Multimap Navigation and Validation System

1
Multi-map Navigation and Validation System

• By
• Yasser Kanouni
• Department of Computer Science
• Old Dominion University
•   
• Research Sponsors
• Professor Irwin Levinstein
• Professor Jay Morris

2
Overview

• Introduction
• Problem Description
• Solution Description
• Data Structure
• Algorithms Description 
• Runtime Caption and Description of the
  Application
• Multimap Validation
• Future Work
• Demonstration

3
Introduction

• Graph Theory utility
• road networks
• Communication networks
• Computer networks
• Facial recognition
• Decision support and intelligent systems

4
Problem Description

• Finding the way around a terrain to facilitate
  navigation for any object.
• Being able to spot similar geometrical forms
  across all the constituents of the terrain.

5
Definitions Assumptions

• Terrain(Master Map) A collection of Areas, which
  may or may not be connected one to another.
• Area (Local Map) a graph of connected nodes.
• Graph undirected.

6
Solution Description

• Grouping a collection of nodes into exclusive
  sets. (Areas)
• Link nodes within each local map.
• Adjacency Matrix per node (Local Trees)
• Nodes maintain neighbors connectivity
  information.
• Inexpensive local map path searches

7
Solution Description(continued)

• Grouping all nodes from all the Local Maps into
  the Master Map.
• Global Search Paths (Global Trees)
• Merging of local Maps when intersection is not an
  empty set

8
Class Diagram
1..
1..
0..
IN
1..
1..
USES
MERGES
1
USES
1
1
1
1
1
1
USES
1
USES
1
1
USES
9
PartitionManager
Merging
Master Map
10
PathManager
Iteration 1
Iteration 2
Iteration 3
Iteration 4
Map
Map
Map
C
C
C
A
A
A
B
B
B
A
A
A
C
C
C
B
Working Node
Checked against Node
Invalid connection Node
11
MapConstructorManager
Iteration 1
Iteration 1
Map
Map
C
C
Nodes to Delete
A
A
B
B
A
A
Iteration 1
C
C
Iteration 2
Iteration 3
Working Node
12
PathSearchManager
Map
Desired Search Source C Destination B
C
A
B
A
C
Working Node
Source Node
Destination Node
13
Complexity Analysis

  Overall applications complexity Maximum
(O(n2), O(n3), O(n3), O(n2)) yields O(n3)  
14
Map Manager Interface
15
Node Manager Interface
16
Graph Sketcher Interface
17
Graph Sketcher Interface
18
Path Search Interface
19
Path Search Interface
20
Graph Validator Interface
21
Graph Validator Interface
22
Future Work

• Alternate shortest path computations
• Directed flow
• Cost
• Distance
• Alternate Validation model
• Correlation criteria
• Allow map rotations and dilations
• Allow permanent positioning of nodes

23
Acknowledgment

• Jay Morris
• Project Guide,
• Old Dominion University
• Irwin Levinstein
• Assistant Professor,
• Old Dominion University
• Stephan Olariu
• Advisor,
• Old Dominion University

24
Demonstration

• Windows application in C using the graphical API
  based on the GDI library within the .NET
  framework.
• Live demonstration of the Navigation Validation
  System Manager.