Constrained Rerouting in Networks: An Integer Programming Formulation
Sam Weyerman*, Ramesh Bhandari, Laboratory for Telecommunications Sciences,
Blake Durtschi, L3 Communications
Given an undirected, weighted graph, G = (V,E), and a pair of vertices s and t, connected
by the shortest path, and an edge (p,q) not lying on the shortest path, how can one change
the graph weights to cause the shortest path between s and t to pass through edge (p,q),
while minimizing the number of other shortest paths (corresponding to other pairs of
vertices) affected by the changes? The minimization objective is necessary to reduce the
chaos in traffic flows that occurs on account of edge weight changes in the network. The
problem is cast as an integer program (IP) motivated by infeasibility analysis, and
subsequently solved using a linear relaxation in conjunction with some variants to reduce
computation time. We validate our algorithm by comparing the variants to each other and
the sliding shortest path algorithm.
Keywords: shortest path, algorithm, weighted graph, undirected, network, optimization,
integer programming, minimal edge weight changes, linear relaxation, rerouting,
constrained.