(A. Ceselli)

Slides on Network Flows (2026)

Here you can find the slides of the 2026 edition

Lecture topics and slides (part 1: flows)

• Lecture 1. Introduction. Modeling with flows. Applications. Slides .
• Lecture 2. Flow algorithms and combinatorial properties of flows (1). Slides .
• Lecture 3. Flow algorithms and combinatorial properties of flows (2). Slides .
• Lecture 4. Min cost flow problems and applications. Slides . Lab session: solving flow problems with GLPK. Data for Max Flow experiments .

Lecture topics and slides (part 2: design)

• Lectures 1 - 2. Introduction. Network connections, components and trees. Applications. Slides .
• Lecture 3. Modeling and solving location problems. Slides .
• Lecture 4. Location problems taxonomy through modeling practice. Some CFLP example data, a sample Julia reading procedure. The lecture whiteboard notes and the corresponding Julia/JuMP models tutorial. Steiner Trees and Forests. Slides . A nice historical perspective on Steiner Problems.

Software

• The GNU linear programming toolkit and its windows pre-compiled binaries ; offers a very flexible framework for flow modeling.
• A few IDE suggestions.
• A nice windows IDE.
• The LEMON libraries; allow efficient embedding of flow and cut computations in your applications.
• The AMPL framework for modeling and solving optimization problems.
• The Julia framework IDE for programming and data analysis.

References

• J. Kleinberg, E. Tardos, Algorithm Design. Pearson, 2014.
• R.K. Ahuja, T.L. Magnanti, J.B. Orlin, Network Flows. Theory, algorithms and applications. Prentice Hall, 1993.
• L. A. Wolsey Integer Programming Wiley, 1998.
• V. Vazirani, Approximation Algorithms Springer, 2003.