Results 11  20
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147
Dynamic Trees and Dynamic Point Location
 In Proc. 23rd Annu. ACM Sympos. Theory Comput
, 1991
"... This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using ..."
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Cited by 44 (9 self)
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This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using a centroid decomposition of the dual tree to drive searches in the primal tree. These trees are maintained via the linkcut trees structure of Sleator and Tarjan, leading to a scheme that achieves vertex insertion/deletion in O(log n) time, insertion/deletion of kedge monotone chains in O(log n + k) time, and answers queries in O(log 2 n) time, with O(n) space, where n is the current size of subdivision S. The techniques described also allow for the dual operations expand and contract to be implemented in O(log n) time, leading to an improved method for spatial pointlocation in a 3dimensional convex subdivision. In addition, the interlacedtree approach is applied to online pointlo...
Splitters and nearoptimal derandomization
"... We present a fairly general method for finding deterministic constructions obeying what we call krestrictions; this yields structures of size not much larger than the probabilistic bound. The structures constructed by our method include (n; k)universal sets (a collection of binary vectors of lengt ..."
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Cited by 35 (1 self)
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We present a fairly general method for finding deterministic constructions obeying what we call krestrictions; this yields structures of size not much larger than the probabilistic bound. The structures constructed by our method include (n; k)universal sets (a collection of binary vectors of length n such that for any subset of size k of the indices, all 2k configurations appear) and families of perfect hash functions. The nearoptimal constructions of these objects imply the very efficient derandomization of algorithms in learning, of fixedsubgraph finding algorithms, and of near optimal threshold formulae. In addition, they derandomize the reduction showing the hardness of approximation of set cover. They also yield deterministic constructions for a localcoloring protocol, and for exhaustive testing of circuits.
Computing the Visibility Graph via Pseudotriangulations
 In Proc. 11th Annu. ACM Sympos. Comput. Geom
, 1995
"... We show that the k free bitangents of a collection of n pairwise disjoint convex plane sets can be computed in time O(k+n log n) and O(n) working space. The algorithm uses only one advanced data structure, namely a splittable queue. We introduce (weakly) greedy pseudotriangulations, whose combinat ..."
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Cited by 31 (2 self)
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We show that the k free bitangents of a collection of n pairwise disjoint convex plane sets can be computed in time O(k+n log n) and O(n) working space. The algorithm uses only one advanced data structure, namely a splittable queue. We introduce (weakly) greedy pseudotriangulations, whose combinatorial properties are crucial for our method. 1 Introduction Consider a collection O of pairwise disjoint convex objects in the plane. We are interested in problems in which these objects arise as obstacles, either in connection with visibility problems where they can block the view from an other geometric object, or in motion planning, where these objects may prevent a moving object from moving along a straight line path. The visibility graph is a central object in such contexts. For polygonal obstacles the vertices of these polygons are the nodes of the visibility graph, and two nodes are connected by an arc if the corresponding vertices can see each other. [9] describes the first nontriv...
A New Efficient Radix Sort
, 1994
"... We present new improved algorithms for the sorting problem. The algorithms are not only efficient but also clear and simple. First, we introduce Forward Radix Sort which combines the advantages of traditional lefttoright and righttoleft radix sort in a simple manner. We argue that this algorithm ..."
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Cited by 30 (7 self)
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We present new improved algorithms for the sorting problem. The algorithms are not only efficient but also clear and simple. First, we introduce Forward Radix Sort which combines the advantages of traditional lefttoright and righttoleft radix sort in a simple manner. We argue that this algorithm will work very well in practice. Adding a preprocessing step, we obtain an algorithm with attractive theoretical properties. For example, n binary strings can be sorted in \Theta i n log i B n log n + 2 jj time, where B is the minimum number of bits that have to be inspected to distinguish the strings. This is an improvement over the previously best known result by Paige and Tarjan. The complexity may also be expressed in terms of H, the entropy of the input: n strings from a stationary ergodic process can be sorted in \Theta \Gamma n log \Gamma 1 H + 1 \Delta\Delta time, an improvement over the result recently presented by Chen and Reif.
Checking Geometric Programs or Verification of Geometric Structures
 IN PROC. 12TH ANNU. ACM SYMPOS. COMPUT. GEOM
, 1996
"... A program checker verifies that a particular program execution is correct. We give simple and efficient program checkers for some basic geometric tasks. We report about our experiences with program checking in the context of the LEDA system. We discuss program checking for data structures that ha ..."
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Cited by 30 (6 self)
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A program checker verifies that a particular program execution is correct. We give simple and efficient program checkers for some basic geometric tasks. We report about our experiences with program checking in the context of the LEDA system. We discuss program checking for data structures that have to rely on userprovided functions.
