Cleaning Tunnel
Problem
Phuoc Le
ICS 311
[email protected]
Graph Formulation
• Edges as tunnel
• Vertices u and v are
two end points of the
edg e = (u, v)
• The cleaning machine
moving along the
edge
Graph Formulation
Tunnel with 1 edge
• Tunnel
• End point u and v
• Cleaning machine
• Contaminated
Number of edge: 1
Clean
Number of machine: 1
Graph Formulation
Tunnel with 3 edges
• Tunnel
• End point u and v
• Cleaning machine
guarded
Number of edges: 3
New
machine
Graph Formulation
Tunnel with 3 edges
• Tunnel
• End point u and v
• Cleaning machine
terminated
Contaminated
tunnel
Number of edges: 3
Number of machines: 2
Cleaned tunnel
Graph Formulation
Tunnel with 4 edges
• Tunnel
• End point u and v
• Cleaning machine
Number of edges: 4
Graph Formulation
Tunnel with 4 edges
• Tunnel
• End point u and v
• Cleaning machine
Machine 1
Guarded
machine 2
Number of edges: 4
Graph Formulation
Tunnel with 4 edges
• Tunnel
• End point u and v
• Cleaning machine
guarded
Number of edges: 4
New location of
machine 1
Graph Formulation
Tunnel with 4 edges
• Tunnel
• End point u and v
• Cleaning machine
Guarded
machine 2
Number of edges: 4
New machine 3
Guarded
machine 1
Graph Formulation
Tunnel with 4 edges
• Tunnel
• End point u and v
• Cleaning machine
Guarded
machine 2
Guarded
machine 1
Terminated machine 3
Number of edges: 4
Number of machines: 3
Graph Formulation
Tunnel with 5 edges
• Tunnel
• End point u and v
• Cleaning machine
Guarded
machine 2
Guarded
machine 1
machine 3 guarded
Number of edges: 5
Graph Formulation
Tunnel with 5 edges
• Tunnel
• End point u and v
• Cleaning machine
machine 2
moved here
machine 1
moved here
machine 3 guarded
Number of edges: 5
Graph Formulation
Tunnel with 5 edges
• Tunnel
• End point u and v
• Cleaning machine
New
machine 4
machine 2
guarded
machine 1
guarded
machine 3 guarded
Number of edges: 5
Graph Formulation
Tunnel with 5 edges
• Tunnel
• End point u and v
• Cleaning machine
machine 2
guarded
machine 1
guarded
Number of edges: 5
Graph (G) = 10 edges
machine 3 guarded
Number of machine: 4
machine 4
terminated
Input
• A graph G = (V, E)
• A set of edges E where E is
tunnel
• A set of vertices Vs where Vs is
starting vertex and Vd where Vd is
destination vertex
Input
• A set of machines m where mi (1
≤ i ≤ km)
• A function max(ei) to return
maximum number of edges at
intersection where ei ( 1 ≤ i ≤ ne)
Input
• A function fm(fi) to return the number of
free machines where (0 ≤ i ≤ km)
• A function mg(Vi) to return the number of
guraded machines where (0 ≤ i ≤ km )
Output
• A function Min_m(G) = max(ei)-1
Constraint
•
•
•
•
Connected graph
The machine must clean the tunnel from
one end point u to v.
The machine can move to the new
location if that machine is in the clean
area
The adjacent edge such that e = (x, y)
and f =(y, z)