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yehnerthannah
yehnerthannah
28.11.2019 • 
Mathematics

We are given a set v of n variables {x1, tn} and a set c of m weak and strict inequalities between the variables, i.e., inequalities of the form x; < x; or xi < xj. the set c of inequalities is called consistent 1 1,2,3, ..} iff there is an assignment of positive integer values to the x3, x2 < xı} is consistent, whereas over the positive integers z+ = variables that satisfies all the inequalities. for example, the set {xı {x1x3, x2 < x1, t3 < x2} is not consistent (a) give an efficient algorithm to determine whether the set c of inequalities is consistent over the positive integers. state precisely the asymptotic running time of your algorithm in terms of n and т. (b) if the set of inequalities has a solution, then it has a unique minimum solution, i.e., a solution in which every variable has the minimum value among all possible solutions. give an efficient algorithm to compute the minimum solution both parts have o(n+ m) solutions. hint: construct a suitable graph and use appropriate algorithms

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