Path Problems In Networks

The algebraic path problem is a generalization of the shortest path problem in graphs. Various instances of this problem have appeared in the literature, and similar solutions have been independently discovered and rediscovered. The repeated appearance of this problem is evidence of its relevance, and was the motivation for writing this text. In this monograph, we briefly survey the extensive theory behind the algebraic path problem. We then proceed to describe various applications of the algebraic path problem that have appeared in the literature, ranging from mobile network routing to social networks.