D. L. Black and D. D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie Mellon University, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....we apply the delayed action model to the general class of relaxed metrical task systems [4, 9] Relaxed task systems are an abstract model for problems where one has to decide when it is appropriate to make expensive configuration changes. This class includes the ski rental problem, page migration [13], file replication [13] network leasing [4] and other problems (see [9] We extend the results of [4, 9] to apply to relaxed task systems with delayed action, e#ectively handling the delayed models of an entire general class of problems. Related Work: In subsequent sections, we will mention ....

....model to the general class of relaxed metrical task systems [4, 9] Relaxed task systems are an abstract model for problems where one has to decide when it is appropriate to make expensive configuration changes. This class includes the ski rental problem, page migration [13] file replication [13], network leasing [4] and other problems (see [9] We extend the results of [4, 9] to apply to relaxed task systems with delayed action, e#ectively handling the delayed models of an entire general class of problems. Related Work: In subsequent sections, we will mention related work relevant to ....

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D.L. Black and D.D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.

....practice. The development of on line algorithms in a tree network utilizes two important techniques: work function and factoring. Via dynamic programming formulation, the work function [12] reconstructs step by step the actions taken by an algorithm given an input sequence. The factoring technique [13] transforms a FA problem in a tree into FA problems on individual edges of the tree, such that the total cost of a tree FA problem is the sum of individual costs of edge FA problems. C. Our contributions The primary contributions in this paper are: 1) A unified framework for the replication ....

D. L. Black and D. D. Sleator, "Competitive algorithms for replication and migration problems," Tech. Rep., Carnegie Mellon University, 1989.

....that uses page migration only for data distribution. 6 Related work The idea of dynamic page migration has been developed since the appearance of the first commercial NUMA architectures more than a decade ago. Aside from several theoretical foundations on the algorithmic side of page migration [5, 6], mechanisms for dynamic page migration in the operating system have been implemented on systems like the BBN Butterfly Plus and the IBM RP3 [7, 15] These systems had no hardware support for cache coherence and the cost of shared memory accesses was determined solely by the location of pages in ....

D. Black and D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, November 1989.

.... requests are to node B) or the two server problem on a triangle with side lengths (1; N; N) nodes A and B have distance 1; initially, the two servers sit on nodes A and C, and the requests alternate between A and B) For the page replication problem, there are optimal 2 competitive deterministic [4] and (1 1 N ) N (1 1 N ) N Gamma1 competitive randomized algorithms against an oblivious adversary [1, 8] A similar bound was obtained by Karlin et al. 6] for the problem of two servers on a (1; N; N) triangle. In this paper, we consider the Bahncard Problem which contains the ....

....if s 1 = s 3 = 0 and if s 2 is maximal, and the definition of SUM implies s 2 c crit . ut So SUM is optimal for the Bahncard Problem. In particular, it is 3 2 competitive for the GBP. For the SRP, it behaves like the well known optimal 2 competitive algorithm which buys at the N th request [4]. However, SUM tends to be pessimistic about the future : It always buys at the latest possible time, namely after it has seen enough regular requests to know for sure that an optimal algorithm would already have bought a Bahncard. In contrast to that, we consider the Optimistic Sum Algorithm ....

D.L. Black and D.D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie Mellon University, 1989.

....y Amos Fiat y Abstract 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 ....

....references. In theory community, only special restricted versions of the problem have been previously addressed, such as 1 ffl Uniprocessor paging [ST85, KMRS88, FKL 88, RS89] the underlying communication networks consists of a single link from memory to cache. ffl File allocation [BS89, BFR92, West91, CLRW93, ABF93a, WY93, Koga93, AK94, LRWY94] infinite nodal capacity is assumed. ffl Uniform network topology [BFR92, ABF93b, AK95] network with clique topology where distances between any pair of nodes are the same. 2 The Model and the Problem 2.1 Basics Network Model. The ....

D.L. Black and D.D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.

....on line algorithms for this problem. 1 Introduction Many on line problems of great practical importance arise in distributed data management. As a result, there has recently been a lot of research interest in problems such as page migration, page replication and distributed paging, see e.g. [BS89, W91, BFR92, ABF93a, ABF93b, K93, AK94, LRWY94]. In page migration and replication problems, a set of memory pages must be distributed in a network of processors, each of which has its local memory, so that a sequence of memory accesses can be processed efficiently. Specifically, the goal is to minimize the communication cost. If a processor p ....

