Simpler pivoting rules using shadow-edge information

Develop simpler pivoting rules for general linear programs that achieve the same effect as the Shifting Shadow pivot rule—namely, escaping degeneracy with controlled Simplex pivots while following a specified shadow edge—without requiring computation of the shadow edge by solving an LP-equivalent problem.

Background

The Shifting Shadow pivot rule relies on prior knowledge of the shadow edge-direction. For 0/1-LPs, the relevant shadow-edge computation can be performed in strongly polynomial time, whereas for general LPs it is stated to be no easier than solving the LP itself. The authors therefore leave unresolved the search for simpler pivoting rules that retain the same degeneracy-escaping and path-control guarantees.