Logarithmic price of buffer downscaling on line metrics

TL;DR

This paper demonstrates that reducing buffer size in the line reordering buffer problem causes a logarithmic increase in cost, establishing the near-optimality of existing online algorithms with larger buffers.

Contribution

It proves a logarithmic lower bound on the performance degradation when buffer size is decreased, confirming the optimality of the MovingPartition algorithm.

Findings

Buffer reduction leads to Omega(log n) performance loss.

MovingPartition algorithm is essentially optimal for buffer size.

Performance gap persists even with small buffer reductions.

Abstract

We consider the reordering buffer problem on a line consisting of n equidistant points. We show that, for any constant delta, an (offline) algorithm that has a buffer (1-delta) k performs worse by a factor of Omega(log n) than an offline algorithm with buffer k. In particular, this demonstrates that the O(log n)-competitive online algorithm MovingPartition by Gamzu and Segev (ACM Trans. on Algorithms, 6(1), 2009) is essentially optimal against any offline algorithm with a slightly larger buffer.