graph_lecture-Sam_Brody

# graph_lecture-Sam_Brody - Euler Cycle A cycle (path that...

This preview shows pages 1–3. Sign up to view the full content.

Euler Cycle A cycle (path that starts and ends at the same node) which traverses each edge exactly once. Bridges of Konigsberg (http://en.wikipedia.org/wiki/Seven_Bridges_of_Konigsberg): Sufficient and Necessary condition: all nodes have an even degree Intuition – each node you reach, you have to be able to leave. That's impossible with odd an odd number of edges – you reach a dead end the last time you get there. Eulerian Path – don't have to stop and end at the same node – at most two nodes have uneven degree (one for start, one for end). Hamiltonian Path A path covering all nodes exactly once. Considered a “hard” problem – no know solution that is more efficient than trying all the possibilities.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Traveling Salesman Problem (TSP) Now looking at graphs where edges have weights. These can be distance, cost, time, etc. This adds a new dimension of complexity. Naturally, we want to minimize the cost. The problem is – find the minimal path that covers all the nodes. Repeats are allowed. In the example
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/20/2012 for the course 790 373 taught by Professor Boros during the Fall '09 term at Rutgers.

### Page1 / 4

graph_lecture-Sam_Brody - Euler Cycle A cycle (path that...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online