(!******************************************************
   Mosel Example Problems
   ======================

   file j2bigbro.mos
   `````````````````
   CCTV surveillance
   
   A town council has determined candidate street intersections  
   where cameras can be installed. A map providing the possible 
   locations is given. Where should the cameras be located
   to monitor all the streets to minimize the total number
   of installed cameras?

   This problem is modeled as a graph-based IP model. Nodes
   in the graph correspond to street intersections where 
   cameras can be installed, and links correspond to the 
   streets connecting nodes. The undirected graph is 
   encoded by a symmetric adjacency matrix. The unique set
   of constraints guarantees that every street needs
   to be surveyed by at least one camera.

   (c) 2008-2022 Fair Isaac Corporation
       author: S. Heipcke, Mar. 2002, rev. Mar. 2022
*******************************************************!)

model "J-2 CCTV surveillance"
 uses "mmxprs"

 declarations
  NODES=1..49
  STREET: dynamic array(NODES,NODES) of integer  ! 1 if a street connects
                                                 ! two nodes, 0 otherwise
  
  place: array(NODES) of mpvar     ! 1 if camera at node, 0 otherwise
 end-declarations

 initializations from 'j2bigbro.dat'
  STREET
 end-initializations

 forall(n,m in NODES | exists(STREET(n,m)) and n<m ) 
  STREET(m,n):= STREET(n,m)

! Objective: number of cameras to install
 Total:= sum(n in NODES) place(n)

! Flow balances in nodes
 forall(n,m in NODES | exists(STREET(n,m)) ) place(n)+place(m) >= 1

 forall(n in NODES) place(n) is_binary

! Solve the problem
 minimize(Total)
 
! Solution printing
 writeln("Total number of cameras: ", getobjval)
 forall(n in NODES | getsol(place(n))>0) write(" ", n)
 writeln
 
end-model