explain how to solve the evacuation-route problem, Macroeconomics

You are the mayor of a beautiful city by the ocean, and your city is connected to the mainland by a set of k bridges. Your city manager tells you that it is necessary to come up with an evacuation plan in the event of a hurricane. Your idea is to add a sign at each intersection pointing the direction of the route to the closest of the k bridges. You realize that this can be modeled as a graph problem, where the street intersections are nodes, the roads are edges, and the edge weights give the driving time between two adjacent intersections. Note that some of the roads in your city are one-way roads.

(a) Explain how to solve the evacuation-route problem in O(mlog n) time, where n is the number of intersections and m is the number of streets connecting two adjacent intersections. Note that the number of bridges k is not a constant, that is, it may depend on n and m. Therefore, a running time of O(k · mlog n) is not an acceptable solution. (Although I will give half credit for such a solution.) The output of your algorithm will be a labeling of the intersections, with an arrow pointing to the road to take to the closest bridge.

(b) Some of the bridges can hold more capacity than others. For 1 ≤ i ≤ k, we associate a positive numeric weight ci with each bridge. To encourage people to use bridges with higher capacity, we treat distances to different bridges differently. In particular, if δ is the actual distance from some intersection to bridge i, we assign it a capacity-weighted distance of δ/ci. Therefore, the higher the bridge capacity is, the lower the weighted distance. Present an O(mlog n) time algorithm to solve the evacuation-route problem using capacity-weighted distances. (Again, I will give half credit for a solution running in O(k · mlog n) time.

Problem 4 additional info: 2b - some of the bridges will be higher capacity. Their weights will be function of (distance/number of lanes) → this will give us shorter weight and we can treat it as a better route to take even though the distance is farther away.


Posted Date: 3/28/2013 6:21:07 AM | Location : United States

Related Discussions:- explain how to solve the evacuation-route problem, Assignment Help, Ask Question on explain how to solve the evacuation-route problem, Get Answer, Expert's Help, explain how to solve the evacuation-route problem Discussions

Write discussion on explain how to solve the evacuation-route problem
Your posts are moderated
Related Questions
A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two hours, find: A) The probability of making exactly four

Q. Describe the Keynes motivation? Keynes' motivation: In good times, when Y is high (above its trend), national income is high (above it trend). Consumers will take this opp

The problem with the Keynesian model We can classify two problems with the Keynesian model as developed so far: 1. Π is exogenous. Although inflation may temporarily deviate

Assume Workers Comp awards $X to workers not working because of injury. $X is set to equal the workers previous wages. Once workers return to work, the award payments stop. Suppose

illustrate and discuss the implications of variou market structures (competitive and noncompetitive) for price determination

Figure below demonstrates a more developed version of the circular flow. In this figure we see how goods flow through various sectors of the economy. Figure Money in the c

Explain determination of national income using aggregate demand-aggregate supply and saving-investment methods for a three sector economy.

One alternative way to calculate the total change in money supply when the Fed injects money into the economy or takes away money from the economy is the amount of money injected o

term paper on determinat and multiplier of money supply

A study by the Information Technology department at WPU revealed company employees receive an average of four e-mails per hour. Assume the arrival of these e-mails is approximated