Metric Clustering via Consistent Labeling
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 28, 2010
- Accession Number
- ADA637878
Entities
People
- Robert Krauthgamer
- Tim Roughgarden
Organizations
- Stanford University