ACM Transactions on Algorithms · 2010 · 53 citations · 6 references
Mathematical ProgrammingCluster ComputingRandomized Lower BoundEngineeringNetwork AnalysisEducationComputational ComplexityUnsupervised Machine LearningCluster TechnologyOnline ProblemData MiningDiscrete MathematicsCombinatorial OptimizationOnline UnitOnline AlgorithmComputer ScienceAlgorithmic Information TheoryNetwork ScienceDeterministic AlgorithmRandomized Algorithm
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.
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Incremental Clustering and Dynamic Information Retrieval
Moses Charikar, Chandra Chekuri, Tomás Feder et al. · SIAM Journal on Computing · 2004 · 234 citations
On‐line and first fit colorings of graphs
András Gyárfás, Jenő Lehel · Journal of Graph Theory · 1988 · 193 citations