1. Consider the following set P of men's and women's preferences.PreferencesMenWomenPreferencesT U VV U TU T VV T SАSDАВCВSTADCВC DA C DCSUBADUVВ(a) Find the stable matching for set P, that would be produced by running the Gale-Shapley algorithm as presented in class, in which the men do the proposing.(b) Set P has k different stable matchings. What is k? If you cannot determine k exactly,give the best upper bound and the best lower bound that you can. Justify yourstatement.

Answered: Image /qna-images/answer/d67f5e13-1ee4-40b4-8e99-012a52c94436.jpg

Answered: 1. Consider the following set P of…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Correct answer will be upvoted else downvoted. Let C={c1,c2,… ,cm} (c1<c2<… <cm) be the arrangement of individuals who hold cardboards of 'C'. Let P={p1,p2,… ,pk} (p1<p2<… <pk) be the arrangement of individuals who hold cardboards of 'P'. The photograph is acceptable if and provided that it fulfills the accompanying requirements: C∪P={1,2,… ,n} C∩P=∅. ci−ci−1≤ci+1−ci(1<i<m). pi−pi−1≥pi+1−pi(1<i<k). Given a cluster a1,… ,an, kindly track down the number of good photographs fulfilling the accompanying condition: ∑x∈Cax<∑y∈Pay. The appropriate response can be huge, so output it modulo 998244353. Two photographs are unique if and provided that there exists no less than one individual who holds a cardboard of 'C' in one photograph yet holds a cardboard of 'P' in the other. Input Each test contains numerous experiments. The main line contains the number of experiments t (1≤t≤200000). Depiction of the experiments follows. The…
Correct answer will upvoted else downvoted. playing a game on a round board with n (2≤n≤106) cells. The cells are numbered from 1 to n so that for every I (1≤i≤n−1) cell I is contiguous cell i+1 and cell 1 is nearby cell n. At first, every cell is unfilled. Omkar and Akmar alternate setting either An or a B on the board, with Akmar going first. The letter should be set on a vacant cell. What's more, the letter can't be put nearby a cell containing a similar letter. A player loses when it is their move and there are not any more substantial moves. Output the number of conceivable particular games where the two players play ideally modulo 109+7. Note that we just consider games where some player has lost and there are not any more substantial moves. Two games are considered unmistakable if the number of turns is unique or for some turn, the letter or cell number that the letter is put on were unique. A move is considered ideal if the move amplifies the player's shot at…
Algorithm A search using the heuristic h(n) = a for some fixed constant a > 0 is guaranteed to find an optimal solution Select one: True False The Perceptron Learning Rule is a sound and complete method for a Perceptron to lear correctly classify any 2-class classification problem Select one: True False systems are Data-driven, where as systems are goal-driven. Select one: a. Backward Chaining & Forward Chaining b. Forward Chaining & Backward Chaining c. Spanning Chaining & Backward Chaining d. None of the above it is a search algorithm that requires less memory Select one: a. Breadth-First Search b. Linear Search c. Optimal Search d. Depth First Search Rationality is? Select one: a. being reasonable b. being sensible c. having good sense of judgment d. All of the above Breadth-first search is similar to minimax search Select one: True False
Consider a Local Search procedure such as Random Hill Climbing which employs the 2-change modification as neighbourhood function and the following instance of the Travelling Salesman Problem: 10 During the execution of the search, the highlighted (in bold) tour is visited. This current tour has a length of (62): [A → C → B → E → D → A] Select ALL correct statements. D a. The 2-change modification neighbourhood for TSP is reversible. O b. None of the statements is correct. O c. The modification, REMOVE ((A, C), (B, E)) and ADD ((A, B), (C, E)), is not a valid 2-change modification. O d. The current tour is a local minimum. O e. REMOVE ((A, D), (B, E)) and ADD ((A, B), (D, E)) is a valid 2-change modification, but not accepted for the next iteration step. O f. The modification, REMOVE ((A, D), (C, B)) and ADD ((C, D), (A, B)), yields in a tour which is accepted for the next iteration step. g. [A → C → B → E → D → A] is a neighbour of the tour [A → E → D → B → C → A] O h. The…
Write the updating rule at iteration k+1 for momentum gradient descent learning with a momentum value of 0.9. Explain how this method improves convergence properties of gradient descent learning.
