  Graph sampling with noise is a fundamental problem in graph signal processing
(GSP). Previous works assume an unbiased least square (LS) signal
reconstruction scheme and select samples greedily via expensive extreme
eigenvector computation. A popular biased scheme using graph Laplacian
regularization (GLR) solves a system of linear equations for its
reconstruction. Assuming this GLR-based scheme, we propose a
reconstruction-cognizant sampling strategy to maximize the numerical stability
of the linear system---\textit{i.e.}, minimize the condition number of the
coefficient matrix. Specifically, we maximize the eigenvalue lower bounds of
the matrix, represented by left-ends of Gershgorin discs of the coefficient
matrix. To accomplish this efficiently, we propose an iterative algorithm to
traverse the graph nodes via Breadth First Search (BFS) and align the left-ends
of all corresponding Gershgorin discs at lower-bound threshold $T$ using two
basic operations: disc shifting and scaling. We then perform binary search to
maximize $T$ given a sample budget $K$. Experiments on real graph data show
that the proposed algorithm can effectively promote large eigenvalue lower
bounds, and the reconstruction MSE is the same or smaller than existing
sampling methods for different budget $K$ at much lower complexity.
