Linear Programming Based Algorithms

Abstract

In Chapter 4, we showed that when a graph is embedded in a suitably constructed Markov decision process, the associated convex domain of discounted occupational measures is a polyhedron with extreme points corresponding to all spanning subgraphs of the given graph. Furthermore, from Theorem 4.1 we learned that a simple cut of the above domain yields a polyhedron the extreme points of which correspond to only two possible types: Hamiltonian cycles and convex combinations of short and noose cycles. These properties, naturally, suggest certain algorithmic approaches to searching for Hamiltonian cycles.