Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Please help to answer only (b) We define the Escape Problem as follows. We are given a directed graph G = (V, E) (picture a

Please help to answer only (b)

We define the Escape Problem as follows. We are given a directed graph G = (V, E) (picture a network of roads). A certain collection of nodes X ? V are designated as populated nodes, and a certain other collection S ? V are designated as safe nodes. (Assume that X and S are disjoint.) In case of an emergency, we want evacuation routes from the populated nodes to the safe nodes. A set of evacuation routes is defined as a set of paths in G so that (i) each node in X is the tail of one path, (ii) the last node on each path lies in S, and (iii) the paths do not share any edges. Such a set of paths gives a way for the occupants of the populated nodes to escape to S, without overly congesting any edge in G.

Please IGNORE (a) Given G, X, and S, show how to decide in polynomial time whether such a set of evacuation routes exists.

Please HELP SOLVE (b) Suppose we have exactly the same problem as in (a), but we want to enforce an even stronger version of the no congestion condition (iii). Thus we change (iii) to say the paths do not share any nodes. With this new condition, show how to decide in polynomial time whether such a set of evacuation routes exists. Also, provide an example with the same G, X, and S, in which the answer is yes to the question in (a) but no to the question in (b).

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Select Healthcare Classification Systems And Databases

Authors: Katherine S. Rowell, Ann Cutrell

1st Edition

0615909760, 978-0615909769

More Books

Students also viewed these Databases questions

Question

What is conservative approach ?

Answered: 1 week ago

Question

What are the basic financial decisions ?

Answered: 1 week ago

Question

Recognize the four core purposes service environments fulfill.

Answered: 1 week ago