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EnergyEfficient Algorithms for . . .
, 2007
"... We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good respons ..."
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Cited by 59 (2 self)
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We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variablespeed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unitsize jobs. We devise a deterministic constant competitive online algorithm and show that
On Rotations and the Generation of Binary Trees
 J. Algorithms
, 1993
"... The rotation graph, G n , has vertex set consisting of all binary trees with n nodes. Two vertices are connected by an edge if a single rotation will transform one tree into the other. We provide a simpler proof of a result of Lucas [7] that G n contains a Hamilton path. Our proof deals directly wi ..."
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Cited by 30 (6 self)
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The rotation graph, G n , has vertex set consisting of all binary trees with n nodes. Two vertices are connected by an edge if a single rotation will transform one tree into the other. We provide a simpler proof of a result of Lucas [7] that G n contains a Hamilton path. Our proof deals directly with the pointer representation of the binary tree. This proof provides the basis of an algorithm for generating all binary trees that can be implemented to run on a pointer machine and to use only constant time between the output of successive trees. Ranking and unranking algorithms are developed for the ordering of binary trees implied by the generation algorithm. These algorithms have time complexity O(n 2 ) (arithmetic operations). We also show strong relationships amongst various representations of binary trees and amongst binary tree generation algorithms that have recently appeared in the literature. Current address: SUNY Brockport, Mathematics & Computer Science Dept., Brockport, ...
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...
Splay trees, DavenportSchinzel sequences, and the deque conjecture
, 2007
"... We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence S, none of whose subsequences are isomorphic to fixed forbidden subsequence. We direct ..."
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Cited by 15 (5 self)
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We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence S, none of whose subsequences are isomorphic to fixed forbidden subsequence. We direct this technique towards Tarjan’s deque conjecture and prove that n deque operations require O(nα ∗ (n)) time, where α ∗ (n) is the minimum number of applications of the inverseAckermann function mapping n to a constant. We are optimistic that this approach could be directed towards other open conjectures on splay trees such as the traversal and split conjectures.
Randomized splay trees: theoretical and experimental results
 Information Processing Letters
"... Abstract Splay trees are selforganizing binary search trees that were introduced by Sleator andTarjan [12]. In this paper we present a randomized variant of these trees. The new algorithm for reorganizing the tree is both simple and easy to implement. We prove that our randomizedsplaying scheme has ..."
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Cited by 6 (0 self)
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Abstract Splay trees are selforganizing binary search trees that were introduced by Sleator andTarjan [12]. In this paper we present a randomized variant of these trees. The new algorithm for reorganizing the tree is both simple and easy to implement. We prove that our randomizedsplaying scheme has the same asymptotic performance as the original deterministic scheme but improves constants in the expected running time. This is interesting in practice becausethe search time in splay trees is typically higher than the search time in skip lists and AVLtrees. We present a detailed experimental study of our algorithm. On request sequencesgenerated by fixed probability distributions, we can achieve improvements of up to 25 % over deterministic splaying. On request sequences that exhibit high locality of reference, theimprovements are minor.
Dynamic optimality and multisplay trees
, 2004
"... The Dynamic Optimality Conjecture [ST85] states that splay trees are competitive (with a constant competitive factor) among the class of all binary search tree (BST) algorithms. Despite 20 years of research this conjecture is still unresolved. Recently Demaine et al. [DHIP04] suggested searching for ..."
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Cited by 3 (2 self)
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The Dynamic Optimality Conjecture [ST85] states that splay trees are competitive (with a constant competitive factor) among the class of all binary search tree (BST) algorithms. Despite 20 years of research this conjecture is still unresolved. Recently Demaine et al. [DHIP04] suggested searching for alternative algorithms which have small, but nonconstant competitive factors. They proposed tango, a BST algorithm which is nearly dynamically optimal – its competitive ratio is £¥¤§¦©¨���¦�¨����� � instead of a constant. Unfortunately, for many access patterns, tango is worse than other BST algorithms by a factor of ¦�¨���¦�¨��� �. In this paper we introduce multisplay trees, which can be viewed as a variant of splay trees. We prove the multisplay access lemma, which resembles the access lemma for splay trees. With different assignment of weights, this lemma allows us to prove various bounds on the performance of multisplay trees. Specifically, we prove that multisplay trees are £¥¤�¦�¨���¦©¨����� �competitive, and amortized £¥¤�¦�¨����� �. This is the first BST data structure to simultaneously achieve these two bounds. In addition, the algorithm is simple enough that we include code for its key parts. This work raises many open questions about the performance of multisplay trees. Does sequential access take linear time? (Our experiments indicate the answer is “yes”.) Are multisplay trees dynamically optimal? How do multisplay trees compare to splay trees? Specifically, are there sequences where one outperformes the other? What can be proved if we allow insertions and deletions in a multisplay tree? 1
KIST: A new encryption algorithm based on splay
"... In this paper, we proposed a new encryption algorithm called KIST. This algorithm uses an asynchronous key sequence and a splay tree. It is very efficient in the usage of both space and time. Some elementary security tests have been done. Key words asynchronous key sequence, splay tree, symmetric ke ..."
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Cited by 1 (0 self)
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In this paper, we proposed a new encryption algorithm called KIST. This algorithm uses an asynchronous key sequence and a splay tree. It is very efficient in the usage of both space and time. Some elementary security tests have been done. Key words asynchronous key sequence, splay tree, symmetric key encryption 1
Indexing Techniques for Temporal Text Containment Queries
"... Many information management systems maintain multiple time stamped versions of documents. The archives of web pages, version control systems, wikis and backup mechanisms are examples of such systems. For such temporally versioned document collections, a search using keywords along the temporal dimen ..."
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Many information management systems maintain multiple time stamped versions of documents. The archives of web pages, version control systems, wikis and backup mechanisms are examples of such systems. For such temporally versioned document collections, a search using keywords along the temporal dimension is valuable. This paper studies the temporal dimension of keyword search in the context of text document collections. The inverted index, which is an integral part of keyword based IR technique, requires several extensions for it to support keyword search over temporal document collections. We propose a number of techniques that explore such extensions. Several experimental results are also presented to compare the proposed solutions.