On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Algorithms for Capacitated Vehicle Routing
SIAM Journal on Computing
Online Scheduling for Sorting Buffers
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The Finite Capacity Dial-A-Ride Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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
Improved online algorithms for the sorting buffer problem
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Reordering buffer management for non-uniform cost models
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Almost tight bounds for reordering buffer management
Proceedings of the forty-third annual ACM symposium on Theory of computing
A note on sorting buffers offline
Theoretical Computer Science
NP-hardness of the sorting buffer problem on the uniform metric
Discrete Applied Mathematics
Optimal online buffer scheduling for block devices
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A bicriteria approximation for the reordering buffer problem
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We consider the sorting buffers problem. Input to this problem is a sequence of requests, each specified by a point in a metric space. There is a ''server'' that moves from point to point to serve these requests. To serve a request, the server needs to visit the point corresponding to that request. The objective is to minimize the total distance traveled by the server in the metric space. In order to achieve this, the server is allowed to serve the requests in any order that requires to ''buffer'' at most k requests at any time. Thus a valid reordering can serve a request only after serving all but k previous requests. In this paper, we consider this problem on the line metric which is motivated by its application to the disc scheduling problem. We present first approximation algorithms with non-trivial approximation ratios in both online and offline settings. On a line metric with n uniformly spaced points, we give a randomized online algorithm with a competitive ratio of O(log^2n) in expectation against an oblivious adversary. In the offline setting, our algorithm yields the first constant-factor approximation and runs in quasi-polynomial time N@?n@?k^O^(^l^o^g^n^) where N is the total number of requests. Our approach is based on a dynamic program that keeps track of the number of pending requests in each of O(logn) line segments that are geometrically increasing in length.