How should the sequential shortest path method be modified

Assignment Help Basic Computer Science

Reference no: EM131129778

(Noninteger Problem Data) Verify that the primal-dual method terminates even when the arc costs are noninteger. (Note, however, that the arc flow bounds must still be integer; the max- flow example of Exercise 3.7 in Chapter 3 applies to the primal-dual method as well, in view of the relation described in Exercise 6.2.) Modify the primal-dual method so that augmenting paths have as few arcs as possible. Show that with this modification, the arc flow bounds need not be integer for the method to terminate. How should the sequential shortest path method be modified so that it terminates even when the problem data are not integer?

Exercise 6.2.) Relation of Primal-Dual and Dijkstra) Consider the shortest path problem with node 1 being the origin and all other nodes being destinations. Formulate this problem as a minimum cost flow problem with the origin having supply N - 1 and all destinations having demand 1. Assume that all arc lengths are nonnegative. Start with all flows and prices equal to zero, and apply the primal-dual method. Show that the method is equivalent to Dijkstra's algorithm. In particular, each augmentation uses a shortest path from the origin to some destination, the augmentations are done in the order of the destinations' proximity to the origin, and upon termination, p1 -pi gives the shortest distance from 1 to each destination i that can be reached from the origin via a forward path.\

Reference no: EM131129778

Questions Cloud

Write the form of the relaxation iteration : Write the form of the relaxation iteration starting from both positive and negative surplus nodes. Show that the method terminates at an optimal flow-price vector pair if a feasible solution exists.

Write a reflection for given article : Write a reflection for "TiIda Swinton's silent gaze to camera at the close of Sally Potter's transgressive film bears, and bears witness to, the pain of history".

Compile and execute the titanic program : In the given Titanic Program I need corrections on. Please make sure the program has NO ERRORS and can compile and execute successfully

Research strategy - quantitative and pragmatic research : Discuss the merits and drawbacks for each. Finally, discuss whether you intend to use one or both in your own research direction for this class. Please choose appropriate approaches for your topic, even if the length of this term may not allow you..

How should the sequential shortest path method be modified : In particular, each augmentation uses a shortest path from the origin to some destination, the augmentations are done in the order of the destinations' proximity to the origin, and upon termination, p1 -pi gives the shortest distance from 1 to eac..

Identify and list the various costs-fixed and variable : Identify and list the various costs-fixed and variable, direct and indirect-required to execute the project. Calculate the break-even point for the project and the expected financial returns.

Calculate two estimates of the firms cost of equity : Bunkhouse Electronics is a recently incorporated firm that makes electronic entertainment systems. Calculate two estimates of the firm's cost of equity. Which estimate seems more reasonable to you Why?

Prepare the entry to record the mortgage loan on december : Pickeril Inc. issues a $600,000, 10%, 10-year mortgage note on December 31, 2010, to obtain financing for a new building. The terms provide for semiannual installment payments of $48,145.

Provide an analysis on apexs assets liabilities and profit : Please provide an analysis on Apex's assets, liabilities, cash, and profit. As well, choose 2 additional components on each of the sheets, and provide your initial impression on the company financial situation.

User Account

All Pages