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97
On Approximating Arbitrary Metrics by Tree Metrics
 In Proceedings of the 30th Annual ACM Symposium on Theory of Computing
, 1998
"... This paper is concerned with probabilistic approximation of metric spaces. In previous work we introduced the method of ecient approximation of metrics by more simple families of metrics in a probabilistic fashion. In particular we study probabilistic approximations of arbitrary metric spaces by \hi ..."
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Cited by 281 (16 self)
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This paper is concerned with probabilistic approximation of metric spaces. In previous work we introduced the method of ecient approximation of metrics by more simple families of metrics in a probabilistic fashion. In particular we study probabilistic approximations of arbitrary metric spaces by \hierarchically wellseparated tree" metric spaces. This has proved as a useful technique for simplifying the solutions to various problems.
A Dynamic Disk SpinDown Technique for Mobile Computing
, 1996
"... We address the problem of deciding when to spin down the disk of a mobile computer in order to extend battery life. Since one of the most critical resources in mobile computing environments is battery life, good energy conservation methods can dramatically increase the utility of mobile systems. We ..."
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Cited by 169 (8 self)
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We address the problem of deciding when to spin down the disk of a mobile computer in order to extend battery life. Since one of the most critical resources in mobile computing environments is battery life, good energy conservation methods can dramatically increase the utility of mobile systems. We use a simple and efficient algorithm based on machine learning techniques that has excellent performance in practice. Our experimental results are based on traces collected from HP C2474s disks. Using this data, the algorithm outperforms several algorithms that are theoretically optimal in under various worstcase assumptions, as well as the best fixed timeout strategy. In particular, the algorithm reduces the power consumption of the disk to about half (depending on the disk's properties) of the energy consumed by a one minute fixed timeout. Since the algorithm adapts to usage patterns, it uses as little as 88% of the energy consumed by the best fixed timeout computed in retrospect. 1 In...
BEYOND COMPETITIVE ANALYSIS
, 2000
"... The competitive analysis of online algorithms has been criticized as being too crude and unrealistic. We propose refinements of competitive analysis in two directions: The first restricts the power of the adversary by allowingonly certain input distributions, while the other allows for comparisons ..."
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Cited by 135 (3 self)
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The competitive analysis of online algorithms has been criticized as being too crude and unrealistic. We propose refinements of competitive analysis in two directions: The first restricts the power of the adversary by allowingonly certain input distributions, while the other allows for comparisons between information regimes for online decisionmaking. We illustrate the first with an application to the paging problem; as a byproduct we characterize completely the work functions of this important special case of the kserver problem. We use the second refinement to explore the power of lookahead in server and task systems.
Competitive Auctions
"... We study a class of singleround, sealedbid auctions for an item in unlimited supply, such as adigital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages bidders to bid their true valuations) and on all inputs yields profit that is withina co ..."
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Cited by 114 (12 self)
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We study a class of singleround, sealedbid auctions for an item in unlimited supply, such as adigital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages bidders to bid their true valuations) and on all inputs yields profit that is withina constant factor of the profit of the optimal single sale price. We justify the use of optimal single price profit as a benchmark for evaluating a competitive auctions profit. We exhibitseveral randomized competitive auctions and show that there is no symmetric deterministic competitive auction. Our results extend to bounded supply markets, for which we also givecompetitive auctions.
The Competitiveness of OnLine Assignments
, 1992
"... Consider the online problem where a number of servers are ready to provide service to a set of customers. Each customer's job can be handled by any of a subset of the servers. Customers arrive onebyone and the problem is to assign each customer to an appropriate server in a manner that will ..."
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Cited by 110 (19 self)
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Consider the online problem where a number of servers are ready to provide service to a set of customers. Each customer's job can be handled by any of a subset of the servers. Customers arrive onebyone and the problem is to assign each customer to an appropriate server in a manner that will balance the load on the servers. This problem can be modeled in a natural way by a bipartite graph where the vertices of one side (customers) appear one at a time and the vertices of the other side (servers) are known in advance. We derive tight bounds on the competitive ratio in both deterministic and randomized cases. Let n denote the number of servers. In the deterministic case we provide an online algorithm that achieves a competitive ratio of k = dlog 2 ne (up to an additive 1) and prove that this is the best competitive ratio that can be achieved by any deterministic online algorithm. In a similar way we prove that the competitive ratio for the randomized case is k 0 = ln(n) (up to an a...
Navigating In Unfamiliar Geometric Terrain
, 1991
"... . Consider a robot that has to travel from a start location s to a target t in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rath ..."
