IEOR_Module_Lab1_Examples - University of California at...

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University of California at Berkeley Engineering 10 Spring 2010 Professor Leachman Optimization Part  Lab #1 Problem 1: Minimum Spanning Tree The National Park Service has recently obtained several hundred square miles of land to be converted into a national park. Cars will not be allowed into the area, but a narrow, winding roadway needs to be built for trams and for jeeps driven by the park rangers. This roadway must connect seven important locations within the park. Because the roadway will be both expensive to build and disruptive to the environment, the NPS wants to build as short a roadway as possible, except that there must be a path from each critical location to each other critical location. The chart below schematically indicates the distance between each pair of critical locations. Find the shortest possible roadway that connects these critical locations (distances are in miles, and only roads that are practical to build are shown). 1 Entrance Overlook Ranger Station #2 Camp Trailhead Waterfall Ranger Station #1 20 40 50 30 70 40 10 40 30 10 50 60
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University of California at Berkeley Engineering 10 Spring 2010 Professor Leachman The network configuration that we are looking for is called the minimal spanning tree (MST) – the combination of edges that connect all nodes in the network with minimal length. The method to solve the problem is illustrated as follows: Step 1: Find the shortest edge in the network. If there are more than one, pick any one randomly. We will choose (Overlook-Ranger Station #1). Highlight this edge. Step 2: Pick the next shortest edge, unless it forms a cycle with the edges already highlighted before. Highlight the edge (Ranger Station #2-Trailhead). 2 Entrance Overlook Ranger Station #2 Camp Trailhead Waterfall Ranger Station #1 20 40 50 30 70 40 10 40 30 10 50 60 Entrance Overlook Ranger Station #2 Camp Trailhead Waterfall Ranger Station #1 20 40 50 30 70 40 10 40 30 10 50 60
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University of California at Berkeley Engineering 10 Spring 2010 Professor Leachman Step 3: If all edges are connected, then we are done. Otherwise, repeat Step 2.
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This note was uploaded on 02/19/2010 for the course ENGINEERIN 72826 taught by Professor Sengupta/leachman/johnson during the Spring '10 term at University of California, Berkeley.

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IEOR_Module_Lab1_Examples - University of California at...

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