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Improved Randomized OnLine Algorithms for the List Update Problem
 PROC. 6TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1995
"... The best randomized online algorithms known so far for the list update problem achieve a competitiveness of p 3 1:73. In this paper we present a new family of randomized online algorithms that beat this competitive ratio. Our improved algorithms are called TIMESTAMP algorithms and achieve a com ..."
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The best randomized online algorithms known so far for the list update problem achieve a competitiveness of p 3 1:73. In this paper we present a new family of randomized online algorithms that beat this competitive ratio. Our improved algorithms are called TIMESTAMP algorithms and achieve a competitiveness of maxf2 \Gamma p; 1 + p(2 \Gamma p)g, for any real number p 2 [0; 1]. Setting p = (3 \Gamma p 5)=2, we obtain a OEcompetitive algorithm, where OE = (1 + p 5)=2 1:62 is the Golden Ratio. TIMESTAMP algorithms coordinate the movements of items using some information on past requests. We can reduce the required information at the expense of increasing the competitive ratio. We present a very simple version of the TIMESTAMP algorithms that is 1:68competitive. The family of TIMESTAMP algorithms also includes a new deterministic 2competitive online algorithm that is different from the MOVETOFRONT rule.
SemiOnline Scheduling With Decreasing Job Sizes
, 1998
"... We investigate the problem of semionline scheduling jobs on m identical parallel machines where the jobs arrive in order of decreasing sizes. We present a complete solution for the preemptive variant of semionline scheduling with decreasing job sizes. We give matching lower and upper bounds on the ..."
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Cited by 27 (2 self)
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We investigate the problem of semionline scheduling jobs on m identical parallel machines where the jobs arrive in order of decreasing sizes. We present a complete solution for the preemptive variant of semionline scheduling with decreasing job sizes. We give matching lower and upper bounds on the competitive ratio for any fixed number m of machines; these bounds tend to 1 2 (1+ p 3) ß 1:36603, as the number of machines goes to infinity. Our results are also best possible for randomized algorithms. For the nonpreemptive variant of semionline scheduling with decreasing job sizes, a result of Graham [SIAM J. Appl. Math. 17(1969), 263269] yields a ( 4 3 \Gamma 1 3m ) competitive deterministic nonpreemptive algorithm. For m = 2 machines, we prove that this algorithm is best possible (it is 7 6 competitive). For m = 3 machines we give a lower bound of (1 + p 37)=6 ß 1:18046. Finally, we present a randomized nonpreemptive 8 7 competitive algorithm for m = 2 machines and pro...
Average Case Analyses of List Update Algorithms, with Applications to Data Compression
 Algorithmica
, 1998
"... We study the performance of the Timestamp (0) (TS(0)) algorithm for selforganizing sequential search on discrete memoryless sources. We demonstrate that TS(0) is better than Movetofront on such sources, and determine performance ratios for TS(0) against the optimal offline and static adversaries ..."
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Cited by 22 (4 self)
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We study the performance of the Timestamp (0) (TS(0)) algorithm for selforganizing sequential search on discrete memoryless sources. We demonstrate that TS(0) is better than Movetofront on such sources, and determine performance ratios for TS(0) against the optimal offline and static adversaries in this situation. Previous work on such sources compared online algorithms only with static adversaries. One practical motivation for our work is the use of the Movetofront heuristic in various compression algorithms. Our theoretical results suggest that in many cases using TS(0) in place of Movetofront in schemes that use the latter should improve compression. Tests using implementations on a standard corpus of test documents demonstrate that TS(0) leads to improved compression.
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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. 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...
Online Scheduling of EqualLength Jobs: Randomization and Restarts Help
"... We consider the following scheduling problem. The input is a set of jobs with equal processing times, where each job is specified by its release time and deadline. The goal is to determine a singleprocessor, nonpreemptive schedule of these jobs that maximizes the number of completed jobs. In th ..."
