Lars Arge and Peter Bro Miltersen. On showing lower bounds for external-memory computational geometry problems. In James Abello and Jeffrey Scott Vitter, editors, External Memory Algorithms and Visualization, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society Press, Providence, RI, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for several graph problems including list ranking, time forward processing, PRAM simulation, connected and biconnected components, expression tree evaluation, lowest common ancestors, topological sorting, etc. are presented in [11] For lower bounds for computational geometry problems in EM, see [3]. Also see [2] for bu er trees, priority queues, and their applications. For the geometric problems discussed in this paper, the best resources will be [6] for WSPD and its applications and [16] for results on proximity problems. We omit the discussion on the state of the art, importance and ....

....are no previous external memory algorithms known. In the companion paper [15] we present EM algorithms for computing spanners of visibility graphs of polygonal obstacles. For Problems 3 and 4, previous results known were those of [13] which only work for the planar case and for K = 1. Also, in [3] it is shown that computing the closest pair of a point set requires sort(N) I Os, which implies the same lower bound for Problems 3 and 4. We extend the time forward processing technique of [1, 11] to certain types of incremental directed acyclic graphs that are generated on the y (Section 2) ....

L. Arge, P. B. Miltersen. On showing lower bounds for external-memory computational geometry problems. In J. Abello, J. S. Vitter (eds.), External Memory Algorithms and Visualization, AMS 1999.

.... nding all nearest neighbors for a set of N points in the plane, dominance problems, and other geometric problems in the plane are discussed in [2, 3, 7, 13, 20] General line segment intersection problems have been studied in [6] For lower bounds on computational geometry problems in EM see [5]. See [4] for bu er trees, priority queues, and their applications. Overview. In Sect. 2, we discuss our solution to the batched range counting problem. In Sect. 3, we use the solution for a special case of this problem to compute K th order graphs for point sets in d dimensions. We also ....

L. Arge, P. B. Miltersen. On showing lower bounds for external-memory computational geometry problems. In J. Abello and J. S. Vitter (eds.), External Memory Algorithms and Visualization. AMS, 1999.

....etc. Managing and making the best use of the memory structure is important when dealing with large data structures that do not fit in the main memory of a single computer. New algorithmic techniques and analysis tools have been developed to address this problem, e.g. for geometric algorithms [1,11,18] and scientific visualization [2, 4] In most terrain visualization systems [5,6,8,12,15 17,19,21] the external memory component is essential for handling real terrain and GIS databases. Hoppe [15] addresses the problem of constructing a progressive mesh of a large terrain using a bottom up ....

L. Arge and P. B. Miltersen. On Showing Lower Bounds for External-Memory Computational Geometry Problems. External Memory Algorithms and Visualization. American Mathematical Society Press, 1999.

....uses the Topology B tree data structure. For the remaining problems, our results are the only efficient external memory algorithms known in higher dimensions. For the K nearest neighbor and K closest pair problems, optimal algorithms were presented in [12] for the case where d = 2 and K = 1. In [2] it is shown that computing the closest pair of a point set requires W(sort(N) I Os, which implies the same lower bound for the general problems we consider in this paper. I O efficient construction of fault tolerant spanners and bounded degree spanners for point sets in the plane and of spanners ....

Lars Arge and P. B. Miltersen. On showing lower bounds for external-memory computational geometry problems. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization. AMS, 1999.

....range searching. 6 7 Miscellaneous There is some work on contour line extraction [AAM 98] and isosurface extraction [CS97] motivated by GIS applications. Vitter and Barve considered external memory algorithms with dynamically changing memory allocations [BV98] Arge and Miltersen [AM98] give a theoretical summary of lower bounds in external memory computational geometry. ....

L. Arge and P. B. Miltersen. On showing lower bounds for externalmemory computational geometry problems. In DIMACS Workshop on External Memory Algorithms and Visualization. The DIMACS series, 1998.

....E V Sort V ) 6 Open Problems Our lower bound proof assumes input in the edge list format, and also assumes a comparison based model. It would be nice to see if the bound holds when these restrictions are removed. One approach could be to use the External Memory Turing Machine model defined in [9]. There is still a small gap between the upper and lower bounds for connectivity. We consider finding an optimal connectivity algorithm a challenging open problem. It would also be interesting to see if the lower bound techniques developed here can be used in proving lower bounds for other data ....

