An optimal on-line algorithm for metrical task systems

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An optimal on-line algorithm for metrical task systems (1992)

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by Allan Borodin , Nathan Linial , Michael E. Saks

Venue:	JOURNAL OF THE ACM
Citations:	209 - 8 self

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@ARTICLE{Borodin92anoptimal,
    author = {Allan Borodin and Nathan Linial and Michael E. Saks},
    title = {An optimal on-line algorithm for metrical task systems},
    journal = {JOURNAL OF THE ACM},
    year = {1992},
    volume = {39},
    pages = {373--382}
}

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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 decision 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 sequence 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) =

Keyphrases

metrical task system optimal online algorithm on-line scheduling algorithm task system state transition cost sequence t1 diagonal entry important algorithm uniform task system task processing cost special case cost matrix expected competitive ratio full knowledge on-line specifically triangle inequality future impact eoery task system additive constant input task sequence general on-line decnion algorithm w-competitive on-line scheduling algorithm equence sl task consists general model competitive ratio optimal offline schedule cost t1 tz dynamic system

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