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44
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Competitive Routing of Virtual Circuits in ATM networks
 IEEE Journal on Selected Areas in Communications
"... Classical routing and admission control strategies achieve provably good performance by relying on an assumption that the virtual circuits arrival pattern can be described by some a priori known probabilistic model. Recently a new online routing framework, based on the notion of competitive analysis ..."
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Cited by 90 (0 self)
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Classical routing and admission control strategies achieve provably good performance by relying on an assumption that the virtual circuits arrival pattern can be described by some a priori known probabilistic model. Recently a new online routing framework, based on the notion of competitive analysis, was proposed. This framework is geared towards design of strategies that have provably good performance even in the case where there are no statistical assumptions on the arrival pattern and parameters of the virtual circuits. The online strategies motivated by this framework are quite different from the minhop and reservationbased strategies. This paper surveys the online routing framework, the proposed routing and admission control strategies, and discusses some of the implementation issues. Research supported by NSF CCR9304971, ARO DAAH049510121, and by Terman Fellowship. EMail: plotkin@cs.stanford.edu, URL: http://theory.stanford.edu/people/plotkin/plotkin.html. 1 Introducti...
On the Online Bin Packing Problem
 Journal of the ACM
, 2001
"... A new framework for analyzing online bin packing algorithms is presented. This framework presents a unified way of explaining the performance of algorithms based on the Harmonic approach [3, 5, 8, 10, 11, 12]. Within this framework, it is shown that a new algorithm, Harmonic++, has asymptotic perfor ..."
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Cited by 59 (3 self)
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A new framework for analyzing online bin packing algorithms is presented. This framework presents a unified way of explaining the performance of algorithms based on the Harmonic approach [3, 5, 8, 10, 11, 12]. Within this framework, it is shown that a new algorithm, Harmonic++, has asymptotic performance ratio at most 1.58889. It is also shown that the analysis of Harmonic+1 presented in [11] is incorrect; this is a fundamental logical flaw, not an error in calculation or an omitted case. The asymptotic performance ratio of Harmonic+1 is at least 1.59217. Thus Harmonic++ provides the best upper bound for the online bin packing problem to date.
Optimal Search and OneWay Trading Online Algorithms
 ALGORITHMICA
, 2001
"... This paper is concerned with the time series search and oneway trading problems. In the (time series) search problem a player is searching for the maximum (or minimum) price in a sequence that unfolds sequentially, one price at a time. Once during this game the player can decide to accept the curre ..."
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Cited by 34 (0 self)
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This paper is concerned with the time series search and oneway trading problems. In the (time series) search problem a player is searching for the maximum (or minimum) price in a sequence that unfolds sequentially, one price at a time. Once during this game the player can decide to accept the current price p in which case the game ends and the player's payoff is p.Intheoneway trading problem a trader is given the task of trading dollars to yen. Each day, a new exchange rate is announced and the trader must decide how many dollars to convert to yen according to the current rate. The game ends when the trader trades his entire dollar wealth to yen and his payoff is the number of yen acquired. The search and oneway trading are intimately related. Any (deterministic or randomized) oneway trading algorithm can be viewed as a randomized search algorithm. Using the competitive ratio as a performance measure we determine the optimal competitive performance for several variants of these problems. In particular, we show that a simple threatbased strategy is optimal and we determine its competitive ratio which yields, for realistic values of the problem parameters, surprisingly low competitive ratios. We also consider and analyze a oneway trading game played against an adversary called Nature where the online player knows the probability distribution of the maximum exchange rate and that distribution has been chosen by Nature. Finally, we consider some applications for a special case of portfolio selection called twoway trading in which the trader may trade back and forth between cash and one asset.
BestFit BinPacking with Random Order
 In 7th Annual ACMSIAM Symposium on Discrete Algorithms
, 1997
"... Bestfit is the best known algorithm for online binpacking, in the sense that no algorithm is known to behave better both in the worst case (when Bestfit has performance ratio 1.7) and in the average uniform case, with items drawn uniformly in the interval [0; 1] (then Bestfit has expected wasted ..."
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Cited by 31 (0 self)
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Bestfit is the best known algorithm for online binpacking, in the sense that no algorithm is known to behave better both in the worst case (when Bestfit has performance ratio 1.7) and in the average uniform case, with items drawn uniformly in the interval [0; 1] (then Bestfit has expected wasted space O(n 1=2 (log n) 3=4 )). In practical applications, Bestfit appears to perform within a few percent of optimal. In this paper, in the spirit of previous work in computational geometry, we study the expected performance ratio, taking the worstcase multiset of items L, and assuming that the elements of L are inserted in random order, with all permutations equally likely. We show a lower bound of 1:08 : : : and an upper bound of 1:5 on the random order performance ratio of Bestfit. The upper bound contrasts with the result that in the worst case, any (deterministic or randomized) online binpacking algorithm has performance ratio at least 1:54 : : :. 1 Introduction 1.1 Backgroun...
The Statistical Adversary Allows Optimal MoneyMaking Trading Strategies (Extended Abstract)
, 1993
"... Andrew Chou Jeremy Cooperstock y Ran ElYaniv z Michael Klugerman x Tom Leighton  November, 1993 Abstract The distributional approach and competitive analysis have traditionally been used for the design and analysis of online algorithms. The former assumes a specific distribution on inputs, whil ..."
