Would multiplying each arc in a network by a constant k change the set of optimal...
Would multiplying each arc in a network by a constant k change the set of optimal solutions of the minimum cost flow problem? Would adding a constant k to each arc cost change the set of optimal solutions.? Explain your reasonings clearly.
Homework Answers
No multiplying each arc with constant k will although increment the flow by k times but the set of edges which were part of optimal solution of minimum cost flow problem will still be optimal solution by making the new flow value across each edge to be k times of previous flow value.
Yes adding constant k to each arc will change the set of optimal solution because the min-cut of original problem may not be the min-cut of new network. More the number of edges in a cut, more the capacity of cut will increase and hence change of flow will not be uniform for all arc.
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Would multiplying each arc in a network by a constant
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In this problem, we explore the effect on the standard deviation
of multiplying each data value in a data set by the same constant.
Consider the data set 17, 5, 10, 9, 4.
(a) Use the defining formula, the computation formula, or a
calculator to compute s. (Round your answer to one decimal place.)
s =
(b) Multiply each data value by 3 to obtain the new data set 51,
15, 30, 27, 12. Compute s. (Round your answer to...
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