R. Tamassia and J. S. Vitter. Optimal cooperative search in fractional cascaded data structures. In Proc. 2nd ACM Symosium on Parallel Algorithms and Architectures, pages 307--316, 1990.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....structures suitable for these intersection queries should be accomplished in O(log n) time using O(n) processors. There are a couple data structures which meet these requirements: the three dimensional extension of the bridged separator tree [LP77, EGS86] introduced by Tamassia and Vitter [TV91, TV90] and the hierarchical representation [DK90] as optimized by Cole and Zajicek [CZ90] The technique used to accomplish the merging process in [AP92] determines, for each edge e 2 CH(P ) CH(Q) whether or not e is an internal, external, or seam edge of CH(CH(P ) CH(Q) these classifications can ....

R. Tamassia and J. S. Vitter. Optimal cooperative search in fractional cascaded data structures. In Proc. 2nd ACM Sympos. Parallel Algorithms Architect., pages 307--316, 1990. To appear in Algorithmica.

....and by DFG Sonderforschungsbereich 376 Massive Parallelitat: Algorithmen, Entwurfsmethoden, Anwendungen . the execution of a single search process. In [20] upper and lower bounds for this problem on the PRAM model can be found. Further work in this direction has been done by Tamassia et al. in [32]. Second, parallelism can be employed in order to execute many search processes at the same time. Such search problems are called multisearch problems. In the technical part of this paper we will treat the following multisearch problem. Given a universe U and a partition of U in segments S = fs 1 ....

R. Tamassia and J.S. Vitter, Optimal cooperative search in fractional cascaded data structures, in: Proc. ACM Symp. Computational Geometry (1990) 307--315.

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R. Tamassia and J. S. Vitter. Optimal cooperative search in fractional cascaded data structures. In Proc. 2nd ACM Symosium on Parallel Algorithms and Architectures, pages 307--316, 1990.

.... et al. 11] bateh fi ltermg: a general method for performing K simultaneous external memory searches in data structures that can be modeled as planar layered dags and in certain fractional cascaded data struc tures; oralroe filtering: A technique based on the work of Tamassia and Vitter [35] that allows I O optimal on line queries in fractional cascaded data structures based on balanced binary trees. cx tcral marriagc before coqucst: an externalmemory analog to the well known technique of Kirkpatrick and Seidel [22] for performing output sensitive hull constructions. We apply ....

....query. More de sirable is a method for preprocessing the data structure so that individual queries can be answered with an optimal O(log B ) I Os. In this section we briefly describe how this can be done with a modified version of a parallel fractional cascading technique of Tamas sia and Vitter [35]. The method of Tamassia and Vitter [35] works with data structures whose underlying graphs are balanced binary trees. Preprocessing takes O(iv) work. Once this is done, individual queries can be answered on a p processor CREW PRAM in O(logp iv) time. The access patterns of the processors during ....

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R. Tamassia and J. S. Vitter, "Optimal Coopera- tive Search in Fractional Cascaded Data Structures," Proc. 2nd AUM SPAA (1990), 307 316.

....each query point, we are to return the identifier of the region in which it lies. In main memory, this problem can be solved in optimal time O( N I )log N) using fractional cascading [7,8] O(N log N) is spent on preprocessing and O(I log N) is needed to perform the queries. Tamassia and Vitter [35] have demonstrated a technique by which the fractional cascading used to solve this problem can be implemented in parallel. Their technique can solve our problem in O( N p K) logp N) time on a PRAM with 9 processors. We can use a method based on their construction, but using in place of 9 to ....

R. Tamassia & J. S. Vitter, "Optimal Cooperative Search in Fractional Cascaded Data Structures," Proc. 2nd ACM SPAA (1990).

....based on implicit 3D Voronoi diagrams is then given in Section 4.3. 4. 1 Test Primitives and Methods for Spatial Point Location There are only two known efficient spatial point location methods for cell complexes that are applicable to 3D Voronoi diagrams: the separating surfaces method [13, 55], which extends the chain method [43] and the persistent planar location method [51] which extends the persistent search tree method [52] Let N be the number of facets of a cell complex C. The query time is O(log 2 N) for both methods. The space used is O(N) for the separating surfaces method ....

....f contains the xy projection of q. Test primitives above below(q; v) and left right(q; v) are used only in degenerate cases (e.g. in the presence of facets parallel to the z axis and in cases where e xy is horizontal) 18 Now, we analyze the separating surfaces method for spatial point location [13, 55] in acyclic cell complexes. Separating surfaces are the 3D analogue of separators of monotone maps. Their existence is guaranteed by the acyclicity of the cell complex. Thus, a point location query consists of traversing a root to leaf path in the separating surface tree, where at each node we ....

R. Tamassia and J. S. Vitter. Optimal cooperative search in fractional cascaded data structures. Algorithmica, 15(2), 1996. 33

.... et al. 11] ffl batch filtering : a general method for performing K simultaneous external memory searches in data structures that can be modeled as planar layered dags and in certain fractional cascaded data structures; ffl on line filtering : A technique based on the work of Tamassia and Vitter [35] that allows I O optimal on line queries in fractional cascaded data structures based on balanced binary trees. ffl external marriage before conquest : an externalmemory analog to the well known technique of Kirkpatrick and Seidel [22] for performing outputsensitive hull constructions. We apply ....

....per query. More desirable is a method for preprocessing the data structure so that individual queries can be answered with an optimal O(log B ) I Os. In this section we briefly describe how this can be done with a modified version of a parallel fractional cascading technique of Tamassia and Vitter [35]. The method of Tamassia and Vitter [35] works with data structures whose underlying graphs are balanced binary trees. Preprocessing takes O(N ) work. Once this is done, individual queries can be answered on a p processor CREW PRAM in O(log p N ) time. The access patterns of the processors during ....

[Article contains additional citation context not shown here]

R. Tamassia and J. S. Vitter, "Optimal Cooperative Search in Fractional Cascaded Data Structures," Proc. 2nd ACM SPAA(1990), 307--316.

....As for the two dimensional case, such query is efficiently answered by performing point location in the 3D Voronoi diagram of S. There are only two known efficient spatial point location methods for cell complexes that are applicable to 3D Voronoi diagrams: the separating surfaces method [5, 26], which extends the chain method [19] and the persistent planar location method [23] which extends the persistent search tree method [24] Let N be the number of facets of a cell complex C. The query time is O(log 2 N) for both methods. The space used is O(N) for the separating surfaces ....

R. Tamassia and J. S. Vitter. Optimal cooperative search in fractional cascaded data structures. Algorithmica, 15(2), 1996.

....spanning tree verification method. Planar st graphs were first introduced by Lempel, Even, and Cederbaum [16] and have a variety of applications in Computational Geometry, motion planning, and VLSI layout. We obtain the given upper bounds by modifying the PRAM algorithms of Tamassia and Vitter [21], and applying the list ranking and the PRAM simulation techniques. 7 Depth First Search and Closed Semi Ring Computation Many algorithms for problems on directed graphs are easily solved in main memory by depth first search (DFS) We analyze the performance of sequential DFS, modifying the ....

R. Tamassia and J. S. Vitter. Optimal cooperative search in fractional cascaded data structures. In Proc. 2nd ACM Symosium on Parallel Algorithms and Architectures, pages 307--316, 1990.

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