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Mathematics Final Year Topic: Correctness Conditions for Dijkstra and Bellman–Ford Shortest-Path Algorithms

This Mathematics final year project examines algorithm correctness through proofs and explicitly constructed weighted-graph examples.

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Why choose this project topic?

A focused study of shortest-path assumptions gives you a specific question in algorithmic graph theory. It examines algorithm correctness through proofs and explicitly constructed weighted-graph examples. The bounded comparison creates room to explain how your evidence supports an interpretation and where the method has limits.

How do edge-weight assumptions determine when the selected shortest-path algorithms return valid distances?

Agree the apparatus or dataset, comparison range and feasible measurement schedule for shortest-path assumptions with your supervisor.

Proposed project objectives

  1. 01Define the materials, variables and comparison conditions for shortest-path assumptions.
  2. 02State each algorithm and its invariant, prove correctness under its assumptions and build bounded examples involving negative edges or negative cycles.
  3. 03Evaluate the measurements or model outputs in relation to this question: How do edge-weight assumptions determine when the selected shortest-path algorithms return valid distances?

A suggested research approach

State each algorithm and its invariant, prove correctness under its assumptions and build bounded examples involving negative edges or negative cycles. Verify path costs independently and distinguish undefined shortest distances from implementation errors. Agree the available resources and record uncertainty, deviations from the protocol and any observations that challenge the initial interpretation.

What you will need

  • Explicit weighted graphs and algorithm definitions
  • Correctness proofs and invariant references
  • Exact path-cost and cycle-verification tools

Keep your project scope clear

A shortest path may not exist in the relevant sense when reachable negative cycles are allowed.

Mathematics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

  1. Chapter 1Introduction
  2. Chapter 2Literature Review
  3. Chapter 3Theory and Methodology
  4. Chapter 4Results and Applications
  5. Chapter 5Summary, Conclusion and Recommendations

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