weighted graphs you don' consider towns that already have an agent notice that this is not the same rule 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 when he' therehe calls you by telephone and 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 care only about the cheapest route from ajoso you ignore the more expensive routeleaving this entry as it was the resulting notebook entries are shown as the last row in table figure shows the situation geographically $ $ bordo $ colina $ ajo $ towns with agents (vertices in treefigure danza fringe towns (not in treee erizo unknown towns (not in treefollowing step in the shortest-path algorithm