Sensitivity analysis on the all pairs q-route flows in a network

Madiagne Diallo (1) , Serigne Gueye (2) , Pascal Berthomé (3)

1 Engenharia Industrial
2 LMAH - Laboratoire de Mathématiques Appliquées du Havre
3 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

Given an undirected edge-weighted network in which one edge capacity is allowed to vary, we propose in this paper a polynomial algorithm that needs only two 2-cuttrees computations to provide the all pairs maximum 2-route flow values. Moreover, we provide an extension to the case where k edge capacities may vary, and show that 2^k 2-cut-trees computations are necessary in order to determine the all pairs maximum 2-route-flow values. This makes our algorithm polynomial whenever k = O(polylog n).

Keywords: multiroute flows; q-route flows; 2-cut-tree; parametric flows; sensitivity Analysis; cut-tree; multi-terminal; multiterminal

Domains: Operations Research [math.OC]

Madiagne Diallo, Serigne Gueye, Pascal Berthomé. Sensitivity analysis on the all pairs q-route flows in a network. International Transactions in Operational Research, 2010, 17 (1), pp.103-117. ⟨10.1111/j.1475-3995.2009.00698.x⟩. ⟨hal-00459975⟩