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In the reordering buffer problem (RBP), a server is asked to process asequence of requests lying in a metric space. To process a request the servermust move to the corresponding point in the metric. The requests can beprocessed slightly out of order; in particular, the server has a buffer ofcapacity k which can store up to k requests as it reads in the sequence. Thegoal is to reorder the requests in such a manner that the buffer constraint issatisfied and the total travel cost of the server is minimized. The RBP arisesin many applications that require scheduling with a limited buffer capacity,such as scheduling a disk arm in storage systems, switching colors in paintshops of a car manufacturing plant, and rendering 3D images in computergraphics.  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 than9OPT using a buffer of capacity 4k + 1 where OPT is the cost of an optimalsolution with buffer capacity k. Constant factor approximations were knownpreviously only for the uniform metric (Avigdor-Elgrabli et al., 2012). Viarandomized tree embeddings, this implies an O(log n) approximation to cost andO(1) approximation to buffer size for general metrics. Previously the bestknown algorithm for arbitrary metrics by Englert et al. (2007) provided anO(log^2 k log n) approximation without violating the buffer constraint.

A Bicriteria Approximation for the Reordering Buffer Problem