....That is, whenever we want to move or copy a page into the local memory of a processor p, there is room for it; no other page needs to be dropped from p s memory. Assuming infinite local capacity, on line migration and replication algorithms with a constant competitive ratio can be developed [BS89, W91, ABF93a, LRWY94]. For instance, Black and Sleator presented a deterministic 3 competitive migration algorithm for the case that the network topology is a tree or a complete uniform network (any two processors are connected by an edge of length 1) For arbitrary network topologies, Awerbuch et al. ABF93a] showed ....

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D.L. Black and D.D. Sleator. Competitive algorithms for replication and migration problems. Technical Report Carnegie Mellon University, CMU-CS-89-201, 1989.

....known, see [12,14,55] In the file replication problem, files are assumed to be read only and we have to determine which local memories should contain copies of the read only files. Constant competitive algorithms are known for specific network topologies such as uniform networks, trees and rings [4,23]. A uniform network is a complete graph in which all edges have the same length. All of the solutions mentioned above assume that the local memories of the processors have infinite capacity. Bartal et al. 15] showed that if the local memories have finite capacity, then no online algorithm for ....

D.L. Black and D.D. Sleator. Competitive algorithms for replication and migration problems. Technical Report Carnegie Mellon University, CMU-CS-89-201, 1989.

.... Page Migration and Other Relaxed Task Systems Yair Bartal Moses Charikar y Piotr Indyk z Abstract 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 ....

.... Sheng86, SD89] However all existing heuristics heavily rely on the non realistic prior knowledge of potential usage patterns of the databases (see the survey paper by Gavish and Sheng [GS90] Theoretical work on page migration, making no such assumptions, was initiated by Black and Sleator [BS89] comparing the cost of an on line page migration algorithm to the cost of an optimal algorithm (known as competitive analysis [ST85] Page migration problems have been further studied in [West91, BFR92, CLRW93, ABF93a, ABF93b, LRWY94, AK95, ABF96, Bart96] We study this problem and the more ....

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D.L. Black and D.D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.

....the more complex constrained file allocation problem, but these names may conflict with other usage. We consider the competitive performance [ST, KMRS, MMS, BLS, BBKTW] of algorithms for these problems, and present algorithms with an optimal or nearly optimal competitive ratio. Black and Sleator [BS] consider competitive algorithms for two partial components of the file allocation family of problems. Our file allocation problem may be viewed as the combined solution to the two subproblems defined in [BS] Another issue is that of global versus distributed management. The question of file ....

....present algorithms with an optimal or nearly optimal competitive ratio. Black and Sleator [BS] consider competitive algorithms for two partial components of the file allocation family of problems. Our file allocation problem may be viewed as the combined solution to the two subproblems defined in [BS]. Another issue is that of global versus distributed management. The question of file allocation is quite different in the context of disk management in a small network of large mainframes versus local cache management in a large scale multiprocessing computer. We show that our competitive data ....

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D.L. Black and D.D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.

....the benchmark that uses page migration only for data distribution. 5. Related work The idea of dynamic page migration has been employed since the appearance of the first commercial NUMA architectures more than a decade ago. Aside from several important theoretical foundations on page migration [21, 22] mechanisms for automatic page migration by the operating system have been implemented in systems like the BBN Butterfly Plus and the IBM RP3 [11, 12] These systems had no hardware supported cache coherence and the cost of shared memory accesses was solely determined by the location of pages in ....

D. Black and D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201. Department of Computer Science, Carnegie-Mellon University, 1989.

....with the competitive analysis [ST85] of distributed data management problems. This approach makes no prior assumptions on the input sequence, and provides a worst case guarantee on the performance of the algorithms. The following are the main problems we survey: The file migration problem [BS89] allows only one copy of each file to be kept in the network. The file allocation problem [BFR92] deals with the more general case where files may be replicated and deleted in response to a sequence of read and write requests. The distributed paging problem [BFR92] further generalizes the ....

