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48155_2006final_sol

# 48155_2006final_sol - 6.034 Final Examination December...

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6.034 Final Examination December 18,2006 ----- \ Name : - -- - - - - - - . - Quiz number Maximum Score Grader There are 30 pages in this final, including this one and a tear-off sheet provided at the end with duplicate drawings and data. You must do Quiz 5. All others are optional.

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Quiz 1 Problem 1: Search (75 points) This problem has a certain resemblance to a problem on Quiz I , but it is not the same. Several 6.034 students are stranded in a strange city at the node marked S. Desperate for a meal, they want to get to Hose's food truck located on the map at the node marked T. All the streets are one-way streets. Each link between node pairs is 1 unit long.
Part A (10 points) Amy calculates how many paths terminating at nodes T or D she would produce if she used the British Museum Algorithm. As expected with the British Museum Algorithm, she does not use an extended list. Her result is: Part B (10 points) David decides to use plain branch and bound, without an extended list and with no estimate of remaining distance, to compute the shortest path between S and T. If there is ever a choice in which path to extend, he picks the path closest to the top of the page. Before he can be sure he has the shortest path, he produces n paths starting at S and ending at a node marked T or D and adds those paths to the queue. In this case, n is Part C (15 points) James thinks it would be better to use an estimate of remaining distance with the basic branch and bound procedure. Also, he does use an extended list. His estimate for each node is the straight-line distance to T. Is James's heuristic admissible? If there is ever a choice in which path to extend, he picks the path closest to the top of the page. Before he can be sure he has the shortest path. he produces n paths starting at S and ending at a node marked T or D and adds those paths to the queue. In this case, n is

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Part D (10 points) Natalya thinks James is on to something, but in her analysis, Natalya uses branch and bound together with a different estimate of remaining distance: Is Natalya heuristic admissible? Natalya uses an extended list. If there is ever a choice in which path to extend, she picks the path closest to the top of the page. Before she can be sure she has the shortest path, she produces n paths starting at S and ending at a node marked T or D and adds those paths to the queue. In this case, n is Part E (20 points) Olga thinks Natalya is on to something and uses the same method, except that Olga's estimate of remaining distance is Natalya's + 1 : El : Is Olga's heuristic admissible? E2: Does Olga get the same path as Natalya? Suppose that Natalya changes her mind and uses different estimates (but still 2 0). Olga's estimates are still Natalya's +l. Can your answer to El change? Again, suppose that Natalya has changed her mind and used different estimates (but still 2 0).
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