Abstract. Range searching over tree cross products – a variant of classic range searching – recently has been introduced by Buchsbaum et al. (Proc. 8th ESA, vol. 1879 of LNCS, pp. 120–131, 2000). A tree cross product consist of hyperedges connecting the nodes of trees T1, . . . , Td. In this context, range searching means to determine all hyperedges connecting a given set of tree nodes. Buchsbaum et al. describe a data structure which supports, besides queries, adding and removing of edges; the tree nodes remain ﬁxed. In this paper we present a new data structure, which additionally provides insertion and deletion of leaves of T1, . . . , Td; it combines the former approach with a novel technique of using search trees superimposed over ordered list maintenance structures. The extra cost for this dynamization is roughly a factor of O(log n/log log n). The trees being dynamic is especially important for maintaining hierarchical graph views, a problem that can be modeled as tree c...

Marcus Raitner

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