Around the world in 30 Days By: Rolando Sanchez. Houston Hometown Family lives there Want to go and visit the neighborhood I once lived in.

Slides:

Advertisements

Similar presentations

1. Find the cost of each of the following using the Nearest Neighbor Algorithm. a)Start at Vertex M.

Advertisements

Design and Analysis of Algorithms Approximation algorithms for NP-complete problems Haidong Xue Summer 2012, at GSU.

Greedy Algorithms Spanning Trees Chapter 16, 23. What makes a greedy algorithm? Feasible –Has to satisfy the problem’s constraints Locally Optimal –The.

Design and Analysis of Algorithms Single-source shortest paths, all-pairs shortest paths Haidong Xue Summer 2012, at GSU.

Chapter 15 Graph Theory © 2008 Pearson Addison-Wesley. All rights reserved.

1 Chapter 15.3 Hamilton Paths and Hamilton Circuits Objectives 1.Understand the definitions of Hamilton paths & Hamilton circuits. 2.Find the number of.

7.3 Kruskal’s Algorithm. Kruskal’s Algorithm was developed by JOSEPH KRUSKAL.

1 Greedy Algorithms. 2 2 A short list of categories Algorithm types we will consider include: Simple recursive algorithms Backtracking algorithms Divide.

A traveling salesman has customers in 5 cities which we will call A, B, C, D, and E. The salesman needs to travel to all 5 cities with his trip starting.

Two Discrete Optimization Problems Problem #2: The Minimum Cost Spanning Tree Problem.

The Travelling Salesman Algorithm A Salesman has to visit lots of different stores and return to the starting base On a graph this means visiting every.

Paris’ top 10 tourist attractions By: Traevon Green.

Shortest Path Algorithms. Kruskal’s Algorithm We construct a set of edges A satisfying the following invariant:  A is a subset of some MST We start with.

Graphs II Robin Burke GAM 376. Admin Skip the Lua topic.

Slide 14-1 Copyright © 2005 Pearson Education, Inc. SEVENTH EDITION and EXPANDED SEVENTH EDITION.

Minimum Spanning Trees

Graph Theory Hamilton Paths and Hamilton Circuits.

Spring 2015 Mathematics in Management Science Network Problems Networks & Trees Minimum Networks Spanning Trees Minimum Spanning Trees.

6.1 Hamilton Circuits and Paths: Hamilton Circuits and Paths: Hamilton Path: Travels to each vertex once and only once… Hamilton Path: Travels to each.

Module 5 – Networks and Decision Mathematics Chapter 23 – Undirected Graphs.

© 2010 Pearson Prentice Hall. All rights reserved. 1 §15.3, Hamilton Paths and Circuits.

Where in the world would you go Marty Absher. Cities  Charlotte, NC  I never go here much.  Carowinds  Charlotte Coliseum.

Spring 2015 Mathematics in Management Science Traveling Salesman Problem Approximate solutions for TSP NNA, RNN, SEA Greedy Heuristic Algorithms.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 4.2, Slide 1 4 Graph Theory (Networks) The Mathematics of Relationships 4.

Minimum spanning trees Aims: To know the terms: tree, spanning tree, minimum spanning tree. To understand that a minimum spanning tree connects a network.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 14.3 Hamilton Paths, and Hamilton Circuits.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 14.4 Trees.

Lecture 19 Greedy Algorithms Minimum Spanning Tree Problem.

Chapter 2: Business Efficiency Lesson Plan Business Efficiency  Visiting Vertices-Graph Theory Problem Hamiltonian Circuits  Vacation Planning Problem.

TSP – Upper Bounds and Lower Bounds Initial problem : Upper Bound A salesman based in Stockton needs to visit shops based in Darlington, Billingham, Middlesbrough,

Chapter 14 Section 4 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Graphs A ‘Graph’ is a diagram that shows how things are connected together. It makes no attempt to draw actual paths or routes and scale is generally inconsequential.

Mathematics in Management Science

CIRCUITS, PATHS, AND SCHEDULES Euler and Königsberg.

SPANNING TREES Lecture 21 CS2110 – Fall Nate Foster is out of town. NO 3-4pm office hours today!

Prims Algorithm for finding a minimum spanning tree

Lecture 19 Minimal Spanning Trees CSCI – 1900 Mathematics for Computer Science Fall 2014 Bill Pine.

