CSCI 570 – Fall 2020 – HW 12 Solution Due November 30st 11:59pm 2020 1. A variation of the satisfiability problem is the MIN 2-SAT problem. The goal in the MIN 2-SAT problem is to find a truth assignment that mini- mizes the number of satisfied clauses. Give the best approximation algo- rithm that you […]
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Discussion 9 1. We’re asked to help the captain of the USC tennis team to arrange a series of matches against UCLA’s team. Both teams have n players; the tennis rating (a positive number, where a higher number can be interpreted to mean a better player) of the i-th member of USC’s team is ti
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Discussion 4 1. Hardy decides to start running to work in San Francisco city to get in shape. He prefers a route that goes entirely uphill and then entirely downhill so that he could work up a sweat uphill and get a nice, cool breeze at the end of his run as he runs faster
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CSCI 570 Homework 5 Due September 30th 1 Graded Problems 1. Give the asymptotic running time of the following recurrences if they can be solved with the Master Theorem. Otherwise, indicate that the Master Theorem does not apply. a. T(n) = 3T(n/3) + b. T(n) = 2T(n/2)+nlogn. c. T (n) = 7T (n/3) + n2
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Discussion 9 1. We’re asked to help the captain of the USC tennis team to arrange a series of matches against UCLA’s team. Both teams have n players; the tennis rating (a positive number, where a higher number can be interpreted to mean a better player) of the i-th member of USC’s team is ti
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1 1. CSCI 570 – Fall 2020 – HW6 – solution Graded problems From the lecture, you know how to use dynamic programming to solve the 0-1 knapsack problem where each item is unique and only one of each kind is available. Now let us consider knapsack problem where you have infinitely many items of
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1 CSCI 570 – Fall 2020 – HW 1 Due Sep 2 Graded Problems State True/False: An instance of the stable marriage problem has a unique stable matching if and only if the version of the Gale-Shapely algorithm where the male proposes and the version where the female proposes both yield the exact same matching.
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V 0 Amortized costanalysis Binary Binomialheap heap Binayheap Fi eiiniEI.in Decrease key U Amortizes Binominlheap FibHeap 04h u Merge On 4 Construct O n Ocn oifi I 0C Oci Ocu oiii ii Jesse V S Sa 8yo 4 14 13 9 4 S S4 Se s Y z t fsy s S3 552 S y
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CSCI 570 – Fall 2020 – HW7 Due October 21st 11:59pm 2020 1 Graded Problems 1. Let us think of character strings as sequences of characters. Given two se- quences X = and Z = , we say that Z is a sub- sequence of X if there is a strictly increasing sequence of k
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a Traveling Salesman TSP Problem Hamiltonian Cycle im A cycle G if itvisitseach a C in Hamiltonian Cycle vertex exactly once Problem statement Given an undirectedgraph G is there a Hamiltonian cycle in G Def is a Show that the Hamiltonian Cycle Problem is NP complete Show that HC is in NP hitofnodes ontheHCinorter A
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