Electrical Engineering and Computer Science

Theory Seminar

Graph Isomorphism and the Lasserre Hierarchy

Aaron Snook

University of Michigan
 
Friday, January 24, 2014
10:30am - 11:30am
3941 BBB

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About the Event

In this paper I show lower bounds for a certain large class of algorithms solving the Graph Isomorphism problem, even on expander graph instances. Spielman [25] shows an algorithm for isomorphism of strongly regular expander graphs that runs in time exp~O(n^(1/3)) (this bound was recently improved to expf~O(n^(1/5))). It has since been an open question to remove the requirement that the graph be strongly regular. Recent algorithmic results show that for many problems the Lasserre hierarchy works surprisingly well when the underlying graph has expansion properties. Moreover, recent work of Atserias and Maneva [3] shows that k rounds of the Lasserre hierarchy is a generalization of the k-dimensional Weisfeiler-Lehman algorithm for Graph Isomorphism. These two facts combined make the Lasserre hierarchy a good candidate for solving graph isomorphism on expander graphs. My main result rules out this promising direction by showing that even Omega(n) rounds of the Lasserre semide nite program hierarchy fail to solve the Graph Isomorphism problem even on expander graphs.

Additional Information

Sponsor: CSE

Open to: Public