Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Locating nearby copies of replicated Internet servers
SIGCOMM '95 Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Bounded Geometries, Fractals, and Low-Distortion Embeddings
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Navigating nets: simple algorithms for proximity search
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Low distortion maps between point sets
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Triangulation and Embedding Using Small Sets of Beacons
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Approximation Algorithms for the 0-Extension Problem
SIAM Journal on Computing
Distributed approaches to triangulation and embedding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Distance estimation and object location via rings of neighbors
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Algorithms on negatively curved spaces
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
On triangulation of simple networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Approximation algorithms for embedding general metrics into trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Geometric rounding: a dependent randomized rounding scheme
Journal of Combinatorial Optimization
| Hi-index | 0.00 |
We design approximation algorithms for a number of fundamental optimization problems in metric spaces, namely computing separating and padded decompositions, sparse covers, and metric triangulations. Our work is the first to emphasize relative guarantees, that compare the produced solution to the optimal one for the input at hand. By contrast, the extensive previous work on these topics has sought absolute bounds that hold for every possible metric space (or for a family of metrics). While absolute bounds typically translate to relative ones, our algorithms provide significantly better relative guarantees, using a rather different algorithm. Our technical approach is to cast a number of metric clustering problems that have been well studied---but almost always as disparate problems---into a common modeling and algorithmic framework, which we call the consistent labeling problem. Having identified the common features of all of these problems, we provide a family of linear programming relaxations and simple randomized rounding procedures that achieve provably good approximation guarantees.