Better Bounds on Online Unit Clustering
نویسندگان
چکیده
Unit Clustering is the problem of dividing a set of points from a metric space into a minimal number of subsets such that the points in each subset are enclosable by a unit ball. We continue work initiated by Chan and Zarrabi-Zadeh on determining the competitive ratio of the online version of this problem. For the one-dimensional case, we develop a deterministic algorithm, improving the best known upper bound of 7/4 by Epstein and van Stee to 5/3. This narrows the gap to the best known lower bound of 8/5 to only 1/15. Our algorithm automatically leads to improvements in all higher dimensions as well. Finally, we strengthen the deterministic lower bound in two dimensions and higher from 2 to 13/6.
منابع مشابه
Online unit clustering in higher dimensions
We revisit the online Unit Clustering problem in higher dimensions: Given a set of n points in R, that arrive one by one, partition the points into clusters (subsets) of diameter at most one, so as to minimize the number of clusters used. In this paper, we work in R using the L∞ norm. We show that the competitive ratio of any algorithm (deterministic or randomized) for this problem must depend ...
متن کاملResearch on Clustering Algorithm Based on Grid Density on Uncertain Data Stream
To solve the clustering algorithm based on grid density on uncertain data stream in adjustment cycle for clustering omissions, the paper proposed an algorithm, named GCUDS, to cluster uncertain data steam using grid structure. The concept of the data trend degree was defined to describe the grade of a data point belonging to some grid unit and the defect of information loss around grid units wa...
متن کاملOnline Packing of Equilateral Triangles
We investigate the online triangle packing problem in which a sequence of equilateral triangles with different sizes appear in an online, sequential manner. The goal is to place these triangles into a minimum number of squares of unit size. We provide upper and lower bounds for the competitive ratio of online algorithms. In particular, we introduce an algorithm which achieves a competitive rati...
متن کاملAdjustable Probability Density Grid-Based Clustering for Uncertain Data Streams
Most existing traditional grid-based clustering algorithms for uncertain data streams that used the fixed meshing method have the disadvantage of low clustering accuracy. In view of above deficiencies, this paper proposes a novel algorithm APDG-CUStream, Adjustable Probability Density Grid-based Clustering for Uncertain Data Streams, which adopts the online component and offline component. In o...
متن کاملOnline unit clustering: Variations on a theme
Online unit clustering is a clustering problem where classification of points is done in an online fashion, but the exact location of clusters can be modified dynamically. We study several variants and generalizations of the online unit clustering problem, which are inspired by variants of packing and scheduling problems in the literature.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Theor. Comput. Sci.
دوره 500 شماره
صفحات -
تاریخ انتشار 2010