An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
Multidimensional binary search trees used for associative searching
Communications of the ACM
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Solving the uncapacitated facility location problem using tabu search
Computers and Operations Research - Anniversary focused issue of computers & operations research on tabu search
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Tree-based partition querying: a methodology for computing medoids in large spatial datasets
The VLDB Journal — The International Journal on Very Large Data Bases
SFCS '75 Proceedings of the 16th Annual Symposium on Foundations of Computer Science
A new and efficient k-medoid algorithm for spatial clustering
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
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Constraint-based local search is an important paradigm in the field of constraint programming, particularly when considering very large optimisation problems. We are motivated by applications in areas such as telecommunications network design, warehouse location and other problems in which we wish to select an optimal set of locations from a two dimensional plane. The problems we are interested in are so large that they are ideal candidates for constraint-based local search methods. Maintaining the objective function incrementally is often a key element for efficient local search algorithms. In the case of two dimensional plane problems, we can often achieve incrementality by exploiting computational geometry. In this paper we present a novel approach to solving a class of placement problems for which Voronoi cell computation can provide an efficient form of incrementality. We present empirical results demonstrating the utility of our approach against the current state of the art.