The cost optimal solution of the multi-constrained multicast routing problem

Miklós Molnár, Alia Bellabas, Samer Lahoud
2012 Computer Networks  
In this paper, we study the cost optimal solution of the well-known multi-constrained multicast routing problem. This problem consists in finding a multicast structure that spans a source node and a set of destination nodes with respect to a set of constraints. This optimization problem is particularly interesting for the multicast network communications that require Quality of Service (QoS) guarantees. Moreover, finding the multicast structure with respect to the defined QoS requirements while
more » ... minimizing a cost function is an NP-difficult optimization problem. According to the state-of-the-art, to solve the multi-constrained multicast routing problem, most of the proposed algorithms search for a multicast tree. In this paper, we demonstrate that the optimal connected partial spanning structure that solves the multi-constrained multicast routing problem can be different from a partial spanning tree. Indeed, we show that the minimum cost solution always corresponds to hierarchy, a recently proposed simple generalization of the tree concept. For that, we define and analyze the partial minimum spanning hierarchies as optimal solutions for the multi-constrained multicast routing problem. Moreover, we propose a branch and cut type exact algorithm that is based on some relevant properties of the hierarchical solutions. Key-words: Multicast, quality of service, multi-constrained Steiner problem, hierarchy, partial minimum spanning hierarchy Routage multi-contraint multicast optimal Résumé : Le routage multi-contraint multicast est un problème NP-difficile. Dans ce papier, nousétudions ce problème et analysons les propriétés de la solution optimale. Contrairementà ce qui est connu dans l'état de l'art, les arbres ne sont pas toujours les structures optimales pour le problème du routage multi-contraint multicast. Notre contribution principale est de définir la nature de la structure optimale pour le problème traité. Nous présentons les hierarchies qui sont des généralisations des arbres et nous prouvons que la solution optimale est toujours une hiérarchie. Nous analysonségalement les propriétés de la solution optimale et défissions un nouvel algorithme branch and cut pour trouver cette solution optimale.
doi:10.1016/j.comnet.2012.04.020 fatcat:lzusw23ehzgfbcgzh2obl6ykzm