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113
Data Compression
 ACM Computing Surveys
, 1987
"... This paper surveys a variety of data compression methods spanning almost forty years of research, from the work of Shannon, Fano and Huffman in the late 40's to a technique developed in 1986. The aim of data compression is to reduce redundancy in stored or communicated data, thus increasing eff ..."
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Cited by 84 (3 self)
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This paper surveys a variety of data compression methods spanning almost forty years of research, from the work of Shannon, Fano and Huffman in the late 40's to a technique developed in 1986. The aim of data compression is to reduce redundancy in stored or communicated data, thus increasing effective data density. Data compression has important application in the areas of file storage and distributed systems. Concepts from information theory, as they relate to the goals and evaluation of data compression methods, are discussed briefly. A framework for evaluation and comparison of methods is constructed and applied to the algorithms presented. Comparisons of both theoretical and empirical natures are reported and possibilities for future research are suggested. INTRODUCTION Data compression is often referred to as coding, where coding is a very general term encompassing any special representation of data which satisfies a given need. Information theory is defined to be the study of eff...
Toward a model for backtracking and dynamic programming
 Comput. Compl
"... We propose a model called priority branching trees (pBT) for backtracking and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. ..."
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Cited by 26 (8 self)
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We propose a model called priority branching trees (pBT) for backtracking and dynamic programming algorithms. Our model generalizes both the priority model of Borodin, Nielson and Rackoff, as well as a simple dynamic programming model due to Woeginger, and hence spans a wide spectrum of algorithms. After witnessing the strength of the model, we then show its limitations by providing lower bounds for algorithms in this model for several classical problems such as Interval Scheduling, Knapsack and Satisfiability.
A best possible bound for the weighted path length of binary search trees
 SIAM Journal on Computing
, 1977
"... Abstract. The weighted path length of optimum binary search trees is bounded above by Y’./3i +2 a. +H where H is the entropy of the frequency distribution, /3i is the total weight of the internal nodes, and aj is the total weight of the leaves. This bound is best possible. A linear time algorithm fo ..."
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Cited by 24 (0 self)
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Abstract. The weighted path length of optimum binary search trees is bounded above by Y’./3i +2 a. +H where H is the entropy of the frequency distribution, /3i is the total weight of the internal nodes, and aj is the total weight of the leaves. This bound is best possible. A linear time algorithm for constructing nearly optimal trees is described. Key words, binary search tree, complexity, average search time, entropy One of the popular methods for retrieving information by its "name " is to store the names in a binary tree. We are given n names B1, Be, , Bn and 2n + 1 frequencies 1, " ", fin, aO, " ", an with /3i +Y aj 1. Here ji is the frequency of encountering name Bi, and aj is the frequency of encountering a name which lies between B and B/I, a0 and an have obvious interpretations [4]. A binary search tree T for the names B1, B2, , Bn is a tree with n interior nodes (nodes having two sons), which we denote by circles, and n + 1 leaves, which we denote by squares. The interior nodes are labeled with the B in increasing order from left to right and the leaves are labeled with the intervals (Bi, B//I) in increasing order from left to right. Let b be the distance of interior node B from
Speeding up Dynamic Programming
 In Proc. 29th Symp. Foundations of Computer Science
, 1988
"... this paper we consider the problem of computing two similar recurrences: the onedimensional case ..."
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Cited by 19 (0 self)
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this paper we consider the problem of computing two similar recurrences: the onedimensional case
SelfOrganizing Data Structures
 In
, 1998
"... . We survey results on selforganizing data structures for the search problem and concentrate on two very popular structures: the unsorted linear list, and the binary search tree. For the problem of maintaining unsorted lists, also known as the list update problem, we present results on the competit ..."
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Cited by 18 (0 self)
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. We survey results on selforganizing data structures for the search problem and concentrate on two very popular structures: the unsorted linear list, and the binary search tree. For the problem of maintaining unsorted lists, also known as the list update problem, we present results on the competitiveness achieved by deterministic and randomized online algorithms. For binary search trees, we present results for both online and offline algorithms. Selforganizing data structures can be used to build very effective data compression schemes. We summarize theoretical and experimental results. 1 Introduction This paper surveys results in the design and analysis of selforganizing data structures for the search problem. The general search problem in pointer data structures can be phrased as follows. The elements of a set are stored in a collection of nodes. Each node also contains O(1) pointers to other nodes and additional state data which can be used for navigation and selforganizati...
