On the online unit clustering problem

Leah Epstein, Rob Van Stee
2010 ACM Transactions on Algorithms  
We continue the study of the online unit clustering problem, introduced by Chan and Zarrabi-Zadeh (Workshop on Approximation and Online Algorithms 2006, LNCS 4368, p.121-131. Springer, 2006. We design a deterministic algorithm with a competitive ratio of 7/4 for the one-dimensional case. This is the first deterministic algorithm that beats the bound of 2. It also has a better competitive ratio than the previous randomized algorithms. Moreover, we provide the first non-trivial deterministic
more » ... bound, improve the randomized lower bound, and prove the first lower bounds for higher dimensions.
doi:10.1145/1868237.1868245 fatcat:pfcmmi5tvfes5pyapkjb7xsfn4