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Reordering buffers for general metric spaces
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Englert, Matthias, Räcke, Harald and Westermann, Matthias (2007) Reordering buffers for general metric spaces. In: ACM symposium on theory of computing. Published in: STOC '07 Proceedings of the thirtyninth annual ACM symposium on Theory of computing pp. 556564. ISBN 9781595936318. doi:10.1145/1250790.1250871
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Official URL: http://dx.doi.org/10.1145/1250790.1250871
Abstract
In the reordering buffer problem, we are given an input sequence of requests for service each of which corresponds to a point in a metric space. The cost of serving the requests heavily depends on the processing order. Serving a request induces cost corresponding to the distance between itself and the previously served request, measured in the underlying metric space. A reordering buffer with storage capacity k can be used to reorder the input sequence in a restricted fashion so as to construct an output sequence with lower service cost. This simple and universal framework is useful for many applications in computer science and economics, e.g., disk scheduling, rendering in computer graphics, or painting shops in car plants.
In this paper, we design online algorithms for the reordering buffer problem. Our main result is a strategy with a polylogarithmic competitive ratio for general metric spaces. Previous work on the reordering buffer problem only considered very restricted metric spaces. We obtain our result by first developing a deterministic algorithm for arbitrary weighted trees with a competitive ratio of O(D · log k), where D denotes the unweighted diameter of the tree, i.e., the maximum number of edges on a path connecting two nodes. Then we show how to improve this competitive ratio to O(log2 k) for metric spaces that are derived from HSTs. Combining this result with the results on probabilistically approximating arbitrary metrics by tree metrics, we obtain a randomized strategy for general metric spaces that achieves a competitive ratio of O(log2 k · log n) in expectation against an oblivious adversary. Here n denotes the number of distinct points in the metric space. Note that the length of the input sequence can be much larger than n.
Item Type:  Conference Item (Paper)  

Subjects:  Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software  
Divisions:  Faculty of Science > Computer Science  
Journal or Publication Title:  STOC '07 Proceedings of the thirtyninth annual ACM symposium on Theory of computing  
Publisher:  ACM  
ISBN:  9781595936318  
Official Date:  11 June 2007  
Dates: 


Page Range:  pp. 556564  
DOI:  10.1145/1250790.1250871  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
Conference Paper Type:  Paper  
Title of Event:  ACM symposium on theory of computing  
Type of Event:  Conference 
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