The orthogonal CNN problem

The online CNN problem had no known competitive algorithms for a long time. Sitters, Stougie and de Paepe showed that there exists a competitive online algorithm for this problem. However, both their algorithm and analysis are quite complicated, and above all, their upper bound for the competitive ratio is 10⁵. In this paper, we examine why this problem seems so difficult. To this end we introduce a nontrivial restriction, orthogonality, against this problem and show that it decreases the competitive ratio dramatically, down to at most 9.