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A unified access bound on comparison-based dynamic dictionaries
- Theoretical Computer Science
"... We present a dynamic comparison-based search structure that supports insertions, deletions, and searches within the unified bound. The unified bound specifies that it is quick to access an element that is near a recently accessed element. More precisely, if w(y) distinct elements have been accessed ..."
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Cited by 8 (1 self)
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We present a dynamic comparison-based search structure that supports insertions, deletions, and searches within the unified bound. The unified bound specifies that it is quick to access an element that is near a recently accessed element. More precisely, if w(y) distinct elements have been accessed since the last access to element y, and d(x, y) denotes the rank distance between x and y among the current set of elements, then the amortized cost to access element x is O(miny log[w(y) + d(x, y) + 2]). This property generalizes the working-set and dynamic-finger properties of splay trees. Preprint submitted to Elsevier Science 31 January 2007 1
Key independent optimality
- In International Symp. on Algorithms and Computation
, 2002
"... A new form of optimality for comparison based static dictionaries is introduced. This type of optimality, keyindependent optimality, is motivated by applications that assign key values randomly. It is shown that any data structure that is key-independently optimal is expected to execute any access s ..."
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Cited by 7 (2 self)
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A new form of optimality for comparison based static dictionaries is introduced. This type of optimality, keyindependent optimality, is motivated by applications that assign key values randomly. It is shown that any data structure that is key-independently optimal is expected to execute any access sequence where the key values are assigned arbitrarily to unordered data as fast as any offline binary search tree algorithm, within a multiplicative constant. Asymptotically tight upper and lower bounds are presented for key-independent optimality. Splay trees are shown to be key-independently optimal. 1
Cache-aware and cache-oblivious adaptive sorting
- In Proc. 32nd International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science
, 2005
"... Abstract. Two new adaptive sorting algorithms are introduced which perform an optimal number of comparisons with respect to the number of inversions in the input. The first algorithm is based on a new linear time reduction to (non-adaptive) sorting. The second algorithm is based on a new division pr ..."
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Cited by 7 (4 self)
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Abstract. Two new adaptive sorting algorithms are introduced which perform an optimal number of comparisons with respect to the number of inversions in the input. The first algorithm is based on a new linear time reduction to (non-adaptive) sorting. The second algorithm is based on a new division protocol for the GenericSort algorithm by Estivill-Castro and Wood. From both algorithms we derive I/O-optimal cache-aware and cache-oblivious adaptive sorting algorithms. These are the first I/Ooptimal adaptive sorting algorithms. 1
Multiple Templates Access of Trees in Parallel Memory Systems
- Proc. of Intern. Parallel Processing Symp. (IPPS
, 1998
"... We study the problem of mapping the N nodes of a data structure on M memory modules so that they can be accessed in parallel by templates i.e. distinct sets of nodes. In literature several algorithms are available for arrays (accessed by rows, columns, diagonals and subarrays) and trees (accessed ..."
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Cited by 4 (3 self)
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We study the problem of mapping the N nodes of a data structure on M memory modules so that they can be accessed in parallel by templates i.e. distinct sets of nodes. In literature several algorithms are available for arrays (accessed by rows, columns, diagonals and subarrays) and trees (accessed by subtrees, root-to-leaf paths, levels, etc.). Although some mapping algorithms for arrays allow conflict-free access to several templates at once (for example rows and columns), no mapping algorithm is known for efficiently accessing subtree, path and level templates in complete binary trees. In our paper, we, first, prove that any mapping algorithm that is conflict-free for tree/level template has \Omega\Gamma M= log M ) conflicts when access is done according to path template and vice versa. Therefore, no mapping algorithm can be found that is conflict-free on both path and tree (or path and level) templates. Our main result is an algorithm for mapping complete binary trees wi...
On adaptive integer sorting
- In 12th Annual European Symposium on Algorithms, ESA 2004
, 2004
"... Abstract. This paper considers integer sorting on a RAM. We show that adaptive sorting of a sequence with qn inversions is asymptotically equivalent to multisorting groups of at most q keys, and a total of n keys. Using the recent O(n √ log log n) expected time sorting of Han and Thorup on each set, ..."
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Cited by 4 (0 self)
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Abstract. This paper considers integer sorting on a RAM. We show that adaptive sorting of a sequence with qn inversions is asymptotically equivalent to multisorting groups of at most q keys, and a total of n keys. Using the recent O(n √ log log n) expected time sorting of Han and Thorup on each set, we immediately get an adaptive expected sorting time of O(n √ log log q). Interestingly, for any positive constant ε, we show that multisorting and adaptive inversion sorting can be performed in (log n)1−ε linear time if q ≤ 2. We also show how to asymptotically improve the running time of any traditional sorting algorithm on a class of inputs much broader than those with few inversions. 1
Compatible Embedding for 2D Shape Animation
- IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2008
"... Abstract—We present new algorithms for the compatible embedding of 2D shapes. Such embeddings offer a convenient way to interpolate shapes having complex, detailed features. Compared to existing techniques, our approach requires less user input, is faster, more robust, and simpler to implement, maki ..."
