A flow model based on polylinking system

We introduce polylinking networks, which is a flow model based on polylinking systems that generalizes the classical flow model of Ford and Fulkerson on acyclic networks and has applications in the context of wireless networks. More precisely, a flow model recently introduced by Avestimehr et al. (Proceedings of the Allerton conference on communication, control, and computing 2007) used in the context of wireless information networks is a special case of the presented model. We define a notion of source-destination cut and derive a max-flow min-cut theorem. Additionally, we present various properties of polylinking networks that can be seen as generalizations of properties for classical flows. Using submodular function minimization and submodular flow algorithms, one can efficiently determine a maximum flow, a minimum source-destination cut, as well as a minimum cost flow. These algorithms lead to new efficient algorithms for the information flow model. An earlier shorter version of this article [9] focused mainly on the relation between the ADT model and linking flows. M. X. Goemans was supported by NSF contract CCF-0829878 and by ONR grant N00014-05-1-0148. R. Zenklusen was supported by the Swiss National Science Foundation, grant number: PBEZP2-129524. M. X. Goemans Department of Mathematics, M.I.T., Room 2-351, Cambridge, MA 20139, USA e-mail: [email protected] S. Iwata Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan e-mail: [email protected] R. Zenklusen (B) Department of Mathematics, M.I.T., Room 2-332, Cambridge, MA 20139, USA e-mail: [email protected]