 
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 nnode