....times. An on line file allocation algorithm must minimize communication costs, over arbitrary sequences of read and write requests issued at different locations over the network. The file allocation problem can be viewed as the generalization of two other basic problems due to Black and Sleator [BS89] The file replication problem where only read requests are issued, and the file migration problem where only one copy of the file may be kept in the network, which admits with write only file allocation. The file allocation solutions can be used only if every processor has enough memory to ....

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D.L. Black and D.D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.

....understand certain randomized algorithms. The notation of unfairness, which has proven to be valuable in other contexts [21, 7] also proves itself here. Our final contribution is to point out an error which has permeated throughout the literature of PRP. In their seminal paper, Black and Sleator [10] state: It is possible to prove that for certain other metrics (for example, when the graph corresponding to the metric is a four node cycle) the best competitive ratio that an on line algorithm can hope for is 5=2. Subsequent authors have interpreted this to mean that 2.5 is a lower bound for the ....

....Discrete Continuous Discrete Continuous Symmetric C 4 Randomized l.b. old new 1:58197 [1] 1:58197 1:58197 1:75037 1:58197 1:58197 1:75037 1:58197 1:75037 Randomized u.b. old new 1:58198 [1] 1:58198 3:16396 [1] 2:37297 2:37297 2:54150 [12] 2:37297 2:36603 Deterministic l.b. old new 2 [10] 1:58197 2:36603 2:31023 2:36603 2:36603 [13] Deterministic u.b. old new 2 [10] 1:58198 4 [1] 2:54150 3 [12] 2:36603 [13] Table 1. Old and new bounds for d 1 in the unit size l 0 model (the classical model) A simpler proof for an old result is denoted by . The continuous model ....

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D.L. Black and D.D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie Mellon University, 1989.

....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 different technique, we also develop the first deterministic distributed file allocation algorithm (using only local information) with poly logarithmic competitive ratio against a globally optimized optimal ....

....standpoints. The 1981 survey paper by Dowdy and Foster [DF82] dealing with the file allocation (or assignment) problem, cites close to a hundred references. First competitive algorithms for special cases of the centralized version of the problem were found by Black and Sleator and by Westbrook [BS89, Wes91] The file allocation problem may be viewed as the combined solution to the two subproblems defined in [BS89] Other special cases of these problems have been considered in [CLRW, LRWY94, WY93] In [BFR92] randomized algorithms have been developed for the general network, with competitive ....

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D.L. Black and D.D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie-Mellon, 1989. 47

....in a significant additional programming burden. The operating system can play a major role in managing placement through the policies and mechanisms of the virtual memory subsystem (e.g. by migrating and replicating shared pages) OS level NUMA memory management is an area of active research [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13]. This body of work has demonstrated that dynamic page placement is indeed effective. In fact, the effectiveness question has been the focus of many of the previous studies that took the approach of proposing an algorithm and evaluating its performance (e.g. by comparing it against some static, ....

David Black and Daniel Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, CarnegieMellon University, November 1989.

....since they move a thread away from the pages in its memory affinity set, that is, the pages that are accessed more frequently by this thread. A page migration algorithm based on the observed reference history of pages can collocate each thread with its memory affinity set on the same node [2]. However, if a thread migrates, the algorithm should aggressively forward the pages in the memory affinity set of the migrated thread to the new home node of the thread, without relying on the past reference history of these pages. The aforementioned implications force the operating system to ....

....due to remote accesses for the processors that compete for the page. Assuming that each remote memory access from the same node to the same page has constant latency, our competitive criterion is equivalent to a criterion that compares the number of references obtained by the reference counters [2]. In reality, on cache coherent systems the remote memory access latency is variable and depends on the type of cache miss that triggers the remote access, the distance in network hops between the home node and the accessing node and contention at the memory module to which the access is issued. ....

[Article contains additional citation context not shown here]

D. Black and D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.

....We develop the first explicit centralized deterministic on line strategy. Previous (deterministic) solutions were complicated and more expensive. Our solution has (asymptotically 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 different techniques, we also develop the first deterministic distributed file allocation algorithm (using only local information) with a poly logarithmic competitive ratio against a globally optimized ....

....standpoints. The 1981 survey paper by Dowdy and Foster [DF82] dealing with the file allocation (or assignment) problem, cites close to a hundred references. The file allocation problem that we deal with in this paper may be viewed as the combined solution to the two subproblems defined in [BS89] file migration and file replication. The file migration problem deals with a single file copy located at some processor in a network. Access requests (reads or writes) are generated in network processors, each such request is associated with the cost of the current distance between the file ....

