Finiteness of the criss-cross algorithm for the linear programming problem with s-monotone index selection rules

The traditional criss-cross algorithm for the linear programming problem is shown to be finite when s-monotone index selection rules are used. The set of s-monotone index selection rules, among others, include the Last In First Out (LIFO) and the Most Often Selected Variable rule (MOSV). The advantage of applying the s-monotone index selection rule is the flexibility it provides in selecting the pivot element while still preserving the guarantee for finiteness. Such flexibility may be used to improve the numerical stability of the algorithm.