A. Borodin, N. Linial, and M. Saks. "An Optimal On-Line Algorithm for Metrical Task Systems". In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....An on line policy proceeds similarly, but cannot anticipate phase changes. At the start of each phase it creates ## experts, one for each permutation of the pages in the working set learned in the previous phase. Each expert then keeps its own view of the cache, and executes a MARKING algorithm [5]. The expert s initial permutation determines the order in which unmarked pages are discarded. Requests to new pages are rented (this time at a loss of 1) until they become marked (requested # times in the phase) Only marked pages are actually fetched into the cache. When all # pages in the cache ....

Allan Borodin, Nathan Linial, and Michael E. Saks. An optimal on-line algorithm for metrical task system. Journal of the ACM (JACM), 39(4):745--763, 1992.

.... called by Sleator and Tarjan [13] the competitive ratio, has been used to analyze algorithms for various data structures, paging, caching, and graph problems (See e.g. 5, 12, 8, 6] and gave rise to elegant generalizations, such as metrical task systems introduced by Borodin, Linial, and Saks [4], and the K server problems introduced by Manasse, McGeoch and Sleator [11] see also [9] Most on line models assume that there is small commonknowledge shared between the online algorithm and the adversary. In particular, online models for graph problems assume that the graph is not known to ....

A. Borodin, N. Linial, and M. E. Saks. An optimal on-line algorithm for metrical task system. J. ACM, 39(4):745--763, 1992.

....) on the competitive factor of any randomized algorithm, even when w is known in advance. Here, ffl can be any positive constant. In addition to being inherently interesting, the layered graph traversal problem is related to other on line problems. It generalizes the Metrical Task Systems problem [BLS] and the k Server problem [MMS] as explained by Fiat et al. FFKRRV] However, in the latter case, the width of the layered graph depends upon the cardinality of the metric space and therefore, layered graph traversal techniques are inadequate for producing solutions to the k server problem. An ....

A. Borodin, N. Linial, M. Saks. An Optimal On-line algorithm for Metrical Task Systems. In Journal of ACM, 39, pp. 745-763, 1992.

....Bounds A result by Yao [Yao77] considerably simplifies the construction of lower bound proofs for randomized on line algorithms. In particular, Yao notes that the complexity of randomized algorithms is connected to the complexity of deterministic algorithms on randomized inputs. Borodin et al. BLS92] extend Yao s theorem to competitive analysis with a theorem, which states that the lower bound on the oblivious competitive ratio for a given problem is greater than the lower bound on the competitive ratio of deterministic on line algorithms, when the request sequences for the problem are ....

A. Borodin, N. Linial, and M. Saks. An optimal on-line algorithm for metrical task systems. Journal of the ACM, 39(4):745--763, 1992.

....how much the performance of the on line algorithm suffers in comparison to the optimal algorithm due to the fact that the on line algorithm cannot predict future requests, since, for example, it does not know the traffic pattern. Competitive analysis can be extended to randomized algorithms [BLS87] i.e. algorithms that use randomization in their decision process. Let E[A(oe) be the expected performance of randomized algorithm A on request sequence oe. Then the competitive ratio for A is the maximum over all request sequences oe of O(oe) E[A(oe) where O(oe) is the performance of the ....

A. Borodin, N. Linial, and M. Saks. An optimal on-line algorithm for metrical task systems. In Proceedings of the 19 Annual ACM Symposium on Theory of Computing, New York City, pages 373--382, may 1987.

....for all w, 2 is a lower bound on the competitive ratio of any deterministic on line layered graph traversal algorithm. Thus arbitrary layered graphs are much harder to traverse than those consisting of disjoint paths. Randomized on line algorithms are addressed in several papers including [BLS, RS, CDRS, FKLMSY, BBKTW, KRR]. An oblivious adversary is one who constructs the sequence of events in advance and deals with the sequence optimally. For this adversary model [BLS] and [FKLMSY] give examples where randomization can improve the competitive ratio exponentially. This adversary models a world in which the on line ....

....than those consisting of disjoint paths. Randomized on line algorithms are addressed in several papers including [BLS, RS, CDRS, FKLMSY, BBKTW, KRR] An oblivious adversary is one who constructs the sequence of events in advance and deals with the sequence optimally. For this adversary model [BLS] and [FKLMSY] give examples where randomization can improve the competitive ratio exponentially. This adversary models a world in which the on line algorithm s actions do not themselves influence future events. One can consider a situation where the on line algorithm s actions have a direct ....

