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
Reordering buffers for general metric spaces
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Exploiting locality: approximating sorting buffers
Journal of Discrete Algorithms
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
Offline sorting buffers on line
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
NP-hardness of the sorting buffer problem on the uniform metric
Discrete Applied Mathematics
A bicriteria approximation for the reordering buffer problem
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
| Hi-index | 0.00 |
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 space; 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 article, we focus our attention on instances of the problem in which the underlying metric is either an evenly-spaced line metric 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 [2006b]. It also refutes their conjecture, stating that a deterministic strategy is unlikely to obtain a nontrivial competitive ratio. (2) We devise a deterministic O(log N log log N)-competitive algorithm for continuous line metrics, where N denotes the length of the input sequence. In this context, we introduce a novel discretization technique of independent interest. (3) We establish the first nontrivial lower bound for the evenly-spaced case, by proving that the competitive ratio of any deterministic algorithm is at least 2 + &sqrt;3/&sqrt;3 ≈ 2.154. This result settles, to some extent, an open question due to Khandekar and Pandit [2006b], who posed the task of attaining lower bounds on the achievable competitive ratio as a foundational objective for future research.