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Error Correcting Codes, Perfect Hashing Circuits, and Deterministic Dynamic Dictionaries
, 1997
"... We consider dictionaries of size n over the finite universe U = and introduce a new technique for their implementation: error correcting codes. The use of such codes makes it possible to replace the use of strong forms of hashing, such as universal hashing, with much weaker forms, such as clus ..."
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Cited by 17 (2 self)
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We consider dictionaries of size n over the finite universe U = and introduce a new technique for their implementation: error correcting codes. The use of such codes makes it possible to replace the use of strong forms of hashing, such as universal hashing, with much weaker forms, such as clustering. We use
Geometric Searching in Walkthrough Animations with Weak Spanners in Real Time
 In Proceedings of the Sixth Annual European Symposium on Algorithms
, 1998
"... We study algorithmic aspects in the management of geometric scenes in interactive walkthrough animations. We consider arbitrarily large scenes consisting of unit size balls. For a smooth navigation in the scene we have to fulfill hard real time requirements. Therefore, we need algorithms whose runni ..."
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Cited by 13 (9 self)
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We study algorithmic aspects in the management of geometric scenes in interactive walkthrough animations. We consider arbitrarily large scenes consisting of unit size balls. For a smooth navigation in the scene we have to fulfill hard real time requirements. Therefore, we need algorithms whose running time is independent of the total number of objects in the scene and that use as small space as possible. In this work we focus on one of the basic operations in our walkthrough system: reporting the objects around the visitor within a certain distance. Previously a randomized data structure was presented that supports reporting the balls around the visitor in an output sensitive time and allows insertion and deletion of objects nearly as fast as searching. These results were achieved by exploiting the fact that the visitor moves "slowly" through the scene. A serious disadvantage of the aforementioned data structure is a big space overhead and the use of randomization. Our first result is ...
Faster Suffix Tree Construction with Missing Suffix Links
 In Proceedings of the Thirty Second Annual Symposium on the Theory of Computing
, 2000
"... We consider suffix tree construction for situations with missing suffix links. Two examples of such situations are suffix trees for parameterized strings and suffix trees for 2D arrays. These trees also have the property that the node degrees may be large. We add a new backpropagation component to ..."
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Cited by 10 (1 self)
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We consider suffix tree construction for situations with missing suffix links. Two examples of such situations are suffix trees for parameterized strings and suffix trees for 2D arrays. These trees also have the property that the node degrees may be large. We add a new backpropagation component to McCreight's algorithm and also give a high probability perfect hashing scheme to cope with large degrees. We show that these two features enable construction of suffix trees for general situations with missing suffix links in O(n) time, with high probability. This gives the first randomized linear time algorithm for constructing suffix trees for parameterized strings.
Dynamic data structures for realtime management of large geometric scenes (Extended Abstract)
, 1997
"... ) M: Fischer, F: Meyer auf der Heide, and W:B. Strothmann Heinz Nixdorf Institute and Department of Computer Science University of Paderborn, D33095 Paderborn, Germany fmafi,fmadh,willyg@unipaderborn.de Abstract We present a data structure problem which describes the requirements of a simple va ..."
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Cited by 9 (1 self)
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) M: Fischer, F: Meyer auf der Heide, and W:B. Strothmann Heinz Nixdorf Institute and Department of Computer Science University of Paderborn, D33095 Paderborn, Germany fmafi,fmadh,willyg@unipaderborn.de Abstract We present a data structure problem which describes the requirements of a simple variant of fully dynamic walkthrough animation: We assume the scene to consist of unit size balls in IR 2 or higher dimensions. The scene may be arbitrarily large and has to be stored in secondary memory (discs) with relatively slow access. We allow a visitor to walk in the scene, and a modeler to update the scene by insertions and deletions of balls. We focus on the realtime requirement of animation systems: For some t (specified by the computation power of (the rendering hardware of) the graphic workstation) the data structure has to guarantee that the balls within distance t of the current visitor's position are presented to the rendering hardware, 20 times per second. Insertions and del...
Linear Hash Functions
, 1999
"... Consider the set # of all linear (or affine) transformations between two vector spaces over a finite field F. We study how good # is as a class of hash functions, namely we consider hashing a set S of size n into a range having the same cardinality n by a randomly chosen function from # and look at ..."
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Cited by 9 (0 self)
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Consider the set # of all linear (or affine) transformations between two vector spaces over a finite field F. We study how good # is as a class of hash functions, namely we consider hashing a set S of size n into a range having the same cardinality n by a randomly chosen function from # and look at the expected size of the largest hash bucket. # is a universal class of hash functions for any finite field, but with respect to our measure different fields behave differently. If the
Static and Dynamic Data Management in Networks
 PROC. OF EUROPAR'97
, 1997
"... We survey strategies for distributing shared objects in large parallel and distributed systems. Examples of such objects are global variables in a parallel program, pages or cache lines in a virtual shared memory system, shared files in a distributed file system, and videos and pictures in a d ..."
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Cited by 1 (1 self)
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We survey strategies for distributing shared objects in large parallel and distributed systems. Examples of such objects are global variables in a parallel program, pages or cache lines in a virtual shared memory system, shared files in a distributed file system, and videos and pictures in a distributed multimedia server. We focus on strategies for distributing, accessing, and (consistently) updating such objects. The strategies are provably efficient with respect to various cost measures. We describe and analyse static, hashing based schemes that minimize the contention at the memory modules in worst case scenarios. Especially, the benefit of redundant placement schemes is discussed. We further take network congestion and bandwidth into account. Here we present schemes that are provably efficient w.r.t. information about access frequencies. Further, dynamic schemes are presented which have good competitive ratio, i.e., are efficient compared to an optimal dynamic distri...
A TopDown Design of a Parallel Dictionary using Skip Lists
, 1994
"... We present a top down design of a parallel PRAM dictionary using skip lists. More precisely, we give algorithms to search, insert and delete k ordered elements in a skip list of n elements in parallel. The algorithms are simple and easy to implement on real machines. All of them are iterative. Th ..."
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Cited by 1 (0 self)
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We present a top down design of a parallel PRAM dictionary using skip lists. More precisely, we give algorithms to search, insert and delete k ordered elements in a skip list of n elements in parallel. The algorithms are simple and easy to implement on real machines. All of them are iterative. They can be implemented in the EREW PRAM model using O(k) processors in expected time O(log n+ log k). The probability that there is a significant deviation from the expected time decreases as O(n \Gamma2 ) in the search and as O(n \Gamma2 + k \Gamma2 ) in the insertion and deletion. 1 Introduction Parallel dictionaries are important data structures widely studied. In a systolic framework, priority queues and search trees were designed by C.E. Leiserson in [13]. Later, M.J. Atallah and S.R. Kosaraju [1] developped a generalized dictionary where a sequence of operations can be pipelined at constant rate. In the PRAM context, W. Paul, U. Vishkin and H. Wagener developed and analyzed ...