Route Inspection
Problem: Theory and
Applications
MS230400041
Mariam Aslam
MSCS
Department of Computer Science
and Information Technology
Virtual University of Pakistan
Introduction
• Overview: The Route Inspection Problem, also
known as the Chinese Postman Problem,
involves finding the shortest path or circuit
that visits every edge of a graph.
• Importance: Crucial for optimizing routes in
various applications like postal delivery,
garbage collection, and network maintenance.
Definition of the Route
Inspection Problem
• Formal Definition: Given a graph, find the
shortest closed path or circuit that visits every
edge at least once.
• Key Terms: Graph, edges, vertices, circuit.
Historical Background
• Origins: Introduced by the Chinese
mathematician Kwan Mei-Ko in 1962.
• Development: Key contributions from Euler’s
work on graph theory and subsequent
advancements.
Graph Theory Basics
• Graph: A collection of vertices (nodes) and
edges (lines connecting nodes).
• Path: A sequence of edges connecting vertices.
• Circuit: A path that starts and ends at the
same vertex.
Chinese Postman Problem
• Introduction: The problem of finding the
shortest closed path in a graph that visits
every edge at least once.
• Difference: Applies to both Eulerian and nonEulerian graphs.
Solving Route Inspection
Problem
Solving Route Inspection
Problem (Cont.)
• Identify Odd
Nodes
•BCDE
• Pairing
• BC – DE
• BD – CE
• BE – CD
Solving Route Inspection
Problem (Cont.)
• Identify Odd Nodes
• BCDE
• Pairing
• BC – DE: 3+4 = 7
• BD – CE: (1+2) + (2+1) = 6
• BE – CD: (3+2+1) + (3+1+2) = 12
• Adding the smallest to the total
• 6 + 24 = 30
Solving Route Inspection
Problem (Cont.)
• Route
• A→B→C→F→C→E→F→E→D→B
→A→D→A
Complexity Analysis
• Time Complexity: Analysis of how the time to
solve the problem scales with input size.
• Space Complexity: Analysis of memory usage.
• Practical Considerations: Efficiency in realworld applications.
Applications
• Real-World Uses:
• Postal Delivery: Optimizing mail delivery
routes.
• Garbage Collection: Efficient trash pickup
routes.
• Network Routing: Optimizing data packet
travel in networks.
• Case Studies: Examples of successful
implementations.
Challenges and Limitations
• Common Challenges: Handling large graphs,
dynamic changes in graph structure.
• Limitations: Current algorithms may not be
optimal for all scenarios.
Recent Advances and Research
• Developments: Latest improvements in
algorithms and techniques.
• Research: Ongoing studies and future
directions in solving the Route Inspection
Problem.
Thankyou!