Question

You need to visit four cities one time each and return home (H) to start your political campaign. The travel costs ($) between all locations are given the table below. H А B с D H 450 510 820 350 A 450 600 550 490 B 510 600 720 680 с 820 550 720 650 D 350 490 680 650 a) Sketch a weighted graph for this problem. b) Starting at B, the greedy algorithm gives BHDACB. Find the total cost for this route. c) Use the edge-picking algorithm to find an efficient route and its total cost. After you are done, write the route so that it starts and ends at H. Remember that you cannot pick more than two edges at any vertex and you cannot close any loop until you have visited all the vertices.

Answer 1

solution H ca) 570 uso Coo BI 820 680 720 490 SO D This is weighted graph for given problem. (b) Now B starting at the greedy algorithm gives BHDACIB find Total cost have add weights of each edge in this path (route ? To Total cost CB,H) + (HD) +10, A2 +CA,C) +CC,B) s10+ 350 tago +550 + 720 $2620 $ 2620 : Total cost Сс) a Using edge - picking algorithm Algorithm says that pick edge with minimum weight Ccost) incident on corresponding verten For this problem start at verter H

From graph the HD observe that edge with minimum cost is M os D Now From reach at verter D edge with minimum cost is DA H 065 D Now reach at verten edge with minimum cost A from Å is AH os no A 969 D :. The efficient route which starts & ends at ver fex H is HDAH And total cost of route 350+ ngo +45o = $ 12go