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» Improved Bounds for Geometric Permutations
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COMPGEOM
2009
ACM
15 years 6 months ago
k-means requires exponentially many iterations even in the plane
The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice....
Andrea Vattani
CORR
2004
Springer
113views Education» more  CORR 2004»
15 years 1 months ago
A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framewo...
Sándor P. Fekete, Jörg Schepers
TCAD
2008
136views more  TCAD 2008»
15 years 1 months ago
A Geometric Programming-Based Worst Case Gate Sizing Method Incorporating Spatial Correlation
We present an efficient optimization scheme for gate sizing in the presence of process variations. Our method is a worst-case design scheme, but it reduces the pessimism involved i...
Jaskirat Singh, Zhi-Quan Luo, Sachin S. Sapatnekar
SODA
2010
ACM
202views Algorithms» more  SODA 2010»
15 years 10 months ago
Counting Inversions, Offline Orthogonal Range Counting, and Related Problems
We give an O(n lg n)-time algorithm for counting the number of inversions in a permutation on n elements. This improves a long-standing previous bound of O(n lg n/ lg lg n) that ...
Timothy M. Chan, Mihai Patrascu
COMPGEOM
2009
ACM
15 years 8 months ago
Epsilon nets and union complexity
We consider the following combinatorial problem: given a set of n objects (for example, disks in the plane, triangles), and an integer L ≥ 1, what is the size of the smallest su...
Kasturi R. Varadarajan