We discussed in class that with n agents, there are n! permutations of agents which resultsin n! different deterministic serial dictatorship mechanisms. Every serial dictatorshipis strategyproof and results in a Pareto optimal outcome (ex post).Consider m >n items to be assigned to n agents. Propose a mechanism that:1. receives as input a full ranked list (strict ordering; no ties) of items from each agent,and based on this input computes an outcome,2. is Pareto optimal (aka Pareto efficient ex post),3. is strategyproof (no agent can benefit from misreporting),4. guarantees the outcome to be envy-free up to one item (EF1).For your answer, 1) justify that your proposed mechanism satisfies each of the itemsabove and 2) given an example that shows the steps of your proposed mechanism.

Pareto ideal A Pareto diagram is a reference chart. The lengths of the bars address recurrence or…

le discussed in class that with n agents, there are n! permutations of agents which n! different deterministic serial dictatorship mechanisms. Every serial dict. strategyproof and results in a Pareto optimal outcome (ex post). Consider m > n items to be assigned to n agents. Propose a mechanism that: 1. receives as input a full ranked list (strict ordering; no ties) of items from eac and based on this input computes an outcome, 2. is Pareto optimal (aka Pareto efficient ex post), 3. is strategyproof (no agent can benefit from misreporting),

le discussed in class that with n agents, there are n! permutations of agents which n! different deterministic serial dictatorship mechanisms. Every serial dict. strategyproof and results in a Pareto optimal outcome (ex post). Consider m > n items to be assigned to n agents. Propose a mechanism that: 1. receives as input a full ranked list (strict ordering; no ties) of items from eac and based on this input computes an outcome, 2. is Pareto optimal (aka Pareto efficient ex post), 3. is strategyproof (no agent can benefit from misreporting),

