Question: 60 points] Let U be a set of tasks and E a set of pairs (u, v) where u,v E U. An ezecution is

60 points] Let U be a set of tasks and E a

set of pairs (u, v) where u,v E U. An ezecution is

60 points] Let U be a set of tasks and E a set of pairs (u, v) where u,v E U. An ezecution is any sequence of elements of U without repetitions. An execution need not contain all tasks An execution u,,u is valid if for every i, 1 (a) Suppose U{a, b, c and E {(a, b), (c, b). Which of the following sequences are valid executions? i. ; ii. , b; ii. , b, ; iv. a, c, b (b) The length of an execution u,..,u is the number k; we have k < jU. Give a polynomial-time algorithm for the following problem: given sets U, E, and a task uE U, what is the minimum length of a valid execution that contains u? Justify the correctness of your algorithm and analyze its worst-case running time. As always, your algorithm should be as efficient (asymptotically) as possible.

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