Algorithms for clustering data
Algorithms for clustering data
Exact and approximation algorithms for clustering
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
ACM Computing Surveys (CSUR)
Approximate clustering via core-sets
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Approximate minimum enclosing balls in high dimensions using core-sets
Journal of Experimental Algorithmics (JEA)
Clustering and reconstructing large data sets
Clustering and reconstructing large data sets
Image Processing - Principles and Applications
Image Processing - Principles and Applications
Polynomial time approximation schemes for base station coverage with minimum total radii
Computer Networks: The International Journal of Computer and Telecommunications Networking
Information Retrieval Architecture and Algorithms
Information Retrieval Architecture and Algorithms
Geometric clustering to minimize the sum of cluster sizes
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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The k-center problem arises in many applications such as facility location and data clustering. Typically, it is solved using a branch and bound tree traversed using the depth first strategy. The reason is its linear space requirement compared to the exponential space requirement of the breadth first strategy. Although the depth first strategy gains useful information fast by reaching some leaves early and therefore assists in pruning the tree, it may lead to exploring too many subtrees before reaching the optimal solution, resulting in a large search cost. To speed up the arrival to the optimal solution, a mixed breadth-depth traversing strategy is proposed. The main idea is to cycle through the nodes of the same level and recursively explore along their first promising paths until reaching their leaf nodes (solutions). Thus many solutions with diverse structures are obtained and a good upper bound of the optimal solution can be achieved by selecting the minimum among them. In addition, we employ inexpensive lower and upper bounds of the enclosing balls, and this often relieves us from calling the computationally expensive exact minimum enclosing ball algorithm. Experimental work shows that the proposed strategy is significantly faster than the naked branch and bound approach, especially as the number of centers and/or the required accuracy increases.