Tree Diagrams A tree is a connected graph in which every edge is a bridge. There can NEVER be a circuit in a tree diagram!

By: Christophe Dufour Chrishon Adams Mischael Joseph.

I can describe the differences between Hamilton and Euler circuits and find efficient Hamilton circuits in graphs. Hamilton Circuits I can compare and.

Today we will… Identify the vertices and edges on a given shape.

Chapter 14 Section 3 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Unit 2 Hamiltonian Circuits. Hamiltonian Circuit: A tour that starts at a vertex of a graph and visits each vertex once and only once, returning to where.

Turn in HW and Classwork sheet from last class. You have 10 minutes to complete the warm- up. After the warm-up, we will finish our notes on algorithms.

Spanning Trees Dijkstra (Unit 10) SOL: DM.2 Classwork worksheet Homework (day 70) Worksheet Quiz next block.

Grade 11 AP Mathematics Graph Theory Definition: A graph, G, is a set of vertices v(G) = {v 1, v 2, v 3, …, v n } and edges e(G) = {v i v j where 1 ≤ i,

Mathematical modeling To describe or represent a real-world situation quantitatively, in mathematical language.

Chapter 2: Business Efficiency Hamiltonian Circuit Visiting Vertices –In some graph theory problems, it is only necessary to visit specific locations (using.

Graphs 1 Neil Ghani University of Strathclyde. Where are we …. We studied lists: * Searching and sorting a list Then we studied trees: * Efficient search.

Hamilton Paths and Hamilton Circuits

Weighted Graphs and traveling Salesperson problem

Minimum Spanning Tree Chapter 13.6.

HAMILTONIAN CIRCUIT ALGORITHMS

Section 14.3 Hamilton Paths, and Hamilton Circuits

Section 14.4 Trees.

Chapter 2: Business Efficiency Business Efficiency

4-4 Graph Theory Trees.

Kruskal’s Algorithm for finding a minimum spanning tree

Advanced Analysis of Algorithms

Warm Up – Friday.

Louisiana Travels.

A path that uses every vertex of the graph exactly once.

Chapter 15 Graph Theory © 2008 Pearson Addison-Wesley.

Chapter 15 Graph Theory © 2008 Pearson Addison-Wesley.

Hamilton Paths and Hamilton Circuits

Euler circuit Theorem 1 If a graph G has an Eulerian path, then it must have exactly two odd vertices. Theorem 2 If a graph G has an Eulerian circuit,

Section 13.4 Trees.

Warm Up – Monday Calculate the Redundancy of the above network.

Traveling Salesman Problems Nearest Neighbor Method

Presentation transcript:

Around the world in 30 Days By: Rolando Sanchez

Houston Hometown Family lives there Want to go and visit the neighborhood I once lived in

Dubai Biggest indoor Ski Facility Palm tree shaped island Best shopping in the world Dubai International Film Festival

Paris Eiffel Tower Super busy atmosphere Notre Dame Louvre

Cabo Miles of wonderful beaches Weather is spectacular Tourist Attraction

Cairo Great Sphinx Pyramids Hieroglyphics and Egyptian Culture

Distance in miles

Price in USD

Tree

NNA / Distance

NNA / Price

SEA Algorithm for Distance

SEA Algorithim for Price

Kruskal’s Algorithm

Tree Diagram a.k.a. “Brute Force Method” Tree diagram to find the shortest route Always needs a starting vertex Takes a long time Gives you the optimal solution ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Initially I had trouble with the tree diagram but after countless tries, I was finally able to understand it. Oh and it does take a long time and you defiantly need patience

Nearest Neighbor Algorithm Heuristic / greedy Quick but not always efficient Always need a starting vertex ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This was by far the most easiest algorithm and it didn’t take as long as brute force.

Kruskal’s Algorithm List the edges from least to greatest Shade the first edge on the list and continue with the rest as long as they don’t form a circuit Continue until a spanning tree results, this will always give you the optimal solution Doesn’t need a starting vertex ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Not bad at all and it was actually quite easy

S.E.A. Algorithm List the edges from least to greatest Then you choose the edge with the lowest weight as long as A vertex never has 3 edges extending from it It doesn’t form a circuit before visiting each vertex It doesn’t need a starting vertex Heuristic / greedy ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The S.E.A. Algorithm was a breeze I didn’t have any difficulties with it.

Sources