Maximum flow under proportional delay constraint

Pierre Bonami (1) , Dorian Mazauric (2) , Yann Vaxès (3)

1 ACRO
2 LIF - Laboratoire d'informatique Fondamentale de Marseille
3 ACRO - Algorithmique, combinatoire et recherche opérationnelle

Given a network and a set of source destination pairs (connections), we con- sider the problem of maximizing the sum of the flow under proportional delay constraints. In this paper, the delay for crossing a link is proportional to the total flow crossing this link. If a connection supports non-zero flow, then the sum of the delay along any path corresponding to that connection must be lower than a given bound. The constraints of delay are on-off constraints because if a connection does not support non-zero flow, then there is no constraint for that connection. The difficulty of the problem comes from the choice of the connections supporting non-zero flow. We first prove a general approximation ratio using linear programming for a variant of the problem. We then prove a Polynomial Time Approximation Scheme when the graph of intersection of the paths has bounded treewidth. We finally prove that the problem is NP-hard even when the network is a tree.

Mots clés: Maximum flow; on-off delay constraints; polynomial time approximation scheme (PTAS); dynamic programming; bounded treewidth; linear programming; NP-hardness

Domaines: Algorithme et structure de données [cs.DS]

Pierre Bonami, Dorian Mazauric, Yann Vaxès. Maximum flow under proportional delay constraint. 2014. ⟨hal-00947049⟩