Louisiana Travels

O2, L3, M2, B4, K4, P3, C3, N3, S2 Task 1 : Not traversable; there are 4 odd nodes To make the network semi-traversable, remove one edge between two odd nodes (this will create a new network that is traversable, because it will have 2 odd nodes) For example, remove the edge between Ponchatoula and Covington OR remove the edge between Covington and New Orleans

P-C has been removed; O2, L3, M2, B4, K4, P2, C2, N3, S2; Travel N, C, S, N, K, B, P, K, M, L, O, B, L

C-N has been removed; O2, L3, M2, B4, K4, P3, C2, N2, S2; Travel P, B, O, L, M, K, P, C, S, N, K, B, L

Task 2: drive from New Orleans to Opelousas, stopping in at Ponchatoula on the return trip.

Task 2a: Shortest Path: N-K-B-O = 144miles (An alternate path NKBLO = 164 miles)

Task 2b: shortest path from Opelousas to New Orleans via Ponchatoula: O-B-P-K-N = 161 miles

63 24 46 24 28 59 40 41 69 33 12 68 74 Task 3 info: Minimum spanning tree; $25000 per mile; edge P-C is not to be upgraded

63 46 24 28 59 40 41 69 33 12 68 74 Task 3a: “Polygon Method”, which eliminates the route of highest distance from each polygon shape, eventually leaving a connected tree network.

Task 3a: “Polygon Method”, Step 1: - Remove C-N from CNSC (Why?) 63 46 24 28 59 40 69 33 12 68 74 Task 3a: “Polygon Method”, Step 1: - Remove C-N from CNSC (Why?)

Task 3a: “Polygon Method”, Step 2: - Remove B-K from BKPB (Why?) 63 46 24 28 59 40 33 12 68 74 Task 3a: “Polygon Method”, Step 2: - Remove B-K from BKPB (Why?)

Task 3a: “Polygon Method”, Step 3: - Remove O-B from OBLO (Why?) 46 24 28 59 40 33 12 68 74 Task 3a: “Polygon Method”, Step 3: - Remove O-B from OBLO (Why?)

Task 3a: “Polygon Method”, Step 3: - Remove M-K from LBPKML (Why?) 46 24 28 59 40 33 12 68 Task 3a: “Polygon Method”, Step 3: - Remove M-K from LBPKML (Why?)

Task 3a: Correct??? 9 nodes connected by 8 edges 46 24 28 59 40 33 12 68 Task 3a: Correct??? 9 nodes connected by 8 edges

46 24 28 59 40 33 12 68 Task 3a: Min span tree weight = 310 miles; (310 miles ×$25000 = $7,750,000)

Task 3a - again, but this time using Kruskal’s Algorithm 63 24 46 24 28 59 40 41 69 33 12 68 74 Task 3a - again, but this time using Kruskal’s Algorithm

Kruskal’s Algorithm Kruskal's algorithm is a minimum-spanning- tree algorithm which finds an edge of the least possible weight that connects any two ‘trees’ in the ‘forest’.

63 46 24 28 59 40 41 69 33 12 68 74 Task 3a: “Kruskal’s Algorithm”, which selects the edges (from smallest to largest) until a connected tree network is formed.

63 46 24 28 59 40 41 69 33 12 68 74 Task 3a: “Kruskal’s Algorithm”, Steps 1 and 2: Select the edges of least weight (12 and 24)

63 46 24 28 59 40 41 69 33 12 68 74 Task 3a: “Kruskal’s Algorithm”, Steps 3 and 4: Select the edges of least weight (28 and 33)

63 46 24 28 59 40 41 69 33 12 68 74 Task 3a: “Kruskal’s Algorithm”, Steps 5 and 6: Select the edges of least weight (40 and 46)

63 46 24 28 59 40 41 69 33 12 68 74 Task 3a: “Kruskal’s Algorithm”, Steps 7: Select the edge of least weight (59)

46 24 28 59 40 33 12 68 Step 8: Select the edge (of least weight) which connects the final node to the tree (68)

46 24 28 59 40 33 12 68 Task 3b info: Travel along the upgraded roads in the most efficient way…

46 24 28 59 40 33 12 68 Task 3b ANS: One road (O-L) is travelled twice; M,L,O,L,B,P,K,N,S,C = 310 + 24 = 334 miles