 
Summary: Approximate classification via earthmover metrics
Aaron Archer # Jittat Fakcharoenphol + Chris Harrelson # Robert Krauthgamer §
Kunal Talwar ¶ ’
Eva Tardos #
Abstract
Given a metric space (X, d), a natural distance measure
on probability distributions over X is the earthmover
metric. We use randomized rounding of earthmover
metrics to devise new approximation algorithms for
two wellknown classification problems, namely, metric
labeling and 0extension.
Our first result is for the 0extension problem. We
show that if the terminal metric is decomposable with
parameter # (e.g., planar metrics are decomposable
with # = O(1)), then the earthmover based linear
program (for 0extension) can be rounded to within an
O(#) factor.
Our second result is an O(log n)approximation for
metric labeling, using probabilistic tree embeddings in
a way very di#erent from the O(log k)approximation
