 
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
expander in it with appropriate dilation and congestion.
We call this an expander flow.
Categories and Subject Descriptors
F.2 [Theory of Computation]: Analysis of Algorithms
General Terms
