  There has been a recent surge in development of first-order methods (FOMs)
for solving huge-scale linear programming (LP) problems. The attractiveness of
FOMs for LP stems in part from the fact that they avoid costly matrix
factorization computation. However, the efficiency of FOMs is significantly
influenced - both in theory and in practice - by certain instance-specific LP
condition measures. Xiong and Freund recently showed that the performance of
the restarted primal-dual hybrid gradient method (PDHG) is predominantly
determined by two specific condition measures: LP sharpness and Limiting Error
Ratio. In this paper we examine the relationship between these two measures,
particularly in the case when the optimal solution is unique (which is generic
- at least in theory), and we present an upper bound on the Limiting Error
Ratio involving the reciprocal of the LP sharpness. This shows that in LP
instances where there is a dual nondegenerate optimal solution, the
computational complexity of restarted PDHG can be characterized solely in terms
of LP sharpness and the distance to optimal solutions, and simplifies the
theoretical complexity upper bound of restarted PDHG for these instances.
