An algorithm with an improved running time bound

Assignment Help Basic Statistics

Reference no: EM131122058

(O (N₁/2A log(NC) Hybrid Auction Algorithm) This exercise, due to Ahuja and Orlin [1987], shows how the auction algorithm can be combined with a more traditional primal-dual method to obtain an algorithm with an improved running time bound. The auction algorithm is used to assign the first N - O )N1/2 persons and the primal-dual method is used to assign the rest. Consider the solution of the assignment problem by the Gauss-Seidel variant of the scaled auction algorithm ( = 1 throughout).

(b) Suppose that at the outset of each subproblem we use a modified GaussSeidel auction procedure in which only persons i with profit margins πi greater than or equal to π0 i -(6N) 1/2 are allowed to place bids. Show that this procedure can be implemented so that at most (6N) 1/2 + 1 iterations are performed at each person node i, and that it terminates in O(N1/2A) time. Furthermore the number of unassigned persons after termination is at most (6N) ^1/2.

(c) Assume that there exists some algorithm X which, given an incomplete assignment S and a price vector p obeying -CS, produces a new pair (S , p ) obeying -CS in O(A) time, with S containing one more assignment than S (Exercise 7.21 indicates how such an algorithm may be constructed). Outline how one would construct an O ( N^1/2 A log(NC)) assignment algorithm. 7.2

Reference no: EM131122058

Questions Cloud

What are defense mechanisms : 350 word essay on, What are defense mechanisms? What are the advantages and disadvantages of using them to cope with stress

Course of the preflow-push algorithm the number : Consider the gap method described at the end of Section 7.3.2. Suppose that in the course of the preflow-push algorithm the number m(k) of nodes that have price equal to k is 0. Let S be the set of nodes with price less than k, and let S be the c..

Maintaining the activation of bodily systems : ____________, released by the adrenal gland, is a hormone that is responsible for maintaining the activation of bodily systems during prolonged stress

Method terminates in a finite number of iterations : Consider the primal-dual method of Chapter 6. Show that if the terms "balanced," "active," and "inactive" are replaced by "-balanced," "-active," and "-inactive," then the resulting method terminates in a finite number of iterations and the final..

An algorithm with an improved running time bound : (O (N1/2A log(NC) Hybrid Auction Algorithm) This exercise, due to Ahuja and Orlin [1987], shows how the auction algorithm can be combined with a more traditional primal-dual method to obtain an algorithm with an improved running time bound.

Evaluate key trends affecting global business environment : Develop a list of entrepreneurial opportunities outside the confines of the company you selected. Each opportunity in your list should have supporting rationale based on your market domain evaluation and PEST analysis.

Complete the details of the following argument : Finally, if each column of the matrix has two components (a 1 and a -1), the sum of its rows is 0, so the matrix is singular, and its determinant is 0.

Method that involves degenerate price rises : (Degenerate Price Rises) In this exercise, we consider a variation of the -relaxation method that involves degenerate price rises. A degenerate price rise changes the price of a node that currently has zero surplus to the maximum possible value th..

Would recommend new formulation of barbecue sauce marketed : Assume you are recommending marketing the new barbecue sauce, use information from the Executive Summary to develop a strong justification for which of the two sub-brand names, "Chicago Style" or "Spicy Blend," should be employed.

User Account

All Pages