New Algorithms for Online Unit Clustering

We study the online unit clustering problem introduced by Chan and Zarrabi-Zadeh at WAOA 2006. The problem in one dimension is as follows: Given a sequence of points on the real line, partition the points into clusters, each enclosable by a unit interval, with the objective of minimizing the number of clusters used. In this paper, we give a brief survey on the existing algorithms for this problem, and compare their efficiency in practice by implementing an deterministic and randomized algorithms proposed thus far for this problem in the literature. Meanwhile, we introduce two new deterministic algorithms that achieve better performance ratios on average in practice.