CHINESE POSTMAN ALGORITHM This is used when we

CHINESE POSTMAN ALGORITHM This is used when we are trying to find the shortest route round a network such all the arcs are travelled along at least once.

Step 1: Identify all the odd vertices Step 2: Form all possible pairings of odd vertices Step 3: For each pairing find the arcs that make the total distance of repeats as small as possible Step 4: Choose the pairing with the smallest sum and add this to the graph Step 5: Find a route that works and add the smallest sum found in Step 4 to the sum of all the weights in the original graph to find the length of the required route.

Add this the network vertices are B, at G, H & Tdepot T and AOdd postman starts the has toto deliver mail Possible pairings: along the streets in the network below. Find a The all shortest extra shown route is: Possible route is: route that means he travels the shortest BGpossible & HT distance. TABEAGHEGHFDFECDTCBCT Route: BEG & HECT You. Length: don’t believe me? 1. 7 + 1. 8 = 3. 5 GTit? Want. BH to & see Route: BEH & GECT Length: 1. 5 + 2. 0 = 3. 5 BT & GH Route: BCT & GH Length: 0. 8 + 0. 9 = 1. 7

T A B C E D Total length of all original paths is 16. 45 km F Add on the extra routes BCT and GH = 1. 7 km Shortest length = 16. 45 + 1. 7 = 18. 15 km G H Route is: T A B E A G H E G H F D F E C D T C B C T