On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Applied operating system concepts
Applied operating system concepts
Modern Operating Systems
Online Scheduling for Sorting Buffers
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Evaluation of online strategies for reordering buffers
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
Online sorting buffers on line
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Reordering buffer management for non-uniform cost models
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Exploiting locality: approximating sorting buffers
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Reordering buffers for general metric spaces
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Evaluation of online strategies for reordering buffers
Journal of Experimental Algorithmics (JEA)
Buffer management for colored packets with deadlines
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Online and offline algorithms for the sorting buffers problem on the line metric
Journal of Discrete Algorithms
An improved competitive algorithm for reordering buffer management
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Almost tight bounds for reordering buffer management
Proceedings of the forty-third annual ACM symposium on Theory of computing
Optimal online buffer scheduling for block devices
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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An instance of the sorting buffer problem consists of a metric space and a server, equipped with a finite-capacity buffer capable of holding a limited number of requests. An additional ingredient of the input is an online sequence of requests, each of which is characterized by a destination in the given metric; whenever a request arrives, it must be stored in the sorting buffer. At any point in time, a currently pending request can be served by drawing it out of the buffer and moving the server to its corresponding destination. The objective is to serve all input requests in a way that minimizes the total distance traveled by the server. In this paper, we focus our attention on instances of the problem in which the underlying metric is either an evenly-spaced or a continuous line metric. Our main findings can be briefly summarized as follows: 1. We present a deterministic O(log n) competitive algorithm for n- point evenly-spaced line metrics. This result improves on a randomized O(log2 n) competitive algorithm due to Khandekar and Pandit. 2. We devise a deterministic O(log N log log N) competitive algorithm for continuous line metrics, where N is the input sequence length. 3. We establish the first non-trivial lower bound for the evenly-spaced case, by proving that the competitive ratio of any deterministic algorithm is at least 2+√3/√3 ≅ 2.154.