A bicriteria approximation for the reordering buffer problem

  • Authors:

  • Siddharth Barman;Shuchi Chawla;Seeun Umboh

  • Affiliations:

  • University of Wisconsin---Madison;University of Wisconsin---Madison;University of Wisconsin---Madison

  • Venue:
  • ESA'12 Proceedings of the 20th Annual European conference on Algorithms
  • Year:
  • 2012

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Abstract

In the reordering buffer problem (RBP), a server is asked to process a sequence of requests lying in a metric space. To process a request the server must move to the corresponding point in the metric. The requests can be processed slightly out of order; in particular, the server has a buffer of capacity k which can store up to k requests as it reads in the sequence. The goal is to reorder the requests in such a manner that the buffer constraint is satisfied and the total travel cost of the server is minimized. The RBP arises in many applications that require scheduling with a limited buffer capacity, such as scheduling a disk arm in storage systems, switching colors in paint shops of a car manufacturing plant, and rendering 3D images in computer graphics. We study the offline version of RBP and develop bicriteria approximations. When the underlying metric is a tree, we obtain a solution of cost no more than 9 OPT using a buffer of capacity 4k+1 where OPT is the cost of an optimal solution with buffer capacity k. Via randomized tree embeddings, this implies an O(logn) approximation to cost and O(1) approximation to buffer size for general metrics. In contrast, when the buffer constraint is strictly enforced, constant-factor approximations are known only for the uniform metric (Avigdor-Elgrabli et al., 2012); the best known approximation ratio for arbitrary metrics is O(log2k logn) (Englert et al., 2007).