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209
Probabilistic Approximation of Metric Spaces and its Algorithmic Applications
 In 37th Annual Symposium on Foundations of Computer Science
, 1996
"... The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized ..."
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Cited by 351 (32 self)
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The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized algorithms for optimization problems on metric spaces, by relating the randomized performance ratio for any metric space to the randomized performance ratio for a set of "simple" metric spaces. We define a notion of a set of metric spaces that probabilisticallyapproximates another metric space. We prove that any metric space can be probabilisticallyapproximated by hierarchically wellseparated trees (HST) with a polylogarithmic distortion. These metric spaces are "simple" as being: (1) tree metrics. (2) natural for applying a divideandconquer algorithmic approach. The technique presented is of particular interest in the context of online computation. A large number of online al...
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 266 (14 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.
Competitive Paging Algorithms
 JOURNAL OF ALGORITHMS 12,685699
, 1991
"... The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. We develop the marking algorithm, a randomized online algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor of ..."
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Cited by 176 (25 self)
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The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. We develop the marking algorithm, a randomized online algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor of 2Hk of optimum. (Where Hk is the kth harmonic number, which is roughly In k.) The best such factor that can be achieved is Hk. This is in contrast to deterministic algorithms, which cannot be guaranteed to be within a factor smaller than k of optimum. An alternative to comparing an online algorithm with the optimum offline algorithm is the idea of comparing it to several other online algorithms. We have obtained results along these lines for the paging problem. Given a set of online algorithms and a set
Searching in The Plane
 INFORMATION AND COMPUTATION
, 1991
"... In this paper we initiate a new area of study dealing with the best way to search a possibly unbounded region for an object. The model for our search algorithms is that we must pay costs proportional to the distance of the next probe position relative to our current position. This model is meant to ..."
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Cited by 146 (0 self)
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In this paper we initiate a new area of study dealing with the best way to search a possibly unbounded region for an object. The model for our search algorithms is that we must pay costs proportional to the distance of the next probe position relative to our current position. This model is meant to give a realistic cost measure for a robot moving in the plane. We also examine the effect of decreasing the amount of a priori information given to search problems. Problems of this type are very simple analogues of nontrivial problems on searching an unbounded region, processing digitized images, and robot navigation. We show that for some simple search problems, the relative information of knowing the general direction of the goal is much higher than knowing the distance to the goal.
The Complexity of Mean Payoff Games on Graphs
 THEORETICAL COMPUTER SCIENCE
, 1996
"... We study the complexity of finding the values and optimal strategies of mean payoff games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudopolynomial time algorithm for the solution of suc ..."
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Cited by 143 (4 self)
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We study the complexity of finding the values and optimal strategies of mean payoff games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudopolynomial time algorithm for the solution of such games, the decision problem for which is in NP " coNP. Finally, we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by Condon. These games are also known to be in NP " coNP, but no polynomial or pseudopolynomial time algorithm is known for them.
A GraphTheoretic Game and its Application to the kServer Problem
 SIAM J. COMPUT
, 1995
"... This paper investigates a zerosum game played on a weighted connected graph G between two players, the tree player and the edge player. At each play, the tree player chooses a spanning tree T and the edge player chooses an edge e. The payoff to the edge player is cost(T; e), defined as follows: If ..."
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Cited by 139 (4 self)
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This paper investigates a zerosum game played on a weighted connected graph G between two players, the tree player and the edge player. At each play, the tree player chooses a spanning tree T and the edge player chooses an edge e. The payoff to the edge player is cost(T; e), defined as follows: If e lies in the tree T then cost(T; e) = 0; if e does not lie in the tree then cost(T; e) = cycle(T; e)=w(e), where w(e) is the weight of edge e and cycle(T; e) is the weight of the unique cycle formed when edge e is added to the tree T. Our main result is that the value of the game on any nvertex graph is bounded above by exp(O( p log n log log n)). The game arises in connection with the kserver problem on a road network; i.e., a metric space that can be represented as a multigraph G in which each edge e represents a road of length w(e). We show that, if the value of the game on G is V al(G; w), then there is a randomized strategy that achieves a competitive ratio of k(1 + V al(G; w)) against any oblivious adversary. Thus, on any nvertex road network, there is a randomized algorithm for the kserver problem that is k exp(O( p log n log log n))competitive against oblivious adversaries. At the heart of our analysis of the game is an algorithm that, for any nvertex weighted, connected multigraph, constructs a spanning tree T such
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 132 (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 Paging With Locality of Reference
 Journal of Computer and System Sciences
, 1991
"... Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations ..."
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Cited by 129 (3 self)
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Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations about the model, citing its inability to discern between LRU and FIFO (algorithms whose performances differ markedly in practice), and the fact that the theoretical competitiveness of LRU is much larger than observed in practice. In addition, we would like to address the following important question: given some knowledge of a program's reference pattern, can we use it to improve paging performance on that program?
Dynamic rightsizing for powerproportional data centers
"... Abstract—Power consumption imposes a significant cost for data centers implementing cloud services, yet much of that power is used to maintain excess service capacity during periods of predictably low load. This paper investigates how much can be saved by dynamically ‘rightsizing ’ the data center ..."
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Cited by 113 (19 self)
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Abstract—Power consumption imposes a significant cost for data centers implementing cloud services, yet much of that power is used to maintain excess service capacity during periods of predictably low load. This paper investigates how much can be saved by dynamically ‘rightsizing ’ the data center by turning off servers during such periods, and how to achieve that saving via an online algorithm. We prove that the optimal offline algorithm for dynamic rightsizing has a simple structure when viewed in reverse time, and this structure is exploited to develop a new ‘lazy ’ online algorithm, which is proven to be 3competitive. We validate the algorithm using traces from two real data center workloads and show that significant costsavings are possible. I.