Propose a problem p which belongs to the class-P. Design an polynomial time algorithm to reduce this problem to another problem q which is also in class-P.
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Propose a problem p which belongs to the class-P. Design an polynomial time
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- A problem called S reduces to a problem called T if a T solver can be used as a subroutine to solve S. In pseudocode: Solves(...): ... SolveT(...) ... Assuming that this reduction is correct, answer the following questions regarding what the reduction tells us. If we know that an algorithm exists for solving Problem S, what does that tell us about Problem T? [ Select ] If we know that an algorithm cannot exist for solving Problem S, what does that tell us about Problem T? [Select ] [ Select ] An algorithm cannot exist for solving Problem TT. what does that tell us about Problem S? If we know An algorithm exists for solving Problem T Nothing [ Select] If we know that an algorithm cannot exist for solving Problem T, what does that tell us about Problem S? [ Select ]A problem called S reduces to a problem called T if a T solver can be used as a subroutine to solve S. In pseudocode: Solves(...): ... SolveT(...) ... Assuming that this reduction is correct, answer the following questions regarding what the reduction tells us. If we know that an algorithm exists for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm cannot exist for solving Problem S, what does that tell us about Problem T? [ Select] If we know that an algorithm exists for solving Problem T, what does that tell us about Problem S? [ Select ] [ Select ] An algorithm cannot exist for solving Problem S,r solving Problem T, what does that tell us about Nothing An algorithm exists for solving Problem SIf we want to prove P = NP, we only need to pick up any one NPC problem and design a polynomial-time algorithm for the problem. If you want to prove P = NP, select one NPC problem based on your preference and describe your idea of a polynomial-time algorithm that solves the problem. It does not have to be a formal algorithm or pseudo-code, a description of your idea of designing such an algorithm would be fine.
- We mentioned that if we want to prove P = NP, we only need to pick up any one NPC problem and design a polynomial-time algorithm for the problem. If you want to prove P = NP, select one NPC problem based on your preference and describe your idea of a polynomial-time algorithm that solves the problem. It does not have to be a formal algorithm or pseudo-code, a description of your idea of designing such an algorithm would be fine.Question 24. Given an implementation of an algorithm, you want to check formally its run-time performancebefore you apply the algorithm to big data sets, in order to prevent endless runs of algorithms on your computer.The check if your algorithm runs endlessly on this data is depending on. . . a) the length of the source code, it is a coding problem.b) function calls in the algorithm, it is a call-graph problem.c) recursion in the algorithm, it is a software design problem.d) the size of your data, it is a big data problem.A problem called S reduces to a problem called T if a T solver can be used as a subroutine to solve S. In pseudocode: Solves(...): ... SolveT(...) Assuming that this reduction is correct, answer the following questions regarding what the reduction tells us. If we know that an algorithm exists for solving Problem S, what does that tell us about Problem T? [ Select ] [ Select ] An algorithm exists for solving Problem T An algorithm cannot exist for solving Problem T solving Problem S, what does that tell us about Nothing If we know that an algorithm exists for solving Problem T, what does that tell us about Problem S? [ Select ] If we know that an algorithm cannot exist for solving Problem T, what does that tell us about Problem S? [Select ]
- If a problem H is NP-Complete, then.. (Multi-choose) For any problem L in NP, there is a polynomial-time reduction from L to H For any problem L in P, there is a polynomial-time reduction from L to H H belongs to the class P H belongs to the class NP ."An output to problem H is either "yes" or "noImagine that you have a problem P that you know is N P-complete. For this problem you have two algorithms to solve it. For each algorithm, some problem instances of P run in polynomial time and others run in exponential time (there are lots of heuristic-based algorithms for real N P-complete problems with this behavior). You can’t tell beforehand for any given problem instance whether it will run in polynomial or exponential time on either algorithm. However, you do know that for every problem instance, at least one of the two algorithms will solve it in polynomial time. (a) What should you do? (b) What is the running time of your solution? 564 Chap. 17 Limits to Computation (c) What does it say about the question of P = N P if the conditions described in this problem existed?A graduate student is working on a problem X. After working on it for several days she is unable to find a polynomial-time solution to the problem. Therefore, she attempts to prove that he problem is NP-complete. To prove that X is NP-complete she first designs a decision version of the problem. She then proves that the decision version is in NP. Next, she chooses SUBSET-SUM, a well-known NP-complete problem and reduces her problem to SUBSET-SUM (i.e., she proves X £p SUBSET-SUM). Is her approach correct? Explain your answer.
- PYTHON/JUPYTER NOTEBOOKS Program a backward solver (i.e. write your code) for an upper triangular system Ux=b. The algorithm is attached for i and j with offset 1. Recall that NumPy and Python have offset 0 for their sequence data types.Determine whether the proposed definition isa valid recursive definition of a function f from the setof nonnegative integers to the set of integers. If f is welldefined, find a formula for f(n) when n is a nonnegativeinteger and prove that your formula is valid. f(0) = 1, f(n) = −f(n − 1) for n ≥ 1Suppose Professor Weine described a deterministic algorithm that runs in polynomial time for a known NP-Complete problem such as the Satisfiability problem How would this impact the class NP (the class of problems that can be solved nondeterministically in polynomial time)? 0. The class P would be strictly larger than the class NP 0. The class NP would be equal to the class P O.It would only impact P but not NP O.It would have no impact on the class NP