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Cited by 22 (4 self)
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Andrew Chou Jeremy Cooperstock y Ran ElYaniv z Michael Klugerman x Tom Leighton  November, 1993 Abstract The distributional approach and competitive analysis have traditionally been used for the design and analysis of online algorithms. The former assumes a specific distribution on inputs, while the latter assumes inputs are chosen by an unrestricted adversary. This paper employs the statistical adversary (recently proposed by Raghavan) to analyze and design online algorithms for twoway currency trading. The statistical adversary approach may be viewed as a hybrid of the distributional approach and competitive analysis. By statistical adversary, we mean an adversary that generates input sequences, where each sequence must satisfy certain general statistical properties. The online algorithms presented in this paper have some very attractive properties. For instance, the algorithms are moneymaking; they are guaranteed to be profitable when the optimal offli...
Competitive solutions for online financial problems
 ACM Comput. Surv
, 1998
"... This article surveys results concerning online algorithms for solving problems related to the management of money and other assets. In particular, the survey focuses on search, replacement, and portfolio selection problems. ..."
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Cited by 14 (0 self)
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This article surveys results concerning online algorithms for solving problems related to the management of money and other assets. In particular, the survey focuses on search, replacement, and portfolio selection problems.
An Optimal Online Algorithm for Bounded Space VariableSized Bin Packing
 SIAM Journal on Discrete Mathematics
, 2000
"... An online algorithm for variablesized bin packing, based on the Harmonic algorithm of Lee and Lee [11], is investigated. This algorithm was proposed by Csirik [4], who proved an upper bound on its performance ratio. The upper bound is improved. Further, it is shown that the algorithm is optimal amo ..."
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Cited by 13 (4 self)
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An online algorithm for variablesized bin packing, based on the Harmonic algorithm of Lee and Lee [11], is investigated. This algorithm was proposed by Csirik [4], who proved an upper bound on its performance ratio. The upper bound is improved. Further, it is shown that the algorithm is optimal among those which use bounded space. An interesting feature of the analysis is that, although it is shown that our algorithm achieves a performance ratio arbitrarily close to the optimum value, it is not known precisely what that value is. The case where bins of capacity 1 and 2 (0; 1) are used is studied in greater detail. It is shown that among algorithms which are allowed to chose , the optimal performance ratio lies in [1:37530; 1:37532]. 1 Introduction Bin packing is one of the oldest and most well studied problems in computer science [5, 3]. Ideas which originated in the study of the bin packing problem have helped shape computer science as we know it today. The idea of nding the bes...
The Design and Analysis of Scheduling Algorithms for RealTime and FaultTolerant Computer Systems
, 1994
"... Many applications are not feasible without the support of realtime and faulttolerant computer systems. Timeliness and dependability are properties that predominantly distinguish a realtime system and a faulttolerant system from other computer systems. In this thesis we address the issue of suppo ..."
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Cited by 12 (4 self)
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Many applications are not feasible without the support of realtime and faulttolerant computer systems. Timeliness and dependability are properties that predominantly distinguish a realtime system and a faulttolerant system from other computer systems. In this thesis we address the issue of supporting timeliness and dependability by studying four fundamental scheduling problems that are inherent to these systems. The realtime systems we consider are the ones in which tasks are executed periodically; each task has an infinite number of requests and there are multiple tasks being executed. There arises a problem of scheduling all requests of the tasks on as few processors as possible such that not a single deadline is missed. This problem has optimal solutions for a single processor system when tasks are preemptive; the RateMonotonic (RM) algorithm is optimal for fixedpriority assignment and the Earliest Deadline First (EDF) is optimal for dynamic priority assignment. However, the problem is intractable for a multiprocessor system. The main goal of this thesis is to design and analyze algorithms for the problem of scheduling a set of periodic, preemptive tasks on as few processors as possible such that task deadlines are met on each processor by the RM algorithm. We give the best online and offline scheduling algorithms for this problem to date with regard to worst case performance and average case performance. The worst case performance of the algorithms is shown to have constant tight bounds through complex analysis and the average case performance is assessed by conducting simulation experiments. Several new schedulability conditions are also obtained for the RM scheduling. The second problem is defined the same way as the first one except that instead of one v...
New Bounds for VariableSized Online Bin Packing
 SIAM Journal on Computing
, 2003
"... In the variablesized online bin packing problem, one has to assign items to bins one by one. The bins are drawn from some fixed set of sizes, and the goal is to minimize the sum of the sizes of the bins used. We present new algorithms for this problem and show upper bounds for them which improve on ..."
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Cited by 9 (5 self)
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In the variablesized online bin packing problem, one has to assign items to bins one by one. The bins are drawn from some fixed set of sizes, and the goal is to minimize the sum of the sizes of the bins used. We present new algorithms for this problem and show upper bounds for them which improve on the best previous upper bounds. We also show the first general lower bounds for this problem. The case in which bins of two sizes, I and c C (0, 1), are used is studied in detail. This investigation leads us to the discovery of several interesting fractallike curves.