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Unformatted text preview: 15-750HW 4115-750 Graduate Algorithms Spring 2009Miller and Dinitz and TangwongsanAssignment 4Due date: Monday, March 30Some Reminders:Read the Policies section on the course web site before you start working on this assignment. Collab-orationispermitted for this assignment; however, you must write up your own solutions.When solving these problems, you should refrain from looking up solutions from outside sources;however, you should feel free to look up, say, Markovs inequality or isoperimetric bounds. For eachproblem, state whether you have seen it before. If you have questions, contact the course staff.Westronglyencourage you to type up your solutions (preferably using LaTeX). Extra-credit will begiven if we use your wonderful write-up in our solutions. You may neatly hand-write your solutions,but if we have trouble reading them, you will be required to type up future solutions.When you give an algorithm, please also explain why it is correct and analyze its running time.Start EARLY!We encourage you to start working on this assignment early and take full advantage ofoffice hours.1Minimum Spanning Trees(25 pts.)While we did not have time to cover them in class, minimum spanning trees are a crucial buildingblock for many more complicated algorithm. We assume that you have seen MSTs before in anundergraduate algorithms class such as 15-451 at CMU. For completeness, we now define themformally. Given an undirected graphG= (V,E) and a weight functionw:eR, aspanningtreeis a connected subgraphTofGcontaining no cycles such that every vertex has degree at least...
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- Spring '09