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...

Advances in network and processor technology have greatly changed the communication and computational power of local-area workstation clusters. However, operating systems still treat workstation clusters as a collection of loosely-connected processors, where each workstation acts as an autonomous and independent agent. This operating system structure makes it difficult to exploit the characteristics of current clusters, such as low-latency communication, huge primary memories, and high-speed processors, in order to improve the performance of cluster applications. This paper describes the design and implementation of global memory management in a workstation cluster. Our objective is to use a single, unified, but distributed memory management algorithm at the lowest level of the operating system. By managing memory globally at this level, all system- and higher-level software, including VM, file systems, transaction systems, and user applications, can benefit from available cluster memory. We have implemented our algorithm in the OSF/1 operating system running on an ATM-connected cluster of DEC Alpha workstations. Our measurements show that on a suite of memory-intensive programs, our system improves performance by a factor of 1.5 to 3.5. We also show that our algorithm has a performance advantage over others that have been proposed in the past.

We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so as to optimize communication costs, but multiple copies must be kept consistent and at least one copy must be stored somewhere in the network at all times. We deal with competitive algorithms for minimizing communication costs, over arbitrary sequences of reads and writes, and arbitrary network topologies. We define the constrained file allocation problem to be the solution of many individual file allocation problems simultaneously, subject to the constraints of local memory size. We give competitive algorithms for this problem on the uniform network topology. We then introduce distributed competitive algorithms for on-line data tracking (a generalization of mobile user tracking [AP1...

This paper deals with the file allocation problem [BFR92] concerning the dynamic optimization of communication costs to access data in a distributed environment. We develop a dynamic file re-allocation strategy that adapts on-line to a sequence of read and write requests whose location and relative frequencies are completely unpredictable. This is achieved by replicating the file in response to read requests and migrating the file in response to write requests while paying the associated communications costs, so as to be closer to processors that access it frequently. We develop first explicit deterministic on-line strategy assuming existence of global information about the state of the network; previous (deterministic) solutions were complicated and more expensive. Our solution has (optimal) logarithmic competitive ratio. The paper also contains the first explicit deterministic data migration [BS89] algorithm achieving the best known competitive ratio for this problem. Using somewhat ...

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

We prove upper and lower bounds on the competitiveness of randomized algorithms for the list update problem of Sleator and Tarjan. We give a simple and elegant randomized algorithm that is more competitive than the best previous randomized algorithm due to Irani. Our algorithm uses randomness only during an initialization phase, and from then on runs completely deterministically. It is the first randomized competitive algorithm with this property to beat the deterministic lower bound. We generalize our approach to a model in which access costs are fixed but update costs are scaled by an arbitrary constant d. We prove lower bounds for deterministic list update algorithms and for randomized algorithms against oblivious and adaptive on-line adversaries. In particular, we show that for this problem adaptive on-line and adaptive off-line adversaries are equally powerful. 1 Introduction Recently much attention has been given to competitive analysis of on-line algorithms [7, 20, 22, 25]. Ro...

FlashDB is a self-tuning database optimized for sensor networks using NAND flash storage. In practical systems flash is used in different packages such as on-board flash chips, compact flash cards, secure digital cards and related formats. Our experiments reveal non-trivial differences in their access costs. Furthermore, databases may be subject to different types of workloads. We show that existing databases for flash are not optimized for all types of flash devices or for all workloads and their performance is thus suboptimal in many practical systems. FlashDB uses a novel self-tuning index that dynamically adapts its storage structure to workload and underlying storage device. We formalize the self-tuning nature of an index as a two-state task system and propose a 3-competitive online algorithm that achieves the theoretical optimum. We also provide a framework to determine the optimal size of an index node that minimizes energy and latency for a given device. Finally, we propose optimizations to further improve the performance of our index. We prototype and compare different indexing schemes on multiple flash devices and workloads, and show that our indexing scheme outperforms existing schemes under all workloads and flash devices we consider.

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.

. The page migration problem is to manage a globally addressed shared memory in a multiprocessor system. Each physical page of memory is located at a given processor, and memory references to that page by other processors incur a cost proportional to the network distance. At times the page may migrate between processors at cost proportional to the distance times D, a page size factor. The problem is to schedule movements on-line so that the total cost of memory references is within a constant factor c of the best off-line schedule. An algorithm that does so is called c-competitive. Black and Sleator gave 3-competitive deterministic on-line algorithms for uniform networks (complete graphs with unit edge lengths) and for trees with arbitrary edge lengths. No good deterministic algorithm is known for general networks with arbitrary edge lengths. We present randomized algorithms for the migration problem that are both simple and better than 3-competitiveagainst an oblivious adversary. We ...

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...