[Article contains additional citation context not shown here]

A. Borodin, N. Linial, and M. Saks. An Optimal On-Line Algorithm for Metrical Task Systems. Journal of the ACM, 39:745--763, 1992.

....the model of [ST] have been proposed [BIRS, KPR] but the question of why on line paging works so well in real life remains an intriguing one. Following [ST] the paper [KMRS] analyzed additional on line strategies for cache management (which is essentially the same as paging in this model) and [BLS] proposed metrical task systems as an abstract model for studying on line algorithms. The following year, Manasse, McGeoch, and Sleator [MMS] introduced what has become perhaps the most well known and well studied on line problem: the k server problem. 2.2 The k Server Problem We imagine the ....

A. Borodin, N. Linial, M. Saks, "An optimal on-line algorithm for metrical task systems," Journal of the ACM, 39(1992), pp. 745--763.

....action model, given a competitive algorithm for the associated metrical task system. Hence we can e#ectively handle an entire general class of problems, generalizing the work of [4, 9] on relaxed metrical task systems to the setting of delayed actions. We begin by defining metrical task systems [14], and then define relaxed metrical task systems. Here we follow [9] Definition 14 A task system, consists of a set of configurations (or states) C and a distance function between any two configurations C 1 , C 2 denoted dist(C 1 , C 2 ) this is the move cost between the ....

A. Borodin, N. Linial, and M. Saks, An Optimal On-Line Algorithm for Metrical Task Systems. In Proc. 19th Ann. ACM Symp on Theory of Computing, pp. 373--382, May 1987.

....are currently pursuing this line of research. Finally, we are hopeful that the techniques presented in this thesis can be applied to analyses of other on line algorithms and be generalized to other on line computational models, such as k servers [19, 17, 18, 20, 13, 9] and metrical task systems [6]. ....

Allan Borodin, Nathan Linial, and Michael E. Saks. An optimal on-line algorithm for metrical task system. Journal of the ACM, 39(4):745-763, October 1992.

....known. Note that number of states in a bene t task system might be super polynomial if the states are not given explicitly. It can be shown that bene t task systems capture also bene t maximization variants of well studied problems, such as the k server problem [16, 9] and metrical task systems [10, 9] (see Section 2) Thus, our results hold for these variants as well, and show that the bene t variants of these problems may be more tractable than their cost minimization variants. Our results We observe that the o ine version of the web server farm problem can be solved in polynomial time. In ....

....dicult to see that this problem can also be modeled by the bene t task system de ned above and thus all our results apply to the bene t version of the k server problem. Similarly, consider the bene t version of a metrical task system. This version is similar to the classical metrical task system [10], with the di erence that each task is associated with a vector of bene ts, one for each state, such that the net bene t after subtracting the transition cost is nonnegative. This model as well can be cast as a bene t task system and our results apply. 3. OFFLINE ALGORITHMFORTHEWEB SERVER FARM ....

A. Borodin, N. Linial and M.E. Saks, \An optimal on-line algorithm for metrical task system". J. ACM, 39(1992), pp. 745-763.

....a benefit problem) is c competitive against P if there exists a constant b such that, c Delta EP [A(oe) b EP [OPT (oe) The following theorem can be derived by Yao s Lemma based on the minimax principle of game theory [Yao] FREQUENCY ASSIGNMENT IN MOBILE AND RADIO NETWORKS 5 Lemma 2. 1 ([BLS]) A real number c is a lower bound on the competitive ratio of randomized on line algorithms against the oblivious adversary if and only if there exists a probability distribution P such that c is a lower bound on the competitive ratio of any deterministic on line algorithm against P. 2.2. ....

A. Borodin, N. Linial, M. Saks, "An optimal on-line algorithm for metrical task systems ", Journal of the Association for Computing Machinery 39(4), pp. 745-763, 1992.

.... global control deterministic algorithms (e.g. 21, 25] to distributed ones by choosing a leader that will run the global control algorithm, while ignoring requests on covered points; for the case of k = n Gamma 1, one can use the algorithm of Borodin, Linial and Saks for metrical task systems [12] which defines a fixed traversal sequence for the single point which is uncovered at any specific time; only a single message of O(1) bits has to be sent to the new uncovered point. In general, however, the behavior of known k server algorithms depends on their entire history, making it impossible ....