[Article contains additional citation context not shown here]

D.L. Black and D.D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie-Mellon, 1989.

....understand certain randomized algorithms. The notation of unfairness, which has proven to be valuable in other contexts [24, 7] also proves itself here. Our final contribution is to point out an error which has permeated throughout the literature of PRP. In their seminal paper, Black and Sleator [10] state: It is possible to prove that for certain other metrics (for example, when the graph corresponding to the metric is a four node cycle) the best competitive ratio that an on line algorithm can hope for is 5=2. Subsequent authors have interpreted this to mean that 2.5 is a lower bound for the ....

....Rings Discrete Continuous Discrete Continuous Symmetric C 4 Randomized l.b. old new 1:58197 [1] 1:58197 1:58197 1:75037 1:58197 1:58197 1:75037 1:58197 1:75037 Randomized u.b. old new 1:58198 [1] 1:58198 3:16396 [1] 2:37297 2:37297 2:54150 [15] 2:37297 2:36603 Deterministic l.b. old new 2 [10] 1:58197 2:36603 2:31023 2:36603 2:36603 Deterministic u.b. old new 2 [10] 1:58198 4 [1] 2:54150 3 [15] 2:36603 [16] Table 1. Old and new bounds for d 1 in the unit size l 0 model (the classical model) A simpler proof for an old result is denoted by . The continuous model is new to this ....

[Article contains additional citation context not shown here]

D. L. Black and D. D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie Mellon University, 1989.

....algorithm which knows the en tire future request sequence. The competitive ratio is the worst case ratio over all inputs. Let A(h) be the cost of an algorithm A over a request sequence h. The competitive ratio of A is defined as Competitive Ratio = max h A(h) Offline(h) Black and Sleator [7] proved a lower bound of 3 on the competitive ratio of object allocation. Algorithm Count proposed by Bartal, Fiat and Rabani [4] was the first optimal deterministic algorithm for uniform networks. Successive algorithms for more general networks have been proposed. Awerbuch, Bartal and Fiat [3] ....

....maintained of the shared object at all times, implying that the solutions tolerate up to (t Gamma 1) failures. We establish a lower bound of 3 on the competitive ratio of any online algorithm that satisfies the fault tolerance constraint. Given the lower bound of 3 for the unconstrained problem [7], this means that lower bound result is not affected by the faulttolerance constraint. In our proof, we will generate a specific history for any given competitive online algorithm, Alg, and show that the cost of an offline adversary with complete knowledge of the history is no more than one third ....

D. Black and D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie-Mellon, 1989.

....Wu In this lecture we describe the page migration problem, giving a 3 competitive randomized algorithm, a 5 competitive deterministic algorithm, and a deterministic algorithm which is 3 competitive for the uniform metric. 10.1 Page Migration In the page migration problem, due to Black and Sleator [BS89], we are given a network, with a single page located at some node in the network. Each request is a node which wishes to access the page, and this request is served by establishing communication between the node x at which the page resides and the node y requesting the page. The cost of this ....

....ffl FLIP is 3 competitive against an adaptive on line adversary. There is also a matching lower bound. West91] The following are some results which have been proved regarding deterministic algorithms for the page migration problem. ffl For a 2 point metric space, we have a lower bound of 3 [BS89]. ffl There are 3 competitive algorithms for uniform and trees networks [BS89] ffl For D = 1, we have a lower bound of 85 27 3:148 [CLRW93] ffl We have 7 competitive [ABF93a] and 4.086 competitive [BCI96] algorithms. 10.1.3 A 5 competitive Deterministic Algorithm This algorithm is a ....

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D.L. Black and D.D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201, Department of Computer Science, CarnegieMellon University, 1989.

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D. L. Black and D. D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie Mellon University, 1989.

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D. L. Black and D. D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.

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D.L. Black and D.D. Sleator. Competitive Algorithms for Replication and Migration Problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.

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D. L. Black and D. D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie Mellon University, 1989.

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D. L. Black and D. D. Sleator. Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Carnegie Mellon University, 1989.

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Black, D. L., and Sleator, D. D. Competitive algorithms for replication and migration problems. Tech. Rep. CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University, 1989.

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