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Summary: Expander Flows, Geometric Embeddings and Graph
Partitioning
Sanjeev Arora
Satish Rao
Umesh Vazirani
ABSTRACT
We give a O(
log n)-approximation algorithm for spars-
est cut, balanced separator, and graph conduc-
tance problems. This improves the O(log n)-approxi-
mation of Leighton and Rao (1988). We use a well-
known semidefinite relaxation with triangle inequality
constraints. Central to our analysis is a geometric the-
orem about projections of point sets in d
, whose proof
makes essential use of a phenomenon called measure
concentration.
We also describe an interesting and natural "certifi-
cate" for a graph's expansion, by embedding an n-node
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