CacheOblivious String Btrees
 IN: PROC. OF PRINCIPLES OF DATABASE SYSTEMS
, 2006
"... Btrees are the data structure of choice for maintaining searchable data on disk. However, Btrees perform suboptimally • when keys are long or of variable length, • when keys are compressed, even when using front compression, the standard Btree compression scheme, • for range queries, and • with r ..."
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Cited by 27 (5 self)
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Btrees are the data structure of choice for maintaining searchable data on disk. However, Btrees perform suboptimally • when keys are long or of variable length, • when keys are compressed, even when using front compression, the standard Btree compression scheme, • for range queries, and • with respect to memory effects such as disk prefetching. This paper presents a cacheoblivious string Btree (COSBtree) data structure that is efficient in all these ways: • The COSBtree searches asymptotically optimally and inserts and deletes nearly optimally. • It maintains an index whose size is proportional to the frontcompressed size of the dictionary. Furthermore, unlike standard frontcompressed strings, keys can be decompressed in a memoryefficient manner. • It performs range queries with no extra disk seeks; in contrast, Btrees incur disk seeks when skipping from leaf block to leaf block. • It utilizes all levels of a memory hierarchy efficiently and makes good use of disk locality by using cacheoblivious layout strategies.
Dynamic Ordered Sets with Exponential Search Trees
 Combination of results presented in FOCS 1996, STOC 2000 and SODA
, 2001
"... We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fullydynamic linear space data structures. This leads to an optimal bound of O ( √ log n/log log n) for searching and updating a dynamic set of n integer keys i ..."
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Cited by 26 (1 self)
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We introduce exponential search trees as a novel technique for converting static polynomial space search structures for ordered sets into fullydynamic linear space data structures. This leads to an optimal bound of O ( √ log n/log log n) for searching and updating a dynamic set of n integer keys in linear space. Here searching an integer y means finding the maximum key in the set which is smaller than or equal to y. This problem is equivalent to the standard text book problem of maintaining an ordered set (see, e.g., Cormen, Leiserson, Rivest, and Stein: Introduction to Algorithms, 2nd ed., MIT Press, 2001). The best previous deterministic linear space bound was O(log n/log log n) due Fredman and Willard from STOC 1990. No better deterministic search bound was known using polynomial space.
On Universal Classes of Extremely Random Constant Time Hash Functions and Their TimeSpace Tradeoff
"... A family of functions F that map [0; n] 7! [0; n], is said to be hwise independent if any h points in [0; n] have an image, for randomly selected f 2 F , that is uniformly distributed. This paper gives both probabilistic and explicit randomized constructions of n ffl wise independent functions, ..."
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Cited by 26 (0 self)
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A family of functions F that map [0; n] 7! [0; n], is said to be hwise independent if any h points in [0; n] have an image, for randomly selected f 2 F , that is uniformly distributed. This paper gives both probabilistic and explicit randomized constructions of n ffl wise independent functions, ffl ! 1, that can be evaluated in constant time for the standard random access model of computation. Simple extensions give comparable behavior for larger domains. As a consequence, many probabilistic algorithms can for the first time be shown to achieve their expected asymptotic performance for a feasible model of computation. This paper also establishes a tight tradeoff in the number of random seeds that must be precomputed for a random function that runs in time T and is hwise independent. Categories and Subject Descriptors: E.2 [Data Storage Representation]: Hashtable representation; F.1.2 [Modes of Computation]: Probabilistic Computation; F2.3 [Tradepffs among Computational Measures]...
Maintaining Minimum Spanning Trees in Dynamic Graphs
 IN PROC. 24TH INTERNATIONAL COLLOQUIUM ON AUTOMATA, LANGUAGES, AND PROGRAMMING (ICALP
, 1997
"... We present the first fully dynamic algorithm for maintaining a minimum spanning tree in time o( # n) per operation. To be precise, the algorithm uses O(n 1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic. An immediate consequence is the first fully dyna ..."
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Cited by 26 (2 self)
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We present the first fully dynamic algorithm for maintaining a minimum spanning tree in time o( # n) per operation. To be precise, the algorithm uses O(n 1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic. An immediate consequence is the first fully dynamic deterministic algorithm for maintaining connectivity and, bipartiteness in amortized time O(n 1/3 log n) per update, with O(1) worst case time per query.
Selfimproving algorithms
 in SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
"... We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an al ..."
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Cited by 24 (4 self)
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We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an algorithm to sort a list of numbers with optimal expected limiting complexity; and (ii) an algorithm to compute the Delaunay triangulation of a set of points with optimal expected limiting complexity. In both cases, the algorithm begins with a training phase during which it adjusts itself to the input distribution, followed by a stationary regime in which the algorithm settles to its optimized incarnation. 1