Results 1  10
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24
An optimal online algorithm for metrical task systems
 Journal of the ACM
, 1992
"... Abstract. In practice, almost all dynamic systems require decisions to be made online, without full knowledge of their future impact on the system. A general model for the processing of sequences of tasks is introduced, and a general online decnion algorithm is developed. It is shown that, for an ..."
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Cited by 186 (9 self)
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Abstract. In practice, almost all dynamic systems require decisions to be made online, without full knowledge of their future impact on the system. A general model for the processing of sequences of tasks is introduced, and a general online decnion algorithm is developed. It is shown that, for an important algorithms. class of special cases, this algorithm is optimal among all online Specifically, a task system (S. d) for processing sequences of tasks consists of a set S of states and a cost matrix d where d(i, j) is the cost of changing from state i to state j (we assume that d satisfies the triangle inequality and all diagonal entries are f)). The cost of processing a given task depends on the state of the system. A schedule for a sequence T1, T2,..., Tk of tasks is a ‘equence sl,s~,..., Sk of states where s ~ is the state in which T ’ is processed; the cost of a schedule is the sum of all task processing costs and state transition costs incurred. An online scheduling algorithm is one that chooses s, only knowing T1 Tz ~.. T’. Such an algorithm is wcompetitive if, on any input task sequence, its cost is within an additive constant of w times the optimal offline schedule cost. The competitive ratio w(S, d) is the infimum w for which there is a wcompetitive online scheduling algorithm for (S, d). It is shown that w(S, d) = 2 ISI – 1 for eoery task system in which d is symmetric, and w(S, d) = 0(1 S]2) for every task system. Finally, randomized online scheduling algorithms are introduced. It is shown that for the uniform task system (in which d(i, j) = 1 for all i, j), the expected competitive ratio w(S, d) =
SelfOrganizing Linear Search
 ACM Computing Surveys
, 1985
"... this article. Two examples of simple permutation algorithms are movetofront, which moves the accessed record to the front of the list, shifting all records previously ahead of it back one position; and transpose, which merely exchanges the accessed record with the one immediately ahead of it in th ..."
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Cited by 29 (3 self)
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this article. Two examples of simple permutation algorithms are movetofront, which moves the accessed record to the front of the list, shifting all records previously ahead of it back one position; and transpose, which merely exchanges the accessed record with the one immediately ahead of it in the list. These will be described in more detail later. Knuth [1973] describes several search methods that are usually more efficient than linear search. Bentley and McGeoch [1985] justify the use of selforganizing linear search in the following three contexts:
Selfimproving algorithms
 in SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
"... We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an al ..."
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Cited by 26 (4 self)
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We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an algorithm to sort a list of numbers with optimal expected limiting complexity; and (ii) an algorithm to compute the Delaunay triangulation of a set of points with optimal expected limiting complexity. In both cases, the algorithm begins with a training phase during which it adjusts itself to the input distribution, followed by a stationary regime in which the algorithm settles to its optimized incarnation. 1
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...
A competitive analysis of the list update problem with lookahead
 Theoret. Comput. Sci
, 1998
"... We consider the question of lookahead in the list update problem: What improvement can be achieved in terms of competitiveness if an online algorithm sees not only the present request to be served but also some future requests? We introduce two different models of lookahead and study the list updat ..."
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Cited by 13 (0 self)
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We consider the question of lookahead in the list update problem: What improvement can be achieved in terms of competitiveness if an online algorithm sees not only the present request to be served but also some future requests? We introduce two different models of lookahead and study the list update problem using these models. We develop lower bounds on the competitiveness that can be achieved by deterministic online algorithms with lookahead. Furthermore we present online algorithms with lookahead that are competitive against static offline algorithms.
LeastRecentlyUsed Caching with Dependent Requests
 Theoretical Computer Science
, 2002
"... We investigate a widely popular LeastRecentlyUsed (LRU) cache replacement algorithm with semiMarkov modulated requests. SemiMarkov processes provide the flexibility for modeling strong statistical correlation, including the widely reported longrange dependence in the World Wide Web page request ..."
