An optimal on-line algorithm for metrical task system

Borodin, Allan; Linial, Nathan; Saks, Michael

doi:10.1145/146585.146588

Cited by 292 publications

(192 citation statements)

References 12 publications

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“…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 [21, 18, 19, 22, 13, 9] and metrical task systems [6].…”

Section: Discussionmentioning

confidence: 99%

A New Competitive Analysis of Randomized Caching

Law¹,

Leiserson²

2000

Algorithms and Computation

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We provide new competitive upper bounds on the performance of the memoryless, randomized caching algorithm RANDOM. Our bounds are expressed in terms of the inherent hit rate a of the sequence of memory references, which is the highest possible hit rate that any algorithm can achieve on the sequence for a cache of a given size. Our results show that RANDOM is (1 -ae-1 /4)/(1 -a)-competitive on any reference sequence with inherent hit rate a. Since our new competitive bound does not scale up with the size k of the cache, it beats the putative Q(lg k) lower bound on the competitiveness of caching algorithms.

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Section: Discussionmentioning

confidence: 99%

A New Competitive Analysis of Randomized Caching

Law¹,

Leiserson²

2000

Algorithms and Computation

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“…For example, the subproblem of finding a good trade-off between serving requests remotely (at a low but repeated communication cost) or migrating nodes together (entailing a potentially high onetime cost α), is essentially a ski rental or rent-or-buy problem [14,15]. A similar tradeoff also arises in the context of online page and server migration problems [5,6], where requests appear in a metric space [7] or graph [3] over time, and need to be served by one [6] or multiple [13] servers. However, in our problem, the number of possible node-cluster configurations is large, rendering it difficult to cast the problem into an online metrical task system.…”

Section: Related Workmentioning

confidence: 99%

Online Balanced Repartitioning

Avin

Loukas

Pacut

et al. 2016

Lecture Notes in Computer Science

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This paper initiates the study of a fundamental online problem called online balanced repartitioning. Unlike the classic graph partitioning problem, our input is an arbitrary sequence of communication requests between nodes, with patterns that may change over time. The objective is to dynamically repartition the n nodes into clusters, each of size k. Every communication request needs to be served either locally (cost 0), if the communicating nodes are collocated in the same cluster, or remotely (cost 1), using intercluster communication, if they are located in different clusters. The algorithm can also dynamically update the partitioning by migrating nodes between clusters at cost α per node migration. Therefore, we are interested in online algorithms which find a good tradeoff between the communication cost and the migration cost, maintaining partitions which minimize the number of inter-cluster communications.We consider settings both with and without cluster-size augmentation. For the former, we prove a lower bound which is strictly larger than k, which highlights an interesting difference to online paging. Somewhat surprisingly, and unlike online paging, we prove that any deterministic online algorithm has a non-constant competitive ratio of at least k, even with augmentation. Our main technical contribution is an O(k log k)-competitive algorithm for the setting with (constant) augmentation.We believe that our model finds interesting applications, e.g., in the context of datacenters, where virtual machines need to be dynamically embedded on a set of (multi-core) servers, and where machines migrations are possible, but costly.

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“…The virtual server migration problem, the facility location problem, the k-server problem and the page migration problem are all instances of metrical task systems (MTS) (e.g., [4], [10]). For metrical task systems, there exist (relatively complex) asymptotically optimal deterministic Θ(n)-competitive algorithms, where n is the state (or "configuration") space, and randomized O(log 2 n log log n)-competitive algorithms given that the state space fulfills the triangle inequality.…”

Section: Related Workmentioning

confidence: 99%

Optimal bounds for online page migration with generalized migration costs

Schneider

Schmid

2013

2013 Proceedings IEEE INFOCOM

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This paper attends to a generalized version of the classic page migration problem where migration costs are not necessarily given by the migration distance only, but may depend on prior migrations, or on the available bandwidth along the migration path. Interestingly, this problem cannot be viewed from a Metrical Task System (MTS) perspective, despite the generality of MTS: The corresponding MTS has an unbounded state space and, thus, an unbounded competitive ratio. Nevertheless, we are able to present an optimal online algorithm for a wide range of problem variants, improving the best upper bounds known so far for more specific problems. For example, we present a tight bound of Θ(log n/ log log n) for the competitive ratio of the virtual server migration problem introduced recently.

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An optimal on-line algorithm for metrical task system

Cited by 292 publications

References 12 publications

A New Competitive Analysis of Randomized Caching

A New Competitive Analysis of Randomized Caching

Online Balanced Repartitioning

Optimal bounds for online page migration with generalized migration costs

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