Results 1  10
of
20
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 ..."
Abstract

Cited by 59 (2 self)
 Add to MetaCart
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 the Dynamic Finger Conjecture for Splay Trees. Part II: The Proof
 SIAM Journal on Computing
"... The following result is shown: On an nnode splay tree, the amortized cost of an access at distance d from the preceding access is O(log(d + 1)). In addition, there is an O(n) initialization cost. The accesses include searches, insertions and deletions. 1 Introduction The reader is advised that ..."
Abstract

Cited by 45 (1 self)
 Add to MetaCart
The following result is shown: On an nnode splay tree, the amortized cost of an access at distance d from the preceding access is O(log(d + 1)). In addition, there is an O(n) initialization cost. The accesses include searches, insertions and deletions. 1 Introduction The reader is advised that this paper quotes results from the companion Part I paper [CMSS93]; in addition, the Part I paper introduces a number of the techniques used here, but in a somewhat less involved way. The splay tree is a selfadjusting binary search tree devised by Sleator and Tarjan [ST85]. They showed that it is competitive with many of the balanced search tree schemes for maintaining a dictionary. Specifically, Sleator and Tarjan showed that a sequence of m accesses performed on a splay tree takes time O(m log n), where n is the maximum size attained by the tree (n m). They also showed that in an amortized sense, up to a constant factor, on sufficiently long sequences of searches, the splay tree has as ...
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 ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
. 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...
A unified access bound on comparisonbased dynamic dictionaries
 Theoretical Computer Science
"... We present a dynamic comparisonbased 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 ..."
Abstract

Cited by 12 (1 self)
 Add to MetaCart
We present a dynamic comparisonbased 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 workingset and dynamicfinger properties of splay trees. Preprint submitted to Elsevier Science 31 January 2007 1
Dynamic Optimality–Almost
 Proc. 45th Annu. IEEE Sympos. Foundations Comput. Sci
"... We present an O(lg lg n)competitive online binary search tree, improving upon the best previous (trivial) competitive ratio of O(lg n). This is the first major progress on Sleator and Tarjan’s dynamic optimality conjecture of 1985 that O(1)competitive binary search trees exist. 1. ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
We present an O(lg lg n)competitive online binary search tree, improving upon the best previous (trivial) competitive ratio of O(lg n). This is the first major progress on Sleator and Tarjan’s dynamic optimality conjecture of 1985 that O(1)competitive binary search trees exist. 1.
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 ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
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 for Skip Lists and BTrees
, 2008
"... Sleator and Tarjan [39] conjectured that splay trees are dynamically optimal binary search trees (BST). In this context, we study the skip list data structure introduced by Pugh [35]. We prove that for a class of skip lists that satisfy a weak balancing property, the workingset bound is a lower bou ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Sleator and Tarjan [39] conjectured that splay trees are dynamically optimal binary search trees (BST). In this context, we study the skip list data structure introduced by Pugh [35]. We prove that for a class of skip lists that satisfy a weak balancing property, the workingset bound is a lower bound on the time to access any sequence. Furthermore, we develop a deterministic selfadjusting skip list whose running time matches the workingset bound, thereby achieving dynamic optimality in this class. Finally, we highlight the implications our bounds for skip lists have on multiway branching search trees such as Btrees, (ab)trees, and other variants as well as their binary tree representations. In particular, we show a selfadjusting Btree that is dynamically optimal both in internal and external memory.
Probabilistic and Online Methods in Machine Learning
, 2001
"... On the surface, the three online machine learning problems analyzed in this thesis may seem unrelated. The first is an online investment strategy introduced by Tom Cover. We begin with a simple analysis that extends to the case of fixedpercentage transaction costs. We then describe an efficient i ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
On the surface, the three online machine learning problems analyzed in this thesis may seem unrelated. The first is an online investment strategy introduced by Tom Cover. We begin with a simple analysis that extends to the case of fixedpercentage transaction costs. We then describe an efficient implementation that runs in time polynomial in the number of stocks. The second problem is kfold cross validation, a popular technique in machine learning for estimating the error of a learned hypothesis. We show that this is a valid technique by comparing it to the holdout estimate. Finally, we discuss work towards a dynamicallyoptimal adaptive binary search tree algorithm. To my mother, Marilyn Kalai. May her PBSCT be as easy on her as my committee was on me. Acknowledgments It should be no surprise that my biggest thanks go to my parents, who somehow created me and gave me a very happy childhood. For as long as I can remember, my father has been teaching me about problem solving and research through puzzles and questions. If I end up with a fraction of his creativity and accomplishments, I will feel very lucky. Since I was a baby, I couldn't have asked for a better role model than my mother. Even if I could have talked at that age, I still wouldn't have asked for one. I came to CMU in large part because of Avrim Blum. After three advisors, I can say with full confidence that Avrim is the best advisor and teacher at CMU. I don't think I would have finished with anyone else. They often say that, by the time you're ready to graduate, you should know your area better than your advisor. If that was a requirement, I would never graduate. I'm moving from one great advisor to another. Next year I'll be at MIT under the supervision of Santosh Vempala. Many thanks to Santosh...
A Functional Perspective of Array Primitives
 In 2nd Fuji Int. Workshop on Functional and Logic Programming
, 1996
"... We propose a set of array primitives, based on experience from structural functional programming. We argue that these primitives provide a right level of abstraction for array computation. These primitives are derived from various perspectives of arrays, with each perspective imposing a particular a ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We propose a set of array primitives, based on experience from structural functional programming. We argue that these primitives provide a right level of abstraction for array computation. These primitives are derived from various perspectives of arrays, with each perspective imposing a particular algebraic structure and demanding specific efficiency requirements. We follow BirdMeertens formalism [7] [22], in particular the approach used by Meijer, Fokkinga, and Paterson [23], when designing these primitives, but also take into consideration efficient issues in their implementations. 1. Motivation Functional programming languages  with the exceptions of APL and SISAL  are not well known for large scale scientific computation. We identify inadequate language support for array operations  again with apology to APL and SISAL  a major reason why they are not widely used for scientific applications. Some functional languages provide little support for array operations, which...
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
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