from this we decide that from now on we won' need to update the entry for the cheapest fare from ajo to bordo this fare will not changeno matter what we find out about other towns we'll put an next to it to show that there' an agent in the town and that the cheapest fare to it is fixed three kinds of town as in the minimum spanning tree algorithmwe're dividing the towns into three categories towns in which we've installed an agentthey're in the tree towns with known fares from towns with an agentthey're on the fringe unknown towns at this point ajo and bordo are category towns because there are agents there category towns form tree consisting of paths that all begin at the starting vertex and that each end on different destination vertex (this is not the same treeof courseas minimum spanning tree some other towns have no agentsbut you know the fares to them because you have agents in adjacent category towns you know the fare from ajo to danza is $ and from bordo to colina is $ because the fares to them are knowndanza and colina are category (fringetowns you don' know anything yet about erizoit' an "unknowntown figure shows these categories at the current point in the algorithm as in the minimum spanning tree algorithmthe algorithm moves towns from the unknown category to the fringe categoryand from the fringe category to the treeas it goes along the third agentin danza at this pointthe cheapest route you know that goes from ajo to any town without an agent is $ the direct route from ajo to danza both the ajo-bordo-colina route at $ and the ajo-bordo-danza route at $ are more expensive you hire another passerby and send her to danza with an $ ticket she reports that from danza it' $ to colina and $ to erizo now you can modify your entry for colina beforeit was $ from ajogoing via bordo now you see you can reach colina for only $ going via danza alsoyou now know fare from ajo to the previously unknown erizoit' $ via danza you note these changesas shown in table and figure table step agents at ajobordoand danza from ajo to bordo colina danza erizo