as that used in the minimum spanning tree problem (the cable tv installationthereyou picked the least expensive single link (edgefrom the connected towns to an unconnected town hereyou pick the least expensive total route from ajo to town with no agent in this particular point in your investigation these two approaches amount to the same thingbecause all known routes from ajo consist of only one edgebut as you send agents to more townsthe routes from ajo will become the sum of several direct edges the second agentin bordo the cheapest fare from ajo is to bordoat $ so you hire passerby and send him to bordowhere he'll be your agent once he' therehe calls you by telephoneand tells you that the bordo stationmaster says it costs $ to ride to colina and $ to danza doing some quick arithmeticyou figure it must be $ plus $ or $ to go from ajo to colina via bordoso you modify the entry for colina you also can see thatgoing via bordoit must be $ plus $ or $ from ajo to danza however--and this is key point--you already know it' only $ going directly from ajo to danza you only care about the cheapest route from ajoso you ignore the more expensive routeleaving this entry as it was the resulting notebook entries are shown in the last row in table figure shows the situation geographically table step agents at ajo and bordo from ajo to bordo colina danza erizo step (via ajoinf (via ajoinf step (via ajo) (via bordo (via ajoinf figure following step in the shortest-path algorithm once we've installed an agent in townwe can be sure that the route taken by the agent to get to that town is the cheapest route whyconsider the present case if there were cheaper route than the direct one from ajo to bordoit would need to go through some other town but the only other way out of ajo is to danzaand that ride is already more expensive than the direct route to bordo adding additional fares to get from danza