Seminar Details:

**LANS Informal Seminar***"On a combinatorial optimization problem involving the graph Laplacian matrix"*

DATE: October 25, 2013

TIME: 15:00:00 - 16:00:00

SPEAKER: Fu Lin, *Postdoctoral Appointee, MCS, Argonne National Labortatory*

LOCATION: Building 240, Room 1406-1407, Argonne National Laboratory

**Description:**

Given a graph Laplacian matrix, we are interested in finding a principal submatrix of fixed size such that the trace of the inverse of the submatrix is minimized. This combinatorial optimization problem arises in a variety of applications including leader-follower consensus networks, sensor localization, and circuit design. Instead of performing an exhaustive search, we develop efficient algorithms that provide lower and upper bounds on the global optimal value. A lower bound is obtained by solving a convex relaxation and an upper bound is obtained by using a greedy algorithm. Furthermore, we significantly reduce the computational complexity by exploiting problem structure (such as separability in the convex relaxation and low-rank update in the greedy algorithm). Illustrative examples ranging from random networks to regular lattices are used to gain interesting insight.

Please send questions or suggestions to Debojyoti Ghosh: ghosh at mcs dot anl dot gov.