The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to low-distortion embeddings in low-dimensional 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 probabilistically-approximates another metric space. We prove that any metric space can be probabilistically-approximated by hierarchically well-separated trees (HST) with a polylogarithmic distortion. These metric spaces are "simple" as being: (1) tree metrics. (2) natural for applying a divide-and-conquer algorithmic approach. The technique presented is of particular interest in the context of on-line computation. A large number of on-line al...

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.

This paper addresses the performance of distributed database systems. Specifically, we present an algorithm for dynamic replication of an object in distributed systems. The algorithm is adaptive in the sense that it changes the replication scheme of the object (i.e. the set of processors at which the object is replicated), as changes occur in the read-write pattern of the object (i.e. the number of reads and writes issued by each processor). The algorithm continuously moves the replication scheme towards an optimal one. We show that the algorithm can be combined with the concurrency control and recovery mechanisms of a distributed database management system. The performance of the algorithm is analyzed theoretically and experimentally. On the way we provide a lower bound on the performance of any dynamic replication algorithm.

Enterprise-scale storage systems, which can contain hundreds of host computers and storage devices and up to tens of thousands of disks and logical volumes, are difficult to design. The volume of choices that need to be made is massive, and many choices have unforeseen interactions. Storage system design is tedious and complicated to do by hand, usually leading to solutions that are grossly overprovisioned, substantially under-performing or, in the worst case, both. To solve the configuration nightmare, we present MINERVA: a suite of tools for designing storage systems automatically. MINERVA uses declarative specifications of application requirements and device capabilities; constraint-based formulations of the various subproblems; and optimization techniques to explore the search space of possible solutions. This paper also explores and evaluates the design decisions that went into MINERVA, using specialized micro and macro-benchmarks. We show that MINERVA can successfully handle a workload with substantial complexity (a decision-support database benchmark). MINERVA created a 16-disk design in only a few minutes that achieved the same performance as a 30-disk system manually designed by human experts. Of equal importance, MINERVA was able to predict the resulting system's performance before it was built.

In this paper, we formulate and provide optimal solutions for a broad class of problems in which a decision-maker is required to select from among numerous competing options. The goal of the decision-maker is to select the option that will have the best future performance. This task is made difficult by the constraint that the decision-maker has no way to predict the future performance of any of the options. Somewhat surprisingly, we find that the decision-maker can still (at least in several important scenarios) pick a winner with high probability. Our result has several applications. For example, consider the problem of scheduling background jobs on a network of workstations (NOW) when very little is known about the future speed or availability of each workstation. In this problem, the goal is to schedule each job on a workstation which will have enough idle capacity to complete the job within a reasonable or ...

Distributed paging [BFR92, ABF93b, AK95] deals with the dynamic allocation of copies of files in a distributed network as to minimize the total communication cost over a sequence of read and write requests. Most previous work deals with the file allocation problem [BS89, West91, CLRW93, ABF93a, WY93, Koga93, AK94, LRWY94] where infinite nodal memory capacity is assumed. In contrast the distributed paging problem makes the more realistic assumption that nodal memory capacity is limited. Former work on distributed paging deals with the problem only in the case of a uniform network topology. This paper gives the first distributed paging algorithm for general networks. The algorithm is competitive in storage and communication. The competitive ratios are poly-logarithmic in the total number of network nodes and the diameter of the network. Johns Hopkins University and Lab. for Computer Science, MIT. Supported by Air Force Contract TNDGAFOSR-86-0078, ARO contract DAAL03-86-K-0171, NSF contract 9114440-CCR, DARPA contract N00014J -92-1799, and a special grant from IBM. E-Mail: baruch@theory.lcs.mit.edu. y Department of Computer Science, School of Mathematics, Tel-Aviv University, Tel-Aviv 69978, Israel. Supported by a grant from the Israeli Academy of Sciences. E-mail: yairb@math.tau.ac.il, fiat@math.tau.ac.il 0 1

The Generalized Steiner Problem (GSP) is defined as follows. We are given a graph with non-negative weights and a set of pairs of vertices. The algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path. Off-line generalized Steiner problem approximation algorithms were given in [AKR91, GW92]. We consider the on-line generalized Steiner problem, in which pairs of vertices arrive on-line and are needed to be connected immediately. We give a simple O(log² n) competitive deterministic on-line algorithm. The previous best algorithm was O( p n log n) competitive [WY93]. We also consider the network connectivity leasing problem which is a generalization of the GSP. Here edges of the graph can be either bought or leased for different costs. We provide simple randomized O(log² n) competitive algorithm based on the on-line generalized Steiner problem result.

We study scheduling problems in battery-operated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadline-based settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variable-speed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unit-size jobs. We devise a deterministic constant competitive online algorithm and show that

This paper introduces a framework for evaluating replica placement algorithms (RPA) for content delivery networks (CDN) as well as RPAs from other fields that might be applicable to current or future CDNs. First, the framework classifies and qualitatively compares RPAs using a generic set of primitives that capture problem definitions and heuristics. Second, it provides estimates for the decision times of RPAs using an analytic model. To achieve accuracy, the model takes into account disk accesses and message sizes, in addition to computational complexity and message numbers that have been considered traditionally. Third, it uses the "goodness" of produced placements to compare RPAs even when they have different problem definitions. Based on these evaluations, we identify open issues and potential areas for future research.

This paper is concerned with the page migration (or file migration) problem [BS89] as part of a large class of on-line 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 k-page migration where we wish to maintain k copies of the page. The page migration problems are concerned with a dilemma common to many on-line 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...