About This Chapter
Problem Solving With Networks - Chapter Summary
Our instructors explain how networks are used to solve problems in this helpful chapter. These lessons cover the use of networks when solving model flow problems and how Dijkstra's algorithm applies to both math and science. Other topics include using bipartite graphs, Prim's algorithm and how to create an activity network. You'll also review the critical path analysis and how it applies to scheduling. After reviewing this chapter, you should be ready to do the following:
- Use minimum spanning trees to find the determination of lower bounds
- Apply the maximum-flow minimum-cut theorem to large-scale problems
- Determine the shortest path between two vertices
- Define the Hungarian algorithm and its applications
- Understand how crashing is used to reduce project completion time
Preparing for a test or exam is easy with our professionally-designed learning tools. Before moving on to the next lesson, you can take the multiple-choice quiz to see if you're ready or if you need to review the lesson again. Our study materials are accessible on any tablet, phone or computer 24 hours a day for a completely flexible experience. An instructor is available to answer your questions if need additional help.
1. Prim's Algorithm: Explanation & Examples
Prim's algorithm is an algorithm used often in graph theory. This lesson will explain what the algorithm is used for, the steps involved in using it, and a real-world example of putting it to practice.
2. Dijkstra's Algorithm: Definition, Applications & Examples
Dijkstra's algorithm is a step-by-step process we can use to find the shortest path between two vertices in a weighted graph. This algorithm enables us to find shortest distances and minimum costs, making it a valuable tool.
3. Critical Path Analysis: Definition & Examples
Critical path analysis is a project management tool used to understand task dependencies and their effect on the project schedule. In this lesson, we show how the critical path can be derived.
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Other chapters within the VCE Further Mathematics: Exam Prep & Study Guide course
- Population & Samples
- Categorical Data Representation
- Numerical Data Representation
- Data Distribution
- Correlation & Causation in Math
- Non-Causal Relationships in Statistics
- Linear Relationships
- Time Series Data
- Recursion & Financial Modeling
- Concepts of Financial Mathematics
- Matrices Overview
- Graphs & Networks
- Paths & Circuits
- Geometric Solids
- Measurement & Trigonometry
- Spherical Geometry
- Applications of Spherical Geometry
- Graphs & Relations
- Linear Programming Overview
- VCE Further Mathematics Flashcards