Composite Path Algebras for Solving Path Problems in Graphs

Abstract

Path problems in graphs can generally be formulated and solved by using an algebraic structure whose instances are called path algebras. Each type of path problem is characterized by a different instance of the structure. This paper proposes a method for combining already known path algebras into new ones. The obtained composite algebras can be applied to solve relatively complex path problems, such as explicit identification of optimal paths or multi-criteria optimization. The paper presents proofs showing that the proposed construction is correct. Also, prospective applications of composite algebras are illustrated by examples. Finally, the paper explores possibilities of making the construction more general.