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Unformatted text preview: Homework 5 CSE 450/598 Spring 2010 Arizona State University Due: Thursday 2/25 before 10:30 1. (4.26) One of the first things you learn in calculus is how to minimize a differentiable function such as y = ax 2 + bx + c , where a > 0. The minimum spanning tree problem, on the other hand, is a minimization problem of a very different flavor: there are now just a finite number of possibilities for how the minimum might be achievedrather than a continuum of possibilitiesand we are interested in how to perform the computation without having to exhaust this (huge) finite number of possibilities. One can ask what happens when these two minimization issues are brought together, and the following question is an example of this. Suppose we have a connected graph G = ( V , E ) . Each edge e now has a time-varying edge cost given by a function f e : R R . Thus, at time t , it has cost f e ( t ) . Well assume that all these functions are positive over their entire range. Observe that the set of edges constituting the minimum spanning tree of G may change over time. Also, of course, the cost of the minimum spanning tree of G becomes a function of the time t ; well denote this function c G ( t ) . A natural problem then becomes: find a value of t at which c G ( t ) is minimized.is minimized....
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