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112
Fast Algorithms for Sorting and Searching Strings
, 1997
"... We present theoretical algorithms for sorting and searching multikey data, and derive from them practical C implementations for applications in which keys are character strings. The sorting algorithm blends Quicksort and radix sort; it is competitive with the best known C sort codes. The searching a ..."
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Cited by 148 (0 self)
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We present theoretical algorithms for sorting and searching multikey data, and derive from them practical C implementations for applications in which keys are character strings. The sorting algorithm blends Quicksort and radix sort; it is competitive with the best known C sort codes. The searching algorithm blends tries and binary search trees; it is faster than hashing and other commonly used search methods. The basic ideas behind the algorithms date back at least to the 1960s, but their practical utility has been overlooked. We also present extensions to more complex string problems, such as partialmatch searching. 1. Introduction Section 2 briefly reviews Hoare's [9] Quicksort and binary search trees. We emphasize a wellknown isomorphism relating the two, and summarize other basic facts. The multikey algorithms and data structures are presented in Section 3. Multikey Quicksort orders a set of n vectors with k components each. Like regular Quicksort, it partitions its input into...
Faster algorithms for the shortest path problem
, 1990
"... Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n vertices, mn edges, and nonnegative integer arc costs bounded by C, a onelevel form of radix heap gives a time b ..."
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Cited by 104 (10 self)
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Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap, is proposed for use in this algorithm. On a network with n vertices, mn edges, and nonnegative integer arc costs bounded by C, a onelevel form of radix heap gives a time bound for Dijkstra's algorithm of O(m + n log C). A twolevel form of radix heap gives a bound of O(m + n log C/log log C). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O(m + n /log C). The best previously known bounds are O(m + n log n) using Fibonacci heaps alone and O(m log log C) using the priority queue structure of Van Emde Boas et al. [17].
Topologically Sweeping Visibility Complexes via Pseudotriangulations
, 1996
"... This paper describes a new algorithm for constructing the set of free bitangents of a collection of n disjoint convex obstacles of constant complexity. The algorithm runs in time O(n log n + k), where k is the output size, and uses O(n) space. While earlier algorithms achieve the same optimal run ..."
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Cited by 86 (9 self)
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This paper describes a new algorithm for constructing the set of free bitangents of a collection of n disjoint convex obstacles of constant complexity. The algorithm runs in time O(n log n + k), where k is the output size, and uses O(n) space. While earlier algorithms achieve the same optimal running time, this is the first optimal algorithm that uses only linear space. The visibility graph or the visibility complex can be computed in the same time and space. The only complicated data structure used by the algorithm is a splittable queue, which can be implemented easily using redblack trees. The algorithm is conceptually very simple, and should therefore be easy to implement and quite fast in practice. The algorithm relies on greedy pseudotriangulations, which are subgraphs of the visibility graph with many nice combinatorial properties. These properties, and thus the correctness of the algorithm, are partially derived from properties of a certain partial order on the faces of th...
External Memory Data Structures
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynami ..."
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Cited by 81 (36 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.
Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions
 Algorithmica
, 1996
"... Small sample spaces with almost independent random variables are applied to design efficient sequential deterministic algorithms for two problems. The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrix multiplication, so ..."
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Cited by 62 (6 self)
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Small sample spaces with almost independent random variables are applied to design efficient sequential deterministic algorithms for two problems. The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrix multiplication, solves the problem of computing witnesses for the Boolean product of two matrices. That is, if A and B are two n by n matrices, and C = AB is their Boolean product, the algorithm finds for every entry Cij = 1 a witness: an index k so that Aik = Bkj = 1. Its running time exceeds that of computing the product of two n by n matrices with small integer entries by a polylogarithmic factor. The second algorithm is a nearly linear time deterministic procedure for constructing a perfect hash function for a given nsubset of {1,..., m}.
Dynamic planar convex hull
 Proc. 43rd IEEE Sympos. Found. Comput. Sci
, 2002
"... In this paper we determine the amortized computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage o ..."
