TY - GEN

T1 - Improved online algorithms for the sorting buffer problem

AU - Gamzu, Iftah

AU - Segev, Danny

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38049162122&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-70918-3_56

DO - 10.1007/978-3-540-70918-3_56

M3 - Conference contribution

AN - SCOPUS:38049162122

SN - 9783540709176

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 658

EP - 669

BT - STACS 2007 - 24th Annual Symposium on Theoretical Aspects of Computer Science, Proceedings

PB - Springer Verlag

T2 - 24th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2007

Y2 - 22 February 2007 through 24 February 2007

ER -