Lars Arge and Peter Bro Miltersen, On Showing Lower Bounds for External-memory Computational Geometry Problems, in External Memory Algorithms and Visualization, James Abello and Jeffery Vitter(Eds.), American Mathematical Society, 1998.

....bound involves a potential argument based upon a togetherness relation [10] A related argument demonstrates the optimality of the algorithm in [99] for sorting N items with K distinct key values. EXTERNAL MEMORY ALGORITHMS AND DATA STRUCTURES 17 Chiang et al. 42] Arge [14] Arge and Miltersen [19], and Kameshwar and Ranade [83] give models and lower bound reductions for several computational geometry and graph problems. Problems like list ranking and expression tree evaluation have the same nonlinear I O lower bound as permuting. Other problems like connected components, biconnected ....

....that the sorting lower bound (3.1) remains valid even if the indivisibility assumption is lifted. However, for an artificial problem related to transposition, Adler [2] showed that removing the indivisibility assumption can lead to faster algorithms. A similar result is shown by Arge and Miltersen [19] for the decision problem of determining if N data item values are distinct. Whether or not the conjecture is true is a challenging theoretical problem. 4. Matrix and Grid Computations Dense matrices are generally represented in memory in row major or columnmajor order. Matrix transposition, ....

L. Arge and P. Miltersen. On showing lower bounds for external-memory computational geometry problems. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization. American Mathematical Society Press, Providence, RI, this volume.

.... Sweeping Based Spatial Join Lars Arge Octavian Procopiuc Sridhar Ramaswamy Torsten Suel Jeffrey Scott Vitter Abstract In this paper, we consider the filter step of the spatial join problem, for the case where neither of the inputs are indexed. We present a new algorithm, Scalable Sweeping Based Spatial Join (SSSJ) that achieves both efficiency on ....

.... Sweeping Based Spatial Join Lars Arge Octavian Procopiuc Sridhar Ramaswamy Torsten Suel Jeffrey Scott Vitter Abstract In this paper, we consider the filter step of the spatial join problem, for the case where neither of the inputs are indexed. We present a new algorithm, Scalable Sweeping Based Spatial Join (SSSJ) that achieves both efficiency on real life ....

[Article contains additional citation context not shown here]

L. Arge and P. B. Miltersen. On showing lower bounds for external-memory computational geometry. Manuscript, 1998.

No context found.

L. Arge and P. B. Miltersen. On showing lower bounds for external-memory computational geometry. Manuscript, 1998.

....they showed that the number of I Os needed to rearrange N elements according to a given permutation is Omega Gamma 28 fN; n log m ng) 1 We define log m n = maxf1; log n= log mg. For extremely small values of M and B the comparison model is assumed in the sorting lower bound see also [16, 17] Taking a closer look at the above bounds for typical values of B and M reveals that because of the large base of the logarithm, log m n is less than 3 or 4 for all realistic values of N and m. Thus in practice the important term is the B term in the denominator of the O(n log m n) O( N B ....

....blocks. In internal memory one can prove what might be called sorting lower bounds O(N log 2 N T ) on a large number of important computational geometry problems. The corresponding bound O(n log m n t) can be obtained for the external versions of the problems either by redoing standard proofs [17, 53], or by using a conversion result from [16] Computational geometry problems in external memory were first considered by Goodrich et al. 53] who developed a number of techniques for designing I O efficient algorithms for such problems. They used their techniques to develop I O algorithms for a ....

L. Arge and P. B. Miltersen. On showing lower bounds for external-memory computational geometry. In preparation.

No context found.

Lars Arge and Peter Bro Miltersen. On showing lower bounds for external-memory computational geometry problems. In James Abello and Jeffrey Scott Vitter, editors, External Memory Algorithms and Visualization, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society Press, Providence, RI, 1999.

No context found.

L. Arge and P. B. Miltersen. On showing lower bounds for external-memory computational geometry problems. In J. Abello and J. S. Vitter, editors, External Memory Algorithms and Visualization, pages 139--160. American Mathematical Society Press, Providence, RI, 1999.

No context found.

Lars Arge and Peter Bro Miltersen, "On showing lower bounds for external-memory computational geometry problems," in External Memory Algorithms and Visualization, James Abello and Jeffrey Scott Vitter, Eds., DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society Press, Providence, Rhode Island, 1999.

No context found.

L. Arge and P. B. Miltersen. On showing lower bounds for external-memory computational geometry. In J. Abello and J. S. Vitter, editors, External memory algorithms and visualization. American Mathematical Society, DIMACS series, 1999.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC