## An optimal online algorithm for metrical task systems (1992)

Venue: | Journal of the ACM |

Citations: | 185 - 9 self |

### BibTeX

@ARTICLE{Borodin92anoptimal,

author = {Allan Borodin and Nathan Linial and Michael E. Saks},

title = {An optimal online algorithm for metrical task systems},

journal = {Journal of the ACM},

year = {1992},

volume = {39},

pages = {373--382}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. In practice, almost all dynamic systems require decisions to be made on-line, without full knowledge of their future impact on the system. A general model for the processing of sequences of tasks is introduced, and a general on-line decnion algorithm is developed. It is shown that, for an important algorithms. class of special cases, this algorithm is optimal among all on-line Specifically, a task system (S. d) for processing sequences of tasks consists of a set S of states and a cost matrix d where d(i, j) is the cost of changing from state i to state j (we assume that d satisfies the triangle inequality and all diagonal entries are f)). The cost of processing a given task depends on the state of the system. A schedule for a sequence T1, T2,..., Tk of tasks is a ‘equence sl,s~,..., Sk of states where s ~ is the state in which T ’ is processed; the cost of a schedule is the sum of all task processing costs and state transition costs incurred. An on-line scheduling algorithm is one that chooses s, only knowing T1 Tz ~.. T’. Such an algorithm is w-competitive if, on any input task sequence, its cost is within an additive constant of w times the optimal offline schedule cost. The competitive ratio w(S, d) is the infimum w for which there is a w-competitive on-line scheduling algorithm for (S, d). It is shown that w(S, d) = 2 ISI – 1 for eoery task system in which d is symmetric, and w(S, d) = 0(1 S]2) for every task system. Finally, randomized on-line scheduling algorithms are introduced. It is shown that for the uniform task system (in which d(i, j) = 1 for all i, j), the expected competitive ratio w(S, d) =

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Citation Context ...act on this basis. This is the starting point of the theory of Markov decision processes [13]. The approach we take here, which was first explicitly studied in the seminal paper of Sleator and Tarjan =-=[21]-=-, is to compare the performance of a strategy that operates with no knowledge of the future with the performance of the optimal “clairvoyant” strategy that has complete knowledge of the future. This r... |

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Citation Context ...n a transition is l\k. Thus, f(k) = f(k – 1) + l/k, so that f(k) = H(k) and the expected cost of the phase (task processing costs + transition costs) is at most 2H(n). ❑ PROOF OF THE LOWER BOUND. Yao =-=[23]-=- has noted that using the von Neumann minimax theorem for two-person games, a lower bound on the performance of randomized algorithms in these (and most other) models can be obtained by choosing any p... |

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Citation Context ...ndomized algorithms for the unit-cost task system has a very nice analogue in the unit-cost k-server problem that is better known as the paging or caching problem. For the paging problem, Fiat et al. =-=[9]-=- have established a 2H(k) upper bound on the expected competitive ratio using a very appealing (and possibly quite practical) randomized algorithm. It is interesting to note that in the (admittedly no... |

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