We give almost tight bounds for the online reordering buffer management problem on the uniform metric. Specifically, we present the first non-trivial lower bounds for this problem by showing that deterministic online algorithms have a competitive ratio of at least Ω( log k/ log log k) and randomized online algorithms have a competitive ratio of at least Ω(log log k), where k denotes the size of the buffer. We complement this by presenting a deterministic online algorithm for the reordering buffer management problem that obtains a competitive ratio of O( √ log k), almost matching the lower bound. This improves upon an algorithm by Avigdor-Elgrabli and Rabani (SODA 2010) that achieves a competitive ratio of O(log k/ log log k).
To complement this, there are nearly matching lower bounds of Ω( log k/log log k) and Ω(log log k) on the competitive ratio of any online deterministic and randomized algorithms, respectively REF .
Almost tight bounds for reordering buffer management
STOC '11
Computer Science