Professor Adam has two children who, unfortunately, dislike each other. The problem is so severe that not only do they refuse to walk to school together, but in fact each one refuses to walk on any block that the other child has stepped on that day. The children have no problem with their paths crossing at a corner. Fortunately both the professor's house and the school are on corners, but beyond that he is not sure if it is going to be possible to send both of his children to the same school. The professor has a map of his town. Show how to formulate the problem of determining if both his children can go to the same school as a maximum-flow problem.
Answer to relevant QuestionsProve that for any pair of vertices u and v and any capacity and flow functions c and f, we have cf (u, v) + cf (v, u) = c(u, v) + c(v, u).Suppose that a maximum flow has been found in a flow network G = (V, E) using a pusher label algorithm. Give a fast algorithm to find a minimum cut in G. We can represent an n-input comparison network with c comparators as a list of c pairs of integers in the range from 1 to n. If two pairs contain an integer in common, the order of the corresponding comparators in the ...Give a counterexample to the conjecture that if there is a path from u to v in a directed graph G, and if d[u] < d[v] in a depth-first search of G, then v is a descendant of u in the depth-first forest produced.A depth-first forest classifies the edges of a graph into tree, back, forward, and cross edges. A breadth-first tree can also be used to classify the edges reachable from the source of the search into the same four ...
Post your question