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We consider the following scheduling problem. The input is a set of jobs with equal processing times, where each job is specified by its release time and deadline. The goal is to determine a singleprocessor, nonpreemptive schedule of these jobs that maximizes the number of completed jobs. In the online version, each job arrives at its release time. We give two online algorithms with competitive ratios below 2 and show several lower bounds on the competitive ratios. First, we give a competitive randomized algorithm. Our algorithm needs only one fair random bit, as it chooses one of two (nearly identical) deterministic algorithms, each with probability . We also show a lower bound of for barely random algorithms, that (with arbitrary probability) choose one of two deterministic algorithms. Next, we give a deterministic competitive algorithm in the model that allows restarts, and we show that in this model the ratio is optimal. For randomized algorithms with restarts we show a lower bound of .
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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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.
Competitive Paging And DualGuided OnLine Weighted Caching And Matching Algorithms
, 1991
"... This thesis presents research done by the author on competitive analysis of online problems. An online problem is a problem that is given and solved one piece at a time. An online strategy for solving such a problem must give the solution to each piece knowing only the current piece and preceding ..."
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Cited by 12 (0 self)
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This thesis presents research done by the author on competitive analysis of online problems. An online problem is a problem that is given and solved one piece at a time. An online strategy for solving such a problem must give the solution to each piece knowing only the current piece and preceding pieces, in ignorance of the pieces to be given in the future. We consider online strategies that are competitive (guaranteeing solutions whose costs are within a constant factor of optimal) for several combinatorial optimization problems: paging, weighted caching, the kserver problem, and weighted matching. We introduce variations on the standard model of competitive analysis for paging: allowing randomization, allowing resourcebounded lookahead, and loose competitiveness, in which performance over a range of fast memory sizes is considered and noncompetitiveness is allowed provided the fault rate is insignificant. Each variation leads to substantially better competitive ratios. We prese...
Competitive OnLine Algorithms for Distributed Data Management
, 1999
"... . Competitive online algorithms for data management in a network of processors are studied in this paper. A data object such as a file or a page of virtual memory is to be read and updated by various processors in the network. The goal is to minimize the communication costs incurred in serving a se ..."
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Cited by 11 (0 self)
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. Competitive online algorithms for data management in a network of processors are studied in this paper. A data object such as a file or a page of virtual memory is to be read and updated by various processors in the network. The goal is to minimize the communication costs incurred in serving a sequence of such requests. Distributed data management on important classes of networkstrees and bus based networks, are studied. Optimal algorithms with constant competitive ratios and matching lower bounds are obtained. Our algorithms use different interesting techniques such as work functions [9] and "factoring." Key words. online algorithms, competitive analysis, memory management, data management. AMS subject classifications. 68Q20, 68Q25. 1. Introduction. The management of data in a distributed network is an important and much studied problem in management science, engineering, computer systems and theory [3, 11]. Dowdy and Foster [11] give a comprehensive survey of research in th...
R.: Advice complexity and barely random algorithms
 RAIRO – Theoretical Informatics and Applications
, 2011
"... Abstract. Recently, a new measurement – the advice complexity – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems ..."
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Abstract. Recently, a new measurement – the advice complexity – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a wellknown scheduling problem, job shop scheduling with unit length tasks, and the paging problem were analyzed within this model. We observe some connections between advice complexity and randomization. Our special focus goes to barely random algorithms, i. e., randomized algorithms that use only a constant number of random bits, regardless of the input size. We apply the results on advice complexity to obtain efficient barely random algorithms for both the job shop scheduling and the paging problem. Furthermore, so far, it has not yet been investigated for job shop scheduling how good an online algorithm may perform when only using a very small (e. g., constant) number of advice bits. In this paper, we answer this question by giving both lower and upper bounds, and also improve the best known upper bound for optimal algorithms. 1
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 ..."
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Cited by 6 (2 self)
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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.