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14
BuyatBulk Network Design
"... Theessenceofthesimplestbuyatbulknetwork designproblemisbuyingnetworkcapacity"wholesale"toguaranteeconnectivityfromallnetwork nodestoacertaincentralnetworkswitch.Capacityissoldwith"volumediscount":themorecapacityisbought,thecheaperisthepriceperunit ofbandwidth.WeprovideO(log2n)r ..."
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Cited by 98 (0 self)
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Theessenceofthesimplestbuyatbulknetwork designproblemisbuyingnetworkcapacity"wholesale"toguaranteeconnectivityfromallnetwork nodestoacertaincentralnetworkswitch.Capacityissoldwith"volumediscount":themorecapacityisbought,thecheaperisthepriceperunit ofbandwidth.WeprovideO(log2n)randomized approximationalgorithmfortheproblem.This solvestheopenproblemin[15].Theonlypreviouslyknownsolutionswererestrictedtospecial cases(Euclideangraphs)[15]. Wesolveadditionalnaturalvariationsofthe problem,suchasmultisinknetworkdesign,as wellasselectivenetworkdesign.Theseproblems canbeviewedasgeneralizationsofthetheGeneralizedSteinerConnectivityandPrizecollecting salesman(KMST)problems. Intheselectivenetworkdesignproblem,some subsetofkwellsmustbeconnectedtothe(single) renery,sothatthetotalcostisminimized.
Optimal PowerDown Strategies
"... We consider the problem of selecting threshold times to transition a device to lowpower sleep states during an idle period. The twostate case in which there is a single active and a single sleep state is a continuous version of the skirental problem. We consider a generalized version in which the ..."
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Cited by 34 (1 self)
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We consider the problem of selecting threshold times to transition a device to lowpower sleep states during an idle period. The twostate case in which there is a single active and a single sleep state is a continuous version of the skirental problem. We consider a generalized version in which there is more than one sleep state, each with its own power consumption rate and transition costs. We give an algorithm that, given a system, produces a deterministic strategy whose competitive ratio is arbitrarily close to optimal. We also give an algorithm to produce the optimal online strategy given a system and a probability distribution that generates the length of the idle period. We also give a simple algorithm that achieves a competitive ratio of 3 + 2 √ 2 ≈ 5.828 for any system.
On the Bahncard Problem
 In Proceedings of the 4th Annual International Computing and Combinatorics Conference (COCOON98), Taipei (ROC
, 1998
"... In this paper, we generalize the SkiRental Problem to the Bahncard Problem which is an online problem of practical relevance for all travelers. The Bahncard is a railway pass of the Deutsche Bundesbahn (the German railway company) which entitles its holder to a 50% price reduction on nearly all ..."
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Cited by 13 (0 self)
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In this paper, we generalize the SkiRental Problem to the Bahncard Problem which is an online problem of practical relevance for all travelers. The Bahncard is a railway pass of the Deutsche Bundesbahn (the German railway company) which entitles its holder to a 50% price reduction on nearly all train tickets. It costs 240 DM, and it is valid for 12 months. Similar bus or railway passes can be found in many other countries. For the common traveler, the decision at which time to buy a Bahncard is a typical online problem, because she usually does not know when and where she will travel next. We show that the greedy algorithm applied by most travelers and clerks at ticket offices is not better in the worst case than the trivial algorithm which never buys a Bahncard. We present two optimal deterministic online algorithms, an optimistic one and a pessimistic one. We further give a lower bound for randomized online algorithms and present an algorithm which we conjecture to be optimal; a proof of the conjecture is given for a special case of the problem. It turns out that the optimal competitive ratio only depends on the price reduction factor (50% for the German Bahncard Problem), but does not depend on the price or validity period of a Bahncard. Keywords: Bahncard Problem, competitive analysis, online algorithm, SkiRental Problem ? The author was partially supported by the EU ESPRIT LTR Project No. 20244 (ALCOMIT). He was further supported by a Habilitation Scholarship of the German Research Foundation (DFG). 1 1
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 11 (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.
Dynamic Session Management for Static and Mobile Users: A Competitive OnLine Algorithmic Approach
"... ..."
Delayed Information and Action in OnLine Algorithms
 39th IEEE symposium on Foundations of Computer Science
, 1998
"... Most online analysis assumes that, at each time step, all relevant information up to that time step is available and a decision has an immediate effect. In many online problems, however, the time relevant information is available and the time a decision has an effect may be decoupled. For example, ..."