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Cited by 53 (1 self)
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In this paper we determine the amortized computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure.
Graph Layout through the VCG Tool
, 1994
"... The VCG tool allows the visualization of graphs that occur typically as data structures in programs. We describe the functionality of the VCG tool, its layout algorithm and its heuristics. Our main emphasis in the selection of methods is to achieve a very good performance for the layout of large gra ..."
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Cited by 52 (0 self)
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The VCG tool allows the visualization of graphs that occur typically as data structures in programs. We describe the functionality of the VCG tool, its layout algorithm and its heuristics. Our main emphasis in the selection of methods is to achieve a very good performance for the layout of large graphs. The tool supports the partitioning of edges and nodes into edge classes and nested subgraphs, the folding of regions, and the management of priorities of edges. The algorithm produces good drawings and runs reasonably fast even on very large graphs.
LOW REDUNDANCY IN STATIC DICTIONARIES WITH CONSTANT QUERY TIME
 SIAM J. COMPUT.
, 2001
"... A static dictionary is a data structure storing subsets of a finite universe U, answering membership queries. We show that on a unit cost RAM with word size Θ(log U), a static dictionary for nelement sets with constant worst case query time can be obtained using B +O(log log U)+o(n) (U) bits ..."
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Cited by 50 (7 self)
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A static dictionary is a data structure storing subsets of a finite universe U, answering membership queries. We show that on a unit cost RAM with word size Θ(log U), a static dictionary for nelement sets with constant worst case query time can be obtained using B +O(log log U)+o(n) (U) bits of storage, where B = ⌈log2 ⌉ is the minimum number of bits needed to represent all nn element subsets of U.
Breaking a TimeandSpace Barrier in Constructing FullText Indices
"... Suffix trees and suffix arrays are the most prominent fulltext indices, and their construction algorithms are well studied. It has been open for a long time whether these indicescan be constructed in both o(n log n) time and o(n log n)bit working space, where n denotes the length of the text. Int ..."
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Cited by 50 (3 self)
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Suffix trees and suffix arrays are the most prominent fulltext indices, and their construction algorithms are well studied. It has been open for a long time whether these indicescan be constructed in both o(n log n) time and o(n log n)bit working space, where n denotes the length of the text. Inthe literature, the fastest algorithm runs in O(n) time, whileit requires O(n log n)bit working space. On the other hand,the most spaceefficient algorithm requires O(n)bit working space while it runs in O(n log n) time. This paper breaks the longstanding timeandspace barrier under the unitcost word RAM. We give an algorithm for constructing the suffix array which takes O(n) time and O(n)bit working space, for texts with constantsize alphabets. Note that both the time and the space bounds are optimal. For constructing the suffix tree, our algorithm requires O(n logffl n) time and O(n)bit working space forany 0! ffl! 1. Apart from that, our algorithm can alsobe adopted to build other existing fulltext indices, such as
Dynamic Programming Search for Continuous Speech Recognition
, 1999
"... Initially introduced in the late 1960s and early 1970s, dynamic programming algorithms have become increasingly popular in automatic speech recognition. There are two reasons why this has occurred: First, the dynamic programming strategy can be combined with avery efficient and practical pruning str ..."
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Cited by 48 (1 self)
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Initially introduced in the late 1960s and early 1970s, dynamic programming algorithms have become increasingly popular in automatic speech recognition. There are two reasons why this has occurred: First, the dynamic programming strategy can be combined with avery efficient and practical pruning strategy so that very large search spaces can be handled. Second, the dynamic programming strategy has turned out to be extremely flexible in adapting to new requirements. Examples of such requirements are the lexical tree organization of the pronunciation lexicon and the generation of a word graph instead of the single best sentence. In this paper, we attempt to systematically review the use of dynamic programming search strategies for smallvocabulary and largevocabulary continuous speech recognition. The following methods are described in detail: search using a linear lexicon, search using a lexical tree, languagemodel lookahead and word graph generation.