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Searching in Constant Time and Minimum Space
, 1995
"... This report deals with techniques for minimal space representation of a subset of elements from a bounded universe so that various types of searches can be performed in constant time. In particular, we introduce a data structure to represent a subset of N elements of [0�:::�M;1] in a number of bits ..."
Abstract

Cited by 9 (7 self)
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This report deals with techniques for minimal space representation of a subset of elements from a bounded universe so that various types of searches can be performed in constant time. In particular, we introduce a data structure to represent a subset of N elements of [0�:::�M;1] in a number of bits close to the informationtheoretic minimum and use the structure to answer membership queries in constant time. Next, we describe a representation of an arbitrary subset of points on an M M grid such that closest neighbour queries (under L1 and L1) can be performed in constant time. This structure requires M 2 + o(M 2) bits. Finally, under a byte overlap model of memory we present an M + o(M) bit, constant time solution to the dynamic onedimensional closest neighbour problem (hence, also unionsplitfind and priority queue problems) on [0�:::�M; 1].
A Probabilistic Minimum Spanning Tree Algorithm
 Information Processing Letters
, 1978
"... This paper is concerned with the problem of computing spanning tree (MST) for n points in a pdimensional space where the "distance" between each pair of points i and j satisfies the relationship' dq max {Ixti  xtql} , where xki is the coordinate of object i along the ktti dimension. This relatio ..."
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Cited by 5 (0 self)
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This paper is concerned with the problem of computing spanning tree (MST) for n points in a pdimensional space where the "distance" between each pair of points i and j satisfies the relationship' dq max {Ixti  xtql} , where xki is the coordinate of object i along the ktti dimension. This relationship is clearly satisfied by all Minkowski metrics dq = [ Ixki  xnjl r] x/r, r > 1
Efficient LargeScale Sweep and Prune Methods with AABB Insertion and Removal
"... We introduce new features for the broad phase algorithm sweep and prune that increase scalability for large virtual reality environments and allow for efficient AABB insertion and removal to support dynamic object creation and destruction. We introduce a novel segmented interval list structure that ..."
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Cited by 2 (0 self)
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We introduce new features for the broad phase algorithm sweep and prune that increase scalability for large virtual reality environments and allow for efficient AABB insertion and removal to support dynamic object creation and destruction. We introduce a novel segmented interval list structure that allows AABB insertion and removal without requiring a full sort of the axes. This algorithm is wellsuited to large environments in which many objects are not moving at once. We analyze and test implementations of sweep and prune that include subdivision, batch insertion and removal, and segmented interval lists. Our tests show these techniques provide higher performance than previous sweep and prune methods, and perform better than octrees in temporally coherent environments.