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Question: Find a maximum flow and a minimum cut in Figure by
(i) the network simplex method,
(ii) the first-labeled, first-scanned method,
(iii) Dinic's algorithm with the Malhotra-Kumar -Maheshwari procedure for finding a blocking flow in the core.
Engineering Mathematics, Engineering
Question : Suppose that G is a directed graph. In class we discussed an algorithm that will determine whether a given vertex can reach every other vertex in the graph (this is the 1-to-many reachability problem). Conside ...
Question : Suppose G is an undirected, connected, weighted graph such that the edges in G have distinct edge weights. Show that the minimum spanning tree for G is unique.
Numerical Analysis Assignment - Q1. Define the following terms: (i) Truncation error (ii) Round-off error Q2. Show that if f(x) = logx, then the condition number, c(x) = |1/logx|. Hence show that log x is ill-conditioned ...
(1) This problem concerns of the proof of the NP-completeness of 300L a) Convert the formula F into a 300L graph b) Find a solution for the 300L instance of F and verify that it is a solution for F F = (Z 1 V Z 2 ) ^ (z ...
Assignment - LP problems The data for all the problems in this HW are included in the LP_problems_xlsx spreadsheet. Problem 1 - Cash Planning A startup investment project needs money to cover its cash flow needs. At the ...
Problem - Consider a closed convex set X ⊂ R d , a function H : X x Ξ ι→ R d , and a deterministic nonnegative sequence {α n } such that n=0 ∑ ∞ α n = ∞ and n=0 ∑ ∞ (α n ) 2 = ∞. Consider an inner product (·, ·) on R d , ...
Question : What is the signed binary sum of 1011100 and 1110101 in decimal? Show all of your work. What is the hexadecimal sum of 9A88 and 4AF6 in hexadecimal and decimal? Show all of your work.
Assignment - LP problems The data for all the problems in this HW are included in the LP_problems_xlsx spreadsheet Problem 1: Cash Planning A startup investment project needs money to cover its cash flow needs. At the en ...
Question : (a) Suppose that you are given an instance of the MST problem on a graph G, with edge weights that are all positive and distinct. Let T be the minimum spanning tree for G returned by Kruskal's algorithm. Now s ...
Q: Undirected vs. directed connectivity. (a) Prove that in any connected undirected graph G = (V, E) there is a vertex v ? V whose removal leaves G connected. (Hint: Consider the DFS search tree for G.) (b) Give an examp ...
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