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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4. The matching game is played in a bipartite graph G = (V1, V2, E) in which edges are connect only vertices Vị to vertices in V2. The players are the vertices in the graph that is Vi U V2. Each player has to select one of its neighbors. Player i gets utility 1 when the selection is mutual (player i selects j and player j selects i) otherwise he gets 0. Provide a formal characterization of the strategy profiles that are pure Nash equilibrium of the matching game. Analyze the complexity of the problems related to pure Nash equilibria for this family of games.
no handwritten Alice and Bob are playing a match to see who is the first to win n games, for some fixed n > 0. Suppose Alice and Bob are equally competent, that is, each of them wins a game with probability 1/2. Further, suppose that they have already played i + j games, of which Alice won i and Bob won j. Give an efficient algorithm to compute the probability that Alice will go on to win the match. For example, if i = n − 1 and j = n − 3, then the probability that Alice will win the match is 7/8, since she must win any of the next three games.
Given the following input instance for the 0/1 Knapsack problem. Show how the algorithm given in the class works on this input instance. Complete the whole (M+1)x(n+1) table, and give the answer for the optimal solution, where M is the capacity of the knapsack and n is the number of objects. Object 1 Object 2 Object 3 Object 4 Object 5 Object 6 Profit p Weight w; | 2 3 3 5 5 1 4 4 5 3 2 5 М-10
Establish the Shortest-Paths Optimality Conditions in the Proposition P. Then, for any v reachable from s, the value of distTo[v] is the length of some path from s to v, with distTo[v] equal to infinity for all v not reachable from s. Let G be an edge-weighted digraph. s is a source vertex in G. distTo[] is a vertex-indexed array of path lengths in G. These numbers represent the lengths of the shortest pathways if and only if each edge e from v to w satisfies the condition that distTo[w] = distTo[v] + e.weight() (i.e., no edge is eligible).
Exercise Consider the following pseudocode for a knapsack problem heuristic with capacity b, and n objects with rewards c and weights a. 1. Set S = (). b = b, I= (1,2.n) 2. repeat 3. Let jl be the index such that cj z ci, i l. 4. I =1-0), S= S () 5. b = b - aj 6. Remove from I all indices i where ai >b 7. until I = ) 8. The objects in set S are the objects in the solution. Implement this algorithm in VBA with n objects and capacity b. First take from the user the values for n and b. Then let rewards be random integer numbers between 5 and 10, and weights be random integer numbers between 1 and 10. Your inputs and solution should be exhibited on an Excel worksheet as well.
Explaination
Exercise 3 Consider calculation of PageRank for a directed graph. Consider two jumping probabilities a and B such that a > B. For every node u, let Pa(u) be the PageRank of u calculated using a and let Pg (u) be the PageRank of u calculated using B. For each of the following statements, indicate whether the statement is true or false and provide a brief explanation for your answer. 1. The inequality Pa (u) > Pg (u) must hold for all nodes u. 2. The inequality Pa(u) > Pg (u) must hold for at least one node u.
Correct answer Will be upvoted else downvoted. subsquare is any square piece of the stand, I. e. any set S(i0,j0,k)={ci,j | i0≤i<i0+k,j0≤j<j0+k}S(i0,j0,k)={ci,j | i0≤i<i0+k,j0≤j<j0+k} with 1≤i0,j0≤n−k+11≤i0,j0≤n−k+1. Kostya actually doesn't have the foggiest idea the number of tiles he wants, so he considers the subsquares of every conceivable size. He doesn't need his restroom to be excessively bright. Assist Kostya with counting for each k≤nk≤n the quantity of subsquares of size k×kk×k that have all things considered qq various shades of tiles. Two subsquares are considered unique if their area on the stand is unique. Input The main line contains two integers nn and qq (1≤n≤15001≤n≤1500, 1≤q≤101≤q≤10) — the size of the stand and the cutoff on the quantity of particular tones in a subsquare. Each of the following nn lines contains nn integers ci,jci,j (1≤ci,j≤n21≤ci,j≤n2): the jj-th integer in the ii-th line is the shade of the tile in the cell (i,j)(i,j).…
Give an instance of STABLEMATCHING where the Propose-Dispose algorithm yields a matching where strictly more women get their most preferred man than men get their most preferred woman.
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
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. (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…