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Cited by 13 (6 self)
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We investigate a widely popular LeastRecentlyUsed (LRU) cache replacement algorithm with semiMarkov modulated requests. SemiMarkov processes provide the flexibility for modeling strong statistical correlation, including the widely reported longrange dependence in the World Wide Web page request patterns. When the frequency of requesting a page n is equal to the generalized Zipf’s law c/n α,α> 1, our main result shows that the cache fault probability is asymptotically, for large cache sizes, the same as in the corresponding LRU system with i.i.d. requests. The result is asymptotically explicit and appears to be the first computationally tractable averagecase analysis of LRU caching with statistically dependent request sequences. The surprising insensitivity of LRU caching performance demonstrates its robustness to changes in document popularity. Furthermore, we show that the derived asymptotic result and simulation experiments are in excellent agreement, even for relatively small cache sizes. Keywords: leastrecentlyused caching, movetofront, Zipf’s law, heavytailed distributions, longrange dependence, semiMarkov processes, averagecase analysis
On the Markov chain for the movetoroot rule for binary search trees
, 1998
"... The movetoroot (MTR) heuristic is a selforganizing rule which attempts to keep a binary search tree in nearoptimal form. It is a tree analogue of the movetofront (MTF) scheme for selforganizing lists. Both heuristics can be modeled as Markov chains. We show that the MTR chain can be deriv ..."
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Cited by 9 (3 self)
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The movetoroot (MTR) heuristic is a selforganizing rule which attempts to keep a binary search tree in nearoptimal form. It is a tree analogue of the movetofront (MTF) scheme for selforganizing lists. Both heuristics can be modeled as Markov chains. We show that the MTR chain can be derived by lumping the MTF chain and give exact formulas for the transition probabilities and stationary distribution for MTR. We also derive the eigenvalues and their multiplicities for MTR. 1 Research for both authors supported by NSF grant DMS9311367. 2 AMS 1991 subject classifications. Primary 60J10; secondary 68P10, 68P05. 3 Keywords and phrases. Markov chains, selforganizing search, binary search trees, movetoroot rule, lumping, eigenvalues, simple exchange, movetofront rule. 1 1 Introduction and Summary There has been much interest in recent years in selforganizing search methods. Hester and Hirschberg (1985) survey the field. Hendricks (1989) is a good introduction with...
Adaptive Heuristics for Binary Search Trees and Constant Linkage Cost
 In Proc. of the 2nd ACMSIAM Symposium on Discrete Algorithms
, 1995
"... We present lower and upper bounds on adaptive heuristics for maintaining binary search trees using a constant number of link or pointer changes for each operation (constant linkage cost (CLC)). We show that no adaptive heuristic with an amortized linkage cost of o(log n) can be competitive. In part ..."
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Cited by 8 (0 self)
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We present lower and upper bounds on adaptive heuristics for maintaining binary search trees using a constant number of link or pointer changes for each operation (constant linkage cost (CLC)). We show that no adaptive heuristic with an amortized linkage cost of o(log n) can be competitive. In particular, we show that any heuristic that performs f(n) = o(log n) promotions (rotations) amortized over each access has a competitive ratio of at least \Omega\Gammaast n=f(n)) against an oblivious adversary, and any heuristic that performs f(n) = o(log n) pointer changes amortized over each access has a competitive ratio of at least\Omega\Gamma log n f(n) log(log n=f(n)) ) against an adaptive online adversary. In our investigation of upper bounds we present four adaptive heuristics: ffl A randomized, worstcaseCLC heuristic (R2P) whose expected search time is within a constant factor of the search time using an optimal tree; that is, it is statically competitive ffl A randomized, expecte...
Adaptive Structuring Of Binary Search Trees Using Conditional Rotations
 IEEE TRANSACTIONS ON KNOWLEDGE & DATA ENGINEERING
, 1987
"... Consider a set A = {A 1 , A 2 ,...,A N } of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S = [s 1 ,s 2 ,...,s N ] and are to be arranged lexicographically using a Binary Search Tree (BST). If S is known a priori, it ..."
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Cited by 6 (2 self)
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Consider a set A = {A 1 , A 2 ,...,A N } of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S = [s 1 ,s 2 ,...,s N ] and are to be arranged lexicographically using a Binary Search Tree (BST). If S is known a priori, it is well known [10] that an optimal BST may be constructed using A and S. We consider the case when S is not known a priori . A new restructuring heuristic is introduced that requires three extra integer memory locations per record. In this scheme the restructuring is performed only if it decreases the Weighted Path Length (WPL) of the overall resultant tree. An optimized version of the latter method which requires only one extra integer field per record has also been presented. Initial simulation results which compare our algorithm with various other static and dynamic schemes seem to indicate that this scheme asymptotically produces trees which are an order of magnitude closer to the optim...