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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There are n men and women, each of which has ranked all n members of the other sex in order of preference. Consider the following algorithm for matching them up: Start with an arbitrary matching and as long as there is a man and woman who prefer each other to whoever they are currently matched with, switch them. Will this algorithm always result in a stable matching? O true O false
Implement the algorithm for an optimal parenthesization of a matrix chain product as dis-cussed in the class.Use the following recursive function as part of your program to print the outcome, assumethe matrixes are namedA1, A2, ..., An.PRINT-OPTIMAL-PARENS(s, i, j){if (i=j) thenprint “A”i else{print “(”PRINT-OPTIMAL-PARENS(s,i,s[i, j])PRINT-OPTIMAL-PARENS(s, s[i, j] + 1, j)print “)”} }a- Test your algorithm for the following cases:1. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is<5,10,3, X,12,5,50, Y,6>.2. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is<5,10,50,6, X,15,40,18, Y,30,15, Z,3,12,5>. 3. Find and print an optimal parenthesization of a matrix-chain product whose sequenceof dimensions is<50,6, X,15,40,18, Y,5,10,3,12,5, Z,40,10,30,5>. X=10 Y=20 Z=30
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…
n = 9. sign and Analysis of Algorithms (3rd ed.) [Levitin 2011-10-09].pdf ✓ 1 2 3 zoom O 4 O 5. How would you modify the dynamic programming algorithm for the coin- collecting problem if some cells on the board are inaccessible for the robot? Apply your algorithm to the board below, where the inaccessible cells are shown by X's. How many optimal paths are there for this board? 1 3 4 5 6 8.1 Three Basic Examples 2 X O 5 XXX 2 O Xo X O Search Fri May 12 291 6. Rod-cutting problem Design a dynamic programming algorithm for the fol- lowing problem. Find the maximum total sale price that can be obtained by cutting a rod of n units long into integer-length pieces if the sale price of a piece i units long is p; for i = 1, 2, ..., n. What are the time and space efficiencies of your algorithm? 7. Shortest-path counting A chess rook can move horizontally or vertically to any square in the same row or in the same column of a chessboard. Find the number of shortest paths by which a rook can move…
3. Suppose that we want to know which agents are connected by a walk of length two in a given network. That is, want to know the set of ordered pairs (i, j) such that there exists a walk of length 2 between any i and j. Define n as the number of nodes and m as the number of links. (a) One way to do this is to input the adjacency matrix A, calculate A², then output all pairs (i, j) for which A(i) > 0. Defining scalar multiplication and addition as "basic operations," up to a constant c, how many "basic operations" are required to calculate A², in terms of n and m? (Hint: First think about how many operations are required to calculate each entry of A², then multiply by the number of entries.) (b) Suppose that we want to know the number of agents who are connected by a walk of length k in a given network, where k≥ 1. Up to a constant, how many basic operations are required to calculate Ak, in terms of n and m? (c) (Harder) We showed in class (Lecture 4) that a simple adaptation of…
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. You are given an integer k and n particular focuses with integer facilitates on the Euclidean plane, the I-th point has arranges (xi,yi). Consider a rundown of all the n(n−1)2 sets of focuses ((xi,yi),(xj,yj)) (1≤i<j≤n). For each such pair, work out the separation from the line through these two focuses to the beginning (0,0). You will likely work out the k-th most modest number among these distances. Input The principal line contains two integers n, k (2≤n≤105, 1≤k≤n(n−1)2). The I-th of the following n lines contains two integers xi and yi (−104≤xi,yi≤104) — the directions of the I-th point. It is ensured that all given focuses are pairwise particular. Output You should output one number — the k-th littlest separation from the beginning. Your answer is considered right if its outright or relative blunder doesn't surpass 10−6. Officially, let your answer be…
3. Suppose that we want to know which agents are connected by a walk of length two in a given network. That is, want to know the set of ordered pairs (i, j) such that there exists a walk of length 2 between any i and j. Define n as the number of nodes and m as the number of links. (a) One way to do this is to input the adjacency matrix A, calculate A2, then output all pairs (i, j) for which A(i) > 0. Defining scalar multiplication and addition as "basic operations," up to a constant c, how many "basic operations" are required to calculate A², in terms of n and m? (Hint: First think about how many operations are required to calculate each entry of A²2, then multiply by the number of entries.) (b) Suppose that we want to know the number of agents who are connected by a walk of length k in a given network, where k≥ 1. Up to a constant, how many basic operations are required to calculate Ak, in terms of n and m? (c) (Harder) We showed in class (Lecture 4) that a simple adaptation of…
Write a recurrence that would be used in dynamic programming for thefollowing problem: Given a rod of length n and an array A of prices thatcontain all prices of all the pieces smaller than n. Determine the maximumvalue obtained by cutting up the rod and selling the pieces. Note that youcould sell the rod at its original length without cutting it.
make Membership Testing AlgorithmInput: a group G operating on f = 1,2,.....n; a permutation g of f = 1,2,.....n; a base and strong enerating set for G; Schreier vectors v I 1 I k, for the stabiliser chainOutput: a boolean result showing if g G is in the group; function is in group(p: permutation; I 1..k+l): boolean; (* return true if the permutation p is in the group G I *)
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…
5.1. Trace the operation of Greedy Best-First Search, applied to the problem of getting to the goal state G from state S given below, for the following heuristic function: h,(N) = sum of the (Manhattan) distances of every tile to its goal position 341 25 876 State S 432 16 578 State G
3. Suppose that we want to know which agents are connected by a walk of length two in a given network. That is, want to know the set of ordered pairs (i, j) such that there exists a walk of length 2 between any i and j. Define n as the number of nodes and m as the number of links. adisconn Batam and m? (d) (Harder) Give conditions in terms of k, m, and n such that the algorithm in part (c) is faster than the run time of the algorithm in part (a). (e) (Harder) Similar to part (c), suppose that we use the adaptation of BFS to determine which pairs of agents are connected by a walk of length k ≥ 1. Give conditions in terms of k, m, and n such that this is faster than the run time of the algorithm in part (b).