The greedy algorithm does not guarantee a Hamiltonian circuit with the smallest weight. True False

(c) Suppose that F - Bin(2m + 1, 5). Use Chebyshev's inequality to bound P[F > m]. From (c), deduce that the probability of a decoding error in the binary sym- metric channel (BSC) with symbol error probability p = can be made arbitrarily small by using a sufficiently long repetition code.

Suppose the following Branch-and-Bound tree is obtained for a pure integer maximization LP:

6. A researcher develop one new prediction algorithm. He want to find out whether hisalgorithm predict a situation faster than the current method. He test his algorithm to makea prediction base on 4 sets of data. He recorded the computation time in microsecond andcompare it with current method and standard method. Table 5 give the computation timefor all method tested.TABLE 5Proposed Method Current Method Standard Method10 11 1313 16 177 9 915 16 19At 2.5% significance level, will you conclude that the computation time taken to predict is thedifferent for each of the three algorithms.

Determine how many times the innermost loop will be iterated when the following algorithm segment is implemented and run. (Assume that  a, b, c, and d  are positive integers. Assume  a ≤ b and c ≤ d.) for i := a to b     for j := c to d         [Statements in body of inner loop.           None contain branching statements that           lead outside the loop.]     next j next i

Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. (a) For the forward recursion formulation of this problem, how many stages are there, and what arethe states for each stage? Stage 1: n = 1 Stage 2: n = 2 origin) ( Stage 3: n = 3 S A B C (b) Use forward recursion to solve this problem. However, instead of using the usual tables, show your work graphically. In particular, start with the given network, where the answers already are given for f (Sn) for four of the nodes; then solve for and fill in f2 (B) and fi* (0). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use forward recursion to solve this problem by manually constructing the usual tables for n = 3, n = 2, and n = 1.…