Constructing Trees in Parallel
, 1989
"... O(log = log n processor as well as O(log n) = log n processor CREW deterministic parallel algorithms are presented for constructing Huffman codes from a given list of frequencies. The time can be reduced to O(logn(log log n) ) on a CRCW model, using only n processors. Also presented i ..."
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Cited by 17 (1 self)
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O(log = log n processor as well as O(log n) = log n processor CREW deterministic parallel algorithms are presented for constructing Huffman codes from a given list of frequencies. The time can be reduced to O(logn(log log n) ) on a CRCW model, using only n processors. Also presented is an optimal O(log n) time, O(n= log n) processor EREW parallel algorithm for constructing a tree given a list of leaf depths when the depths are monotonic.
Bounding the Depth of Search Trees
 The Computer Journal
, 1993
"... For an ordered sequence of n weights, Huffman's algorithm constructs in time and space O(n) a search tree with minimum average path length, or, which is equivalent, a minimum redundancy code. However, if an upper bound B is imposed on the length of the codewords, the best known algorithms for t ..."
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Cited by 16 (5 self)
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For an ordered sequence of n weights, Huffman's algorithm constructs in time and space O(n) a search tree with minimum average path length, or, which is equivalent, a minimum redundancy code. However, if an upper bound B is imposed on the length of the codewords, the best known algorithms for the construction of an optimal code have time and space complexities O(Bn 2 ). A new algorithm is presented, which yields suboptimal codes, but in time O(n log n) and space O(n). Under certain conditions, these codes are shown to be close to optimal, and extensive experiments suggest that in many practical applications, the deviation from the optimum is negligible. 1. Motivation and Introduction We consider the set B(n; b) of extended binary trees with n leaves, labelled 1 to n, and with depth b, henceforth called brestricted trees. An extended binary tree is a binary tree in which every internal node has two sons (here, and in what follows, we use the terminology of Knuth [16, pp. 399...
Succinct greedy graph drawing in the hyperbolic plane
 In Proc. 16th Int. Symp. Graph Drawing
, 2008
"... Abstract. We describe an efficient method for drawing any nvertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed geometrically, simply by having each vertex that r ..."
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Cited by 16 (4 self)
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Abstract. We describe an efficient method for drawing any nvertex simple graph G in the hyperbolic plane. Our algorithm produces greedy drawings, which support greedy geometric routing, so that a message M between any pair of vertices may be routed geometrically, simply by having each vertex that receives M pass it along to any neighbor that is closer in the hyperbolic metric to the message’s eventual destination. More importantly, for networking applications, our algorithm produces succinct drawings, in that each of the vertex positions in one of our embeddings can be represented using O(log n) bits and the calculation of which neighbor to send a message to may be performed efficiently using these representations. These properties are useful, for example, for routing in sensor networks, where storage and bandwidth are limited. 1
Efficient ExpectedCase Algorithms for Planar Point Location
, 2000
"... . Planar point location is among the most fundamental search problems in computational geometry. Although this problem has been heavily studied from the perspective of worstcase query time, there has been surprisingly little theoretical work on expectedcase query time. We are given an nvertex ..."
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Cited by 13 (4 self)
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. Planar point location is among the most fundamental search problems in computational geometry. Although this problem has been heavily studied from the perspective of worstcase query time, there has been surprisingly little theoretical work on expectedcase query time. We are given an nvertex planar polygonal subdivision S satisfying some weak assumptions (satisfied, for example, by all convex subdivisions). We are to preprocess this into a data structure so that queries can be answered efficiently. We assume that the two coordinates of each query point are generated independently by a probability distribution also satisfying some weak assumptions (satisfied, for example, by the uniform distribution). In the decision tree model of computation, it is wellknown from information theory that a lower bound on the expected number of comparisons is entropy(S). We provide two data structures, one of size O(n 2 ) that can answer queries in 2 entropy(S) + O(1) expected number...