Combinatorics in pure mathematics
Handbook of combinatorics (vol. 2)
Performance modeling for realistic storage devices
Performance modeling for realistic storage devices
Placement of Records on a Secondary Storage Device to Minimize Access Time
Journal of the ACM (JACM)
On the Optimality of the Probability Ranking Scheme in Storage Applications
Journal of the ACM (JACM)
The Effect of a Capacity Constraint on the Minimal Cost of a Partition
Journal of the ACM (JACM)
Clustering for edge-cost minimization (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Least-distortion Euclidean embeddings of graphs: products of cycles and expanders
Journal of Combinatorial Theory Series B
Minimizing Expected Head Movement in One-Dimensional and Two-Dimensional Mass Storage Systems
ACM Computing Surveys (CSUR)
A 7/8-approximation algorithm for metric Max TSP
Information Processing Letters
Algorithmic Studies in Mass Storage Systems
Algorithmic Studies in Mass Storage Systems
Operating Systems Theory
Stochastic Analysis of Computer Storage
Stochastic Analysis of Computer Storage
Optimal Data Placement on Disks: A Comprehensive Solution for Different Technologies
IEEE Transactions on Knowledge and Data Engineering
The output of a cache under the independent reference model: where did the locality of reference go?
Proceedings of the joint international conference on Measurement and modeling of computer systems
Expander flows, geometric embeddings and graph partitioning
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for asymmetric TSP by decomposing directed regular multigraphs
Journal of the ACM (JACM)
Dynamic data reallocation in disk arrays
ACM Transactions on Storage (TOS)
35/44-Approximation for asymmetric maximum TSP with triangle inequality
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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We consider model based estimates for set-up time. The general setting we are interested in is the following: given a disk and a sequence of read/write requests to certain locations, we would like to know the total time of transitions (set-up time) when these requests are served in an orderly fashion. The problem becomes nontrivial when we have, as is typically the case, only the counts of requests to each location rather then the whole input, and we can only hope to estimate the required time. Models that estimate set-up time have been suggested and heavily used as far back as the sixties. However, not much theory exists to enable a qualitative understanding of such models. To this end we introduce several properties such as (i) super-additivity which means that the set-up time estimate decreases as the input data is refined (ii) monotonicity which means that more activity produces more set-up time, (iii) Dominance which means that one model always produces higher estimates than a second model and (iv) approximation guarantees for the estimate with respect to the worst possible time, by which we can study different models. We provide criteria for super-additivity and monotonicity to hold for popular models such as the Partial Markov model (PMM). The criteria show that the estimate produced by these models will be monotone for any reasonable system. We also show that the independent reference model (IRM) based estimate functions as a worst case estimate in the sense that the estimate is guaranteed to be at least half of the actual set-up time. We also show that it dominates the PMM based estimates. Using our criteria we prove that PMM based estimates are always super additive when applied to the special metrics that correspond to seek times of disk drives. To establish our theoretical results we use the theory of finite metric spaces, and en route show a result of independent interest in that theory, which is a strengthening of a theorem of J.B. Kelly [J.B. Kelly, Hypermetric spaces and metric transforms, in: O. Shisha (Ed.), Inequalities III, 1972, pp. 149-158] about the properties of metrics that are formed by concave functions on the line.