For this problem, we will explore the issue of truthfulness in the StableMatching Problem and specifically in the Gale-Shapley algorithm. Thebasic question is: Can a man or a woman end up better off by lying abouthis or her preferences? More concretely, we suppose each participant hasa true preference order. Now consider a woman w. Suppose w prefers manm to m, but both m and m are low on her list of preferences. Can it be thecase that by switching the order of m and m on her list of preferences (i.e.,by falsely claiming that she prefers m to m) and running the algorithmwith this false preference list, w will end up with a man m that she trulyprefers to both m and m? (We can ask the same question for men, butwill focus on the case of women for purposes of this question.)Resolve this question by doing one of the following two things: (a) Give a proof that, for any set of preference lists, switching theorder of a pair on the list cannot improve a woman’s partner in the GaleShapley…
In a single iteration of the iterative improvement algorithm for maximum bipartite matching, the current matching ?M is updated to a bigger matching ?′M′. For an arbitrary ?0n0 show a scenario with |?|≥?0|M|≥n0 such that ?M and ?′M′ have no edges in common.
1. Consider the generalization of stable matching problem where a certain man-woman pairs are forbidden. The set of forbidden pairs is denoted as F. Each man m ranks all the woman w for which (m, w) ¢ F and each woman w ranks all the man m for which (m, w) ¢ F. Consider the following algorithm for finding a stable matching that consists of only unforbidden pairs: Initially all mE M and w e W are free; S = Ø While there is a man m who is free and hasn't proposed to every woman w for which (m, w) ¢ F Choose such a man m Let w be the highest-ranked woman in m's preference list to which m has not yet proposed If w is free: Add (m, w) to solution S Else (w is current matched with m'): If w prefers m' to m m remains free Else Replace (m', w) by (m, w) in S Return solution S Answer true or false for the following questions: (a) Any woman w remains engaged from the point at which she receives her first proposal, and the se- quence of partners to which she is engaged get better and better. (b)…
Correct answer will be upvoted else downvoted. Code and output screenshot. Anticipating calculations utilized in VK have effectively assessed the likelihood for every occasion to occur. Occasion in line I and section j will occur with likelihood ai,j⋅10−4. Every one of the occasions are autonomous together. How about we call the table winning if there exists a line to such an extent that all n occasions on it occur. The line could be any flat line (cells (i,1),(i,2),… ,(i,n) for some I), any upward line (cells (1,j),(2,j),… ,(n,j) for some j), the fundamental corner to corner (cells (1,1),(2,2),… ,(n,n)), or the antidiagonal (cells (1,n),(2,n−1),… ,(n,1)). View the likelihood of your table to be winning, and output it modulo 31607 (see Output area). Input The primary line contains a solitary integer n (2≤n≤21) — the elements of the table. The I-th of the following n lines contains n integers ai,1,ai,2,… ,ai,n (0<ai,j<104). The likelihood of occasion in cell…
Suppose that a manufacturing company builds n different types of robots, sayrobots 1, 2, . . . , n. These robots are made from a common set of m types of materials, saymaterials 1, 2, . . . , m. The company has only a limited supply of materials for each year,the amount of materials 1, 2, . . . , m are limited by the numbers b1, b2, . . . , bm, respectively.Building robot i requires an aij amount from material j. For example, building robot 1requires a11 from material 1, a12 from material 2, etc. Suppose the profit made by sellingrobot i is pi. Write an integer linear program for maximizing the annual profit for thecompany
What does ?_i represent in the context of maximal margin classifiers. λ_i= y_i ((w^T x_i+b))/(||w||) Choose all that apply. a. Cosine similarity b. Geometric margin c. Distance of x_i from hyperplane d. Class boundary
Correct answer will be upvoted else Multiple Downvoted. Computer science. Players alternate, Alice moves first. Each turn a player picks any component and eliminates it from the exhibit. In the event that Alice picks even worth, she adds it to her score. On the off chance that the picked esteem is odd, Alice's score doesn't change. Essentially, on the off chance that Bob picks odd worth, he adds it to his score. On the off chance that the picked esteem is even, Bob's score doesn't change. On the off chance that there are no numbers left in the cluster, the game finishes. The player with the most noteworthy score wins. Assuming the scores of the players are equivalent, a draw is announced. For instance, assuming n=4 and a=[5,2,7,3], the game could go as follows (there are different choices): On the principal move, Alice picks 2 and get two focuses. Her score is presently 2. The exhibit an is presently [5,7,3]. On the subsequent move, Bob picks 5 and get five…

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