A. Borodin, N. Linial, and M. Saks. An Optimal On-Line Algorithm for Metrical Task Systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

....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 generalization of some original task system problem [BLS87] Given a c competitive algorithm for a task system we show how to obtain a deterministic O(c 2 ) and randomized O(c) competitive algorithms for the corresponding relaxed task system. The result implies first deterministic algorithms for k page migration by using k server [MMS88] algorithms, ....

....is D times larger than the distance (note that in both these problems this is a natural parameter) 1.1 Relaxed Task Systems In this section we provide formal definitions of relaxed task systems and description of our results. The general theorems are formulated in the context of task systems ( BLS87] Definition 1 A task system, P , consists of a set of configurations (or states) C and a distance function between any two configurations C 1 ; C 2 2 C, denoted dist(C 1 ; C 2 ) this is the move cost between the configurations) The task system consists of a set of requests, called tasks. A ....

[Article contains additional citation context not shown here]

A. Borodin, N. Linial, and M. Saks. An Optimal On-Line Algorithm for Metrical Task Systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

....in the context of two basic file allocation problems, and primarily address issues of communications efficiency. We define the file allocation problem and 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 ....

....algorithm. The competitive ratio is c if for all event sequences, online cost) c Theta (off line cost) some additive constant. A competitive algorithm with a competitive ratio of c is called strictly competitive if the additive constant is zero. Models for on line problems are presented in [BLS], MMS] BBKTW] Competitive analysis of distributed data management algorithms begins with Karlin et al. in [KMRS] who analyze competitive algorithms for snoopy caching on a bus connected PRAM. If the on line algorithm may use randomization to process events then the competitive ratio is ....

[Article contains additional citation context not shown here]

A. Borodin, N. Linial, and M. Saks. An Optimal On-Line Algorithm for Metrical Task Systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

....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 algorithmic problems, including metrical task systems [BLS87], server problems [MMS88] distributed paging [BFR92] and dynamic storage rearrangement [FMRW95] are defined in terms of some metric space. Typically for these problems, there are linear lower bounds on the competitive ratio of deterministic algorithms. Although randomization against an ....

....randomization against an oblivious adversary has the potential of overcoming these high ratios, very little progress has been made in the analysis. We demonstrate the use of our technique by obtaining substantially improved results for two different on line problems. For metrical task systems [BLS87] we give first sub linear randomized competitive ratio for a large set of metric spaces. For constrained file migration [BFR92] we give first randomized algorithms for general networks with polylogarithmic competitive ratio. International Computer Science institute, 1947 Center Street, Berkeley ....

[Article contains additional citation context not shown here]

A. Borodin, N. Linial, and M. Saks. An Optimal On-Line Algorithm for Metrical Task Systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

No context found.

A. Borodin, N. Linial, and M. Saks. "An Optimal On-Line Algorithm for Metrical Task Systems". In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

No context found.

A. Borodin, N. Linial, and M. Saks (1992), "An optimal on-line algorithm for metrical task systems", Journal of the Association for Computing Machinery 39(4), pp. 745--763.

No context found.

A. Borodin, N. Linial, and M. Saks. An Optimal On-Line Algorithm for Metrical Task Systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

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A. Borodin, N. Linial, and M. E. Saks. An optimal on-line algorithm for metrical task system. J. ACM, 39(4):745-763, 1992.

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A. Borodin, N. Linial, and M. Saks. An optimal on-line algorithm for metrical task system. Journal of the ACM, 39(4):745--763, 1992.

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A. Borodin, N. Linial, and M.E. Saks. An optimal on-line algorithm for metrical task system. Journal of the ACM, 39(4):745-763, 1992.

No context found.

A. Borodin, N. Linial, and M. Saks. An optimal on-line algorithm for metrical task systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

No context found.

A. Borodin, N. Linial, and M. Saks. An optimal on-line algorithm for metrical task systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

No context found.

A. Borodin, N. Linial, and M. Saks. An Optimal On-Line Algorithm for Metrical Task Systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

No context found.

A. Borodin, N. Linial, and M. Saks. An Optimal On-Line Algorithm for Metrical Task Systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373--382, May 1987.

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