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Cited by 95 (3 self)
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. Consider a robot that has to travel from a start location s to a target t in an environment with opaque obstacles that lie in its way. The robot always knows its current absolute position and that of the target. It does not, however, know the positions and extents of the obstacles in advance; rather, it finds out about obstacles as it encounters them. We compare the distance walked by the robot in going from s to t to the length of the shortest (obstaclefree) path between s and t in the scene. We describe and analyze robot strategies that minimize this ratio for different kinds of scenes. In particular, we consider the cases of rectangular obstacles aligned with the axes, rectangular obstacles in more general orientations, and wider classes of convex bodies both in two and three dimensions. For many of these situations, our algorithms are optimal up to constant factors. We study scenes with nonconvex obstacles, which are related to the study of mazetraversal. We also show scenes ...
OnLine Routing of Virtual Circuits with Applications to Load Balancing and Machine Scheduling
, 1993
"... In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and descr ..."
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Cited by 87 (4 self)
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In this paper we study the problem of online allocation of routes to virtual circuits (both pointtopoint and multicast) where the goal is to minimize the required bandwidth. We concentrate on the case of permanent virtual circuits (i.e., once a circuit is established, it exists forever), and describe an algorithm that achieves an O(log n) competitive ratio with respect to maximum congestion, where n is the number of nodes in the network. Informally, our results show that instead of knowing all of the future requests, it is sufficient to increase the bandwidth of the communication links by an O(log n) factor. We also show that this result is tight, i.e. for any online algorithm there exists a scenario in which O(log n) increase in bandwidth is necessary. We view virtual circuit routing as a generalization of an online load balancing problem, defined as follows: jobs arrive on line and each job must be assigned to one of the machines immediately upon arrival. Assigning a job to a machine increases this machine’s load by an amount that depends both on the job and on the machine. The goal is to minimize the maximum load. For the related machines case, we describe the first algorithm that achieves constant competitive ratio. For the unrelated case (with n machines), we describe a new method that yields O(log n)competitive
Better Bounds For Online Scheduling
 SIAM JOURNAL ON COMPUTING
, 1997
"... We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986c ..."
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Cited by 86 (5 self)
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We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal, Fiat, Karloff and Vohra [3] gave a deterministic online algorithm that is 1.986competitive. Karger, Phillips and Torng [11] generalized the algorithm and proved an upper bound of 1.945. The best lower bound currently known on the competitive ratio that can be achieved by deterministic online algorithms it equal to 1.837. In this paper we present an improved deterministic online scheduling algorithm that is 1.923competitive, for all m 2. The algorithm is based on a new scheduling strategy, i.e., it is not a generalization of the approach by Bartal et al. Also, the algorithm has a simple structure. Furthermore, we develop a better lower bound. We prove that, for general m, no deterministic online scheduling algorithm can be better than 1.852competitive.
Online file caching
 In Proc. of the 9th Annual ACMSIAM Symp. on Discrete algorithms
, 1998
"... Consider the following file caching problem: in response to a sequence of requests for files, where each file has a specified size and retrieval cost, maintain a cache of files of total size at most some specified k so as to minimize the total retrieval cost. Specifically, when a requested file is n ..."
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Cited by 85 (3 self)
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Consider the following file caching problem: in response to a sequence of requests for files, where each file has a specified size and retrieval cost, maintain a cache of files of total size at most some specified k so as to minimize the total retrieval cost. Specifically, when a requested file is not in the cache, bring it into the cache, pay the retrieval cost, and choose files to remove from the cache so that the total size of files in the cache is at most k. This problem generalizes previous paging and caching problems by allowing objects of arbitrary size and cost, both important attributes when caching files for worldwideweb browsers, servers, and proxies. We give a simple deterministic online algorithm that generalizes many wellknown paging and weightedcaching strategies, including leastrecentlyused, firstinfirstout,
Competitive Routing of Virtual Circuits with Unknown Duration
 In Proc. 5th ACMSIAM Symposium on Discrete Algorithms
, 1994
"... In this paper we present a strategy to route unknown duration virtual circuits in a highspeed communication network. Previous work on virtual circuit routing concentrated on the case where the call duration is known in advance. We show that by allowing O(log n) reroutes per call, we can achieve O(lo ..."
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Cited by 65 (15 self)
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In this paper we present a strategy to route unknown duration virtual circuits in a highspeed communication network. Previous work on virtual circuit routing concentrated on the case where the call duration is known in advance. We show that by allowing O(log n) reroutes per call, we can achieve O(log n) competitive ratio with respect to the maximum load (congestion) for the unknown duration case, were n is the number of nodes in the network. This is in contrast to the ( 4p n)lower bound on the competitive ratio for this case if no rerouting is allowed [3]. Our routing algorithm can be also applied in the context of machine load balancing of tasks with unknown duration. We present an algorithm that makes O(log n) reassignments per task and achieves O(log n) competitive ratio with respect to the load, where n is the number of parallel machines. For a special case of unit load tasks we design a constant competitive algorithm. The previously known algorithms that achieve up to polylogarithmic competitive ratio for load balancing of tasks with unknown duration dealt only with special cases of related machines case and unitload tasks with restricted assignment[4,11].