Edge Walker Technique

1
Edge Walker Technique

• Pick a corner of the network.
• Begin walking an edge until you hit an odd-valent
  vertex.
• Start an edge and connect to next vertex.
• If that vertex is now even, repeat step 2.
• If that vertex is now odd, begin a new edge.
• Continue until you have walked around the entire
  graph.

2
Non-Rectangular Networks

• Locate all odd valences.
• Pair vertices w/ each other by finding the
  shortest path between each pair.
• Note shortest path leads to least total
  distance traveled

3
Visiting Vertices
4
Suppose

• Rather than crossing an edge, and stopping at
  various spots (parking control, mail delivery)
• You just need to get to a vertex. (Package
  delivery, location inspection)

5
Hamiltonian Circuits

• Hamiltonian circuits tour that starts at a
  vertex of a graph and ends at the same vertex and
  visits each vertex once and only once
• How does this differ from an Euler circuit??
• (see next slide)

6
Differences between Euler and Hamiltonian

• Euler concerned with crossing each edge of the
  graph only once while beginning and ending at the
  same vertex
• Hamiltonian concerned with visiting each vertex
  only once while beginning and ending at the same
  vertex

7
Difference number 2

• Unlike Euler, there is no simple method to
  determining if a graph has a Hamiltonian circuit.
• However, some special graphs do not have
• Hamiltonian circuits
• vertical column of m vertices and a vertical
  column of n vertices where m gt n

8
Using Hamiltonian Circuits to plan for vacation

• Apply weights weights incorporate factors
  the impact travel plans
• ex. Distances, cost, time, profit
• Minimum-cost Hamiltonian Circuit Ham. Circuit
  with the lowest possible sum of weights of its
  edges

9
Homework

• Read sections 2.1, 2.2
• Pg. 29
• 45a, 47, 49, 51