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Cited by 3 (0 self)
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Most online analysis assumes that, at each time step, all relevant information up to that time step is available and a decision has an immediate effect. In many online problems, however, the time relevant information is available and the time a decision has an effect may be decoupled. For example, when making an investment, one might not have completely uptodate information on market prices. Similarly, a buy or sell order might only be executed some time later in the future. We introduce and explore natural delayed models for several wellknown online problems. Our analyses demonstrate the importance of considering timeliness in determining the competitive ratio of an online algorithm. For many problems, we demonstrate that there exist algorithms with small competitive ratios even when large delays affect the timeliness of information and the effect of decisions.
RENT, LEASE OR BUY: RANDOMIZED ALGORITHMS FOR MULTISLOPE SKI RENTAL
"... Abstract. In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a onetime setup cost (“buying price”), and cost proportional to the duration of the us ..."
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Abstract. In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a onetime setup cost (“buying price”), and cost proportional to the duration of the usage (“rental rate”). The larger the price, the smaller the rent. The actual usage time is determined by an adversary, and the goal of an algorithm is to minimize the cost by choosing the best option at any point in time. Multislope Ski Rental is a natural generalization of the classical Ski Rental problem (where the only options are pure rent and pure buy), which is one of the fundamental problems of online computation. The Multislope Ski Rental problem is an abstraction of many problems where online decisions cannot be modeled by just two options, e.g., power management in systems which can be shut down in parts. In this paper we study randomized algorithms for Multislope Ski Rental. Our results include the best possible online randomized strategy for any additive instance, where the cost of switching from one option to another is the difference in their buying prices; and an algorithm that produces an ecompetitive randomized strategy for any (nonadditive) instance. 1.
Competitive Optimal OnLine Leasing
, 1999
"... Consider an online player who needs some equipment (e.g., a computer) for an initially unknown number of periods. At the start of each period it is determined whether the player will need the equipment during the current period and the player has two options: to pay a leasing fee c and rent the eq ..."
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Consider an online player who needs some equipment (e.g., a computer) for an initially unknown number of periods. At the start of each period it is determined whether the player will need the equipment during the current period and the player has two options: to pay a leasing fee c and rent the equipment for the period, or to buy it for a larger amount P. The total cost incurred by the player is the sum of all leasing fees and perhaps one purchase. The above problem, called the leasing problem (in computer science folklore it is known as the skirental problem), has received considerable attention in the economic literature. Using the competitive ratio as a performance measure this paper is concerned with determining the optimal competitive online policy for the leasing problem. For the simplest version of the leasing problem (as described above) it is known and readily derived that the optimal deterministic competitive performance is achieved by leasing for the first k − 1 times and then buying, where k = P/c. This strategy pays at most 2 − 1/k times the optimal offline cost. When considering alternative financial transactions one must consider their net present value. Thus, accounting for the interest rate is an essential feature of any reasonable financial model. In this paper we determine both deterministic and randomized optimal online leasing strategies while accounting for the interest
www.stacsconf.org RENT, LEASE OR BUY: RANDOMIZED ALGORITHMS FOR MULTISLOPE SKI RENTAL
, 2008
"... Abstract. In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a onetime setup cost (“buying price”), and cost proportional to the duration of the us ..."
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Abstract. In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a onetime setup cost (“buying price”), and cost proportional to the duration of the usage (“rental rate”). The larger the price, the smaller the rent. The actual usage time is determined by an adversary, and the goal of an algorithm is to minimize the cost by choosing the best option at any point in time. Multislope Ski Rental is a natural generalization of the classical Ski Rental problem (where the only options are pure rent and pure buy), which is one of the fundamental problems of online computation. The Multislope Ski Rental problem is an abstraction of many problems where online decisions cannot be modeled by just two options, e.g., power management in systems which can be shut down in parts. In this paper we study randomized algorithms for Multislope Ski Rental. Our results include the best possible online randomized strategy for any additive instance, where the cost of switching from one option to another is the difference in their buying prices; and an algorithm that produces an ecompetitive randomized strategy for any (nonadditive) instance. 1.
Abstract
"... We consider the problem of selecting threshold times to transition a device to lowpower sleep states during an idle period. The twostate case in which there is a single active and a single sleep state is a continuous version of the skirental problem. We consider a generalized version in which the ..."
Abstract
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We consider the problem of selecting threshold times to transition a device to lowpower sleep states during an idle period. The twostate case in which there is a single active and a single sleep state is a continuous version of the skirental problem. We consider a generalized version in which there is more than one sleep state, each with its own power consumption rate and transition costs. We give an algorithm that, given a system, produces a deterministic strategy whose competitive ratio is arbitrarily close to optimal. We also give an algorithm to produce the optimal online strategy given a system and a probability distribution that generates the length of the idle period. We also give a simple algorithm that achieves a competitive ratio of 3 + 2 √ 2 ≈ 5.828 for any system. 1