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Lec 16

# Lec 16 - Team 3 Pooja Mehta Alkey Pandya Vishal Baheti...

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Team 3: Pooja Mehta, Alkey Pandya, Vishal Baheti, Khang Nguyen November 5, 2010 IEOR 151 Lecture Notes Seven Bridges of Kongisberg Impossible to have an Euler tour if a network has more than two odd vertices Odd Vertex: a vertex that has an odd number of arcs leading to it Travelling Salesman Problem (TSP) Model Objective: Find a tour that visits each vertex exactly once and whose total length is as small as possible. Let G =( V , E ) be a complete undirected graph with vertices V , | V |= n , and the edges E and let d ij be the length of edge ( i , j ). Algorithm for Minimum Spanning Tree (MST) 1. Find the shortest arc in the network. If there are more than one, pick any one randomly. Highlight this arc and the nodes connected. 2. Pick the next shortest arc, unless it forms a cycle with the arcs already highlighted before. Highlight the arc and the nodes connected. 3. If all arcs are connected, then we are done. Otherwise, repeat Step 2. A Minimum Spanning Tree Based Heuristic 1. Construct a minimum spanning tree 2. Let the root be an arbitrary vertex

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Lec 16 - Team 3 Pooja Mehta Alkey Pandya Vishal Baheti...

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