A faster implementation of the Goemans-Williamson clustering algorithm
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Quick and good facility location
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Evaluation of multicast routing algorithms for real-time communication on high-speed networks
Proceedings of the IFIP Sixth International Conference on High Performance Networking VI
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Quick k-Median, k-Center, and Facility Location for Sparse Graphs
SIAM Journal on Computing
Universal approximations for TSP, Steiner tree, and set cover
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Fast construction of nets in low dimensional metrics, and their applications
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On hierarchical routing in doubling metrics
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Metric Facility Location Problems
SIAM Journal on Computing
Reoptimization of Steiner Trees
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Reoptimization of Steiner trees: Changing the terminal set
Theoretical Computer Science
On the hardness of reoptimization
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
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In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees that need to be constructed for different groups of users. In our model we allow a preprocessing phase, when some information of the input graph G = (V, E) is stored in a limited size data structure. Next, the data structure enables processing queries of the form "solve problem A for an input S ⊆ V". We consider problems like STEINER FOREST, FACILITY LOCATION, k-Median, k-Center and TSP in the case when the graph induces a doubling metric. Our main results are data structures of near-linear size that are able to answer queries in time close to linear in |S|. This improves over typical worst case reuniting time of approximation algorithms in the classical setting which is Ω(|E|) independently of the query size. In most cases, our approximation guarantees are arbitrarily close to those in the classical setting. Additionally, we present the first fully dynamic algorithm for the Steiner tree problem.