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Cited by 4 (0 self)
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Abstract—We present new algorithms for the compatible embedding of 2D shapes. Such embeddings offer a convenient way to interpolate shapes having complex, detailed features. Compared to existing techniques, our approach requires less user input, is faster, more robust, and simpler to implement, making it ideal for interactive use in practical applications. Our new approach consists of three parts. First, our boundary matching algorithm locates salient features using the perceptually-motivated principles of scalespace and uses these as automatic correspondences to guide an elastic curve matching algorithm. Second, we simplify boundaries while maintaining their parametric correspondence and the embedding of the original shapes. Finally, we extend the mapping to shapes ’ interiors via a new compatible triangulation algorithm. The combination of our algorithms allows us to demonstrate 2D shape interpolation with instant feedback. The proposed algorithms exhibit a combination of simplicity, speed, and accuracy that has not been achieved in previous work.
Toward a Universal Mapping Algorithm for Accessing Trees in Parallel Memory Systems
, 1998
"... We study the problem of mapping the N nodes of a complete t-ary tree on M memory modules so that they can be accessed in parallel by templates, i.e. distinct sets of nodes. Typical templates for accessing trees are subtrees, root-to-leaf paths, or levels which will be referred to as elementary templ ..."
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Cited by 3 (2 self)
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We study the problem of mapping the N nodes of a complete t-ary tree on M memory modules so that they can be accessed in parallel by templates, i.e. distinct sets of nodes. Typical templates for accessing trees are subtrees, root-to-leaf paths, or levels which will be referred to as elementary templates. In this paper, we first propose a new mapping algorithm for accessing both paths and subtrees of size M with an optimal number of conflicts (i.e., only one conflict) when the number of memory modules is limited to M . We also propose another mapping algorithm for a composite template, say V (as versatile), such that its size is not fixed and an instance of V is composed of any combination of c instances of elementary templates. The number of conflicts for accessing an S-node instance of template V is O ` S p M log M + c ' and the memory load is 1 + o(1) where load is defined as the ratio between the maximum and minimum number of data items mapped onto each memory module. 1. In...
Adaptive comparison-based algorithms for evaluating set queries
, 2004
"... c○Mehdi Mirzazadeh 2004I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. In this thesis we study a problem ..."
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Cited by 3 (1 self)
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c○Mehdi Mirzazadeh 2004I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. In this thesis we study a problem that arises in answering boolean queries submitted to a search engine. Usually a search engine stores the set of IDs of documents containing each word in a pre-computed sorted order and to evaluate a query like “computer AND science ” the search engine has to evaluate the union of the sets of documents containing the words “computer ” and “science”. More complex queries will result in more complex set expressions. In this thesis we consider the problem of evaluation of a set expression with union and intersection as operators and ordered sets as operands. We explore properties of comparison-based algorithms for the problem. A proof of a set expression is the set of comparisons that a comparison-based algorithm performs before it can determine the result of the expression. We discuss the properties of the proofs of set expressions and based on how complex the smallest proofs of a set expression E are, we define a measurement for determining how difficult it is for E to be computed. Then, we design an algorithm that is adaptive to the difficulty of the input expression and we show that the running time of the algorithm is roughly proportional to difficulty of the input expression, where the factor is roughly logarithmic in the number of the operands of the input expression. Key words: Adaptive algorithm, comparison-based algorithm, search engines, algorithms.
Putting your data structure on a diet
- In preparation (2006). [Ask Jyrki for details
, 2007
"... Abstract. Consider a data structure D that stores a dynamic collection of elements. Assume that D uses a linear number of words in addition to the elements stored. In this paper several data-structural transformations are described that can be used to transform D into another data structure D ′ that ..."
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Cited by 2 (2 self)
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Abstract. Consider a data structure D that stores a dynamic collection of elements. Assume that D uses a linear number of words in addition to the elements stored. In this paper several data-structural transformations are described that can be used to transform D into another data structure D ′ that supports the same operations as D, has considerably smaller memory overhead than D, and performs the supported operations by a small constant factor or a small additive term slower than D, depending on the data structure and operation in question. The compaction technique has been successfully applied for linked lists, dictionaries, and priority queues.
Shortest Paths with Single-Point Visibility Constraints
"... This paper studies the problem of finding the shortest path between two points in presence of single-point visibility constraints. In this type of constraints, there should be at least one point on the output path from which a fixed viewpoint is visible. The problem is studied in various domains ..."
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Cited by 2 (1 self)
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This paper studies the problem of finding the shortest path between two points in presence of single-point visibility constraints. In this type of constraints, there should be at least one point on the output path from which a fixed viewpoint is visible. The problem is studied in various domains including simple polygons, polygonal domains, polyhedral surfaces. The method is based on partitioning the boundary of the visibility region to a number of intervals according to shortest path structure of their points to both source and destination. The result for the two dimensional domains is worst-case optimal

