SIGACT News Online Algorithms Column 33

Abstract

For this issue, Matthias Englert has contributed an alternative and simpler proof of a result by Gamzu and Segev, which was in ACM Transactions on Algorithms in 2009. The problem considered in this paper was the reordering bu↵er problem on the line. Gamzu and Segev were the first to give an O(log n)-competitive algorithm for this problem, and there has been no improvement on this since then, leaving a gap with the best known lower bound of 2.154 by the same authors. Matthias’ proof shows that this result can be slightly improved (a smaller hidden constant) and simplified. Who is going to be the first to give a constant competitive algorithm, or show that this cannot be done?