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61
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 260 (13 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.
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 118 (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.
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 90 (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 ...
Competitive Auctions
, 2002
"... We study a class of singleround, sealedbid auctions for items in unlimited supply, such as digital goods. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages buyers to bid their utility) and yields profit that is roughly within a constant factor of ..."
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Cited by 79 (11 self)
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We study a class of singleround, sealedbid auctions for items in unlimited supply, such as digital goods. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages buyers to bid their utility) and yields profit that is roughly within a constant factor of the profit of optimal fixed pricing for all inputs. We justify the use of optimal fixed pricing as a benchmark for evaluating competitive auction profit. We show that several randomized auctions are truthful and competitive and that no truthful deterministic auction is competitive. Our results extend to bounded supply markets, for which we also get truthful and competitive auctions.
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 68 (2 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,
On the limits of cacheobliviousness
 IN PROC. 35TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 2003
"... In this paper, we present lower bounds for permuting and sorting in the cacheoblivious model. We prove that (1) I/O optimal cacheoblivious comparison based sorting is not possible without a tall cache assumption, and (2) there does not exist an I/O optimalcacheoblivious algorithm for permuting, ..."
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Cited by 40 (7 self)
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In this paper, we present lower bounds for permuting and sorting in the cacheoblivious model. We prove that (1) I/O optimal cacheoblivious comparison based sorting is not possible without a tall cache assumption, and (2) there does not exist an I/O optimalcacheoblivious algorithm for permuting, not even in the presence of a tall cache assumption.Our results for sorting show the existence of an inherent tradeoff in the cacheoblivious model between the strength of the tall cache assumption and the overhead for the case M >> B, and show that Funnelsort and recursive binary mergesort are optimal algorithms in the sense that they attain this tradeoff.
Geometric Algorithms for Online Optimization
 Journal of Computer and System Sciences
, 2002
"... In this paper, we consider a natural online version of linear optimization: the problem has to be solved repeatedly over a sequence of periods, where the objective direction for the upcoming period is unknown. This models online versions of optimization problems, such as maxcut, variants of cluster ..."
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Cited by 35 (1 self)
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In this paper, we consider a natural online version of linear optimization: the problem has to be solved repeatedly over a sequence of periods, where the objective direction for the upcoming period is unknown. This models online versions of optimization problems, such as maxcut, variants of clustering, and also the classic online binary search tree problem. We present algorithms for this problem that are (1 + epsilon)competitive with the optimal static solution chosen in hindsight. Our algorithms and proofs are motivated by geometric considerations.
Scanning and traversing: maintaining data for traversals in a memory hierarchy
 In Proceedings of the 10th Annual European Symposium on Algorithms
, 2002
"... Abstract. We study the problem of maintaining a dynamic ordered set subject to insertions, deletions, and traversals of k consecutive elements. This problem is trivially solved on a RAM and on a simple twolevel memory hierarchy. We explore this traversal problem on more realistic memory models: the ..."
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Cited by 32 (11 self)
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Abstract. We study the problem of maintaining a dynamic ordered set subject to insertions, deletions, and traversals of k consecutive elements. This problem is trivially solved on a RAM and on a simple twolevel memory hierarchy. We explore this traversal problem on more realistic memory models: the cacheoblivious model, which applies to unknown and multilevel memory hierarchies, and sequentialaccess models, where sequential block transfers are less expensive than random block transfers. 1
Competitive Auctions for Multiple Digital Goods
 In Proc. 9th European Symposium on Algorithms
, 2001
"... Abstract Competitive auctions encourage consumers to bid their utility values while achieving revenueclose to that of fixed pricing with perfect market analysis. These auctions were introduced in [4] in the context of selling an unlimited number of copies of a single item (e.g.,rights to watch amovi ..."
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Cited by 30 (8 self)
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Abstract Competitive auctions encourage consumers to bid their utility values while achieving revenueclose to that of fixed pricing with perfect market analysis. These auctions were introduced in [4] in the context of selling an unlimited number of copies of a single item (e.g.,rights to watch amovie broadcast). In this paper we study the case of multiple items (e.g.,concurrent broadcast of several movies). We show several auctions that are competitive for this case. The underlyingauction mechanisms are more sophisticated than in the single item case,and require solving an interesting optimization problem.
On Page Migration and Other Relaxed Task Systems
, 1997
"... This paper is concerned with the page migration (or file migration) problem [BS89] as part of a large class of online problems. The page migration problem deals with the management of pages residing in a network of processors. In the classical problem there is only one copy of each page which is ..."
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Cited by 28 (4 self)
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This paper is concerned with the page migration (or file migration) problem [BS89] as part of a large class of online problems. The page migration problem deals with the management of pages residing in a network of processors. In the classical problem there is only one copy of each page which is accessed by different processors over time. The page is allowed to be migrated between processors. However a migration incurs higher communication cost than an access (proportionally to the page size). The problem is that of deciding when and where to migrate the page in order to lower access costs. A more general setting is the kpage migration where we wish to maintain k copies of the page. The page migration problems are concerned with a dilemma common to many online problems: determining when is it beneficial to make configuration changes. We deal with the relaxed task systems model which captures a large class of problems of this type, that can be described as the generalizati...