. Find a max flow in this network from s to t, and show the final...
graph below represents a network and the capacities are the sumber written on edges. The source is node a, and the target is node h. a. 10 (e) Show a fow of size 7 units going from the source a to the target h. (Write on the graph, next to the capacity, how many units of flow go through each edge.) (b) Consider the cut (L, R), wbere L (o) and R-(d.e.cf.s.Al, Indicate the edges crosig show that this cut...
5 Network Flow, 90p. Consider the below flow network, with s the source and t the sink. 5 4 1. (10p) Draw a flow with value 8. (You may write it on top of the edges in the graph above, or draw a new graph.) You are not required to show how you construct the flow (though it may help you to apply say the Edmonds-Karp algorithm). 2. (5p) List a cut with capacity 8. (You may draw it in...
et NV,E] be a capacitated directed network with unique fixed source and unique fixed sink, no edges into the source, and no edges out of the sink. To eadh vertex u,e V, assign a number μj equal to 0 or-1. To each edge (Unuj)e E, assign a number yy defined by yy -max (0, H, - Hj). (See the discussion immediately preceding Example 10.) a. Prove that-t +pj + yi,2 0 for all i and j. b. Prove that yy...
You are given a flow network G with n >4 vertices. Besides the source sand the sink t, you are also given two other special vertices u and v belonging to G. Describe an algorithm which finds a cut of the smallest possible capacity among all cuts in which vertex u is at the same side of the cut as the sources and vertex v is at the same side as sink t. Hint: it is enough to ad two...
We will look at how the Ford-Fulkerson Algorithm operates on the following network.Each edge is annotated with the current flow (initially zero) and the edge's capacity. In general, a flow of x along an edge with capacity y is shown as x / y.(a) Show the residual graph that will be created from this network with the given (empty) flow. In drawing a residual graph, to show a forward edge with capacity x and a backward edge with capacity y,...
10 points) Use the Max Flow algorithm to find the maximum flow through the network shown below and also give a minimum cut to verify that is the correct value. A (4,0) B (5,0) (3,0) (5,0) (4,0) E S (13,0) (6.0) D (4,0) (6,0) (3,0) (14,0) (6.0) (12,0) (2,0) с (3,0) (5,0) F
Let (G, s, t, c) be a flow network G = (V, E), A directed edge e = (m u) is called always fu ir f(e) e(e) forall maximum fiows f: it is called sometimes fullit f(e)for some but not all maximum flows: it is caled never fulit f(e) <c(e) for all maximum flows. Let (S, V S be a cut. That is, s E S,teV S. We say the edge u, ) is crossing the cut ifu E SandrEV\...
Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears at most once) from s to t that goes via v. Create a flow network by making v a source. Add a new vertex Z as a sink. Join s, t with two directed edges of capacity...
find max flow and min cut from Source O to Sink T