This study deals with the facility location problem of locating a set
V
p
of
p
facilities on a graph such that the subgraph induced by
V
p
is connected. We consider the connected
p
-median problem on a cactus graph
G
whose vertices and edges have nonnegative weights. The aim of a connected
p
-median problem is to minimize the sum of weighted distances from every vertex of a graph to the nearest vertex in
V
p
. We provide an
O
n
2
p
2
time algorithm for the connected
p
-median problem, where
n
is the number of vertices.
A branch-and-price algorithm for the robust single-source capacitated facility location problem under demand uncertainty
