An on-line graph coloring algorithm with sublinear performance ratio
Discrete Mathematics
Developments from a June 1996 seminar on Online algorithms: the state of the art
Incremental Clustering and Dynamic Information Retrieval
SIAM Journal on Computing
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
A randomized algorithm for online unit clustering
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
An improved algorithm for online unit clustering
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Online clustering with variable sized clusters
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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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 lower bound, improve the randomized lower bound, and prove the first lower bounds for higher dimensions.