DM OR. Networks. Graphs : Koenigsberg bridges. Leonard Euler problem (1736). Nodes. Edges. Is there a walk which uses each edge exactly once ?. Build two more bridges . Each such walk has to enter and leave any given node . The degree of any node has to be even .
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Leonard Euler problem (1736)
Eachsuch walk has to enter and leaveanygivennode. Thedegree of anynodehas to be even.
Travelling salesman problem
2 d 7 h 2 m Length:
2 d 4 h 37 m
29 d 11 h 21 m Length:
Enumeration – impractical
An example of the so calledgreedy algorithm –itdoeswhat’sbestin a given step not lookingattheotherstages of the problem (usuallyineffective – hereitiseffective!)
One can do a maximalspanningtreethe same way
4 cars/m on route A-D-E-G
3 cars/m ojnroute A-B-E-G
4 cars/m on route A-C-F-G
Total flowbetween A and G is11 cars/m