Before joining CBU, I completed the PhD programme at the Faculty of Mathematics and Natural Sciences at UiB, focusing on integer programming and combinatorial optimization. You can read more in the corresponding press release. A translation to english is available below.
Math and code of the best independent subnetwork
[Phillippe Samer defends his doctoral thesis on Thursday 21 December 2023, for the PhD degree at the University of Bergen with the dissertation titled "Polyhedra and algorithms for problems bridging notions of connectivity and independence".]
Three simple problems asking for the optimal piece of a network that meets some notion of independence. Problems so simple to state, yet taking over four years of PhD work to reach small contributions in a few directions within algorithms and optimization. Four years of thinking, reading, discussing and coding (plus wishful thinking and serendipity), motivated by the numerous applications that each of those network design problems may have in telecommunication and utilities, facility location, phylogenetics, among many other application domains of operations research and optimization.
The work is on basic research. All three problems boil down to picking dots and lines in a diagram (representing a graph). Still, if such diagram models compatible donor-patient pairs in a kidney transplant program, or alternative transportation means in a freight distribution system, the results can be easily tailored towards intelligent prototypes to support decision-making.
Interestingly, the mathematical structure behind each of those problems is a polyhedron - just like the Platonic solids, albeit a higher dimensional one. About half of the contributions in the present thesis concern improved understanding of those geometric structures. That is, theorems about the possible description of the polyhedron representing all feasible solutions to each of the problems.
Beyond shedding light on that invisible underpinning, the polyhedral point of view also leads to improved algorithms to face the network design problems. The new geometric descriptions translate to linear inequalities in integer programming formulations, and stronger computational results when we solve harder examples of those optimization problems.
All algorithms and tools developed throughout this work are shared in free, open-source code repositories, fostering reuse, further research and new applications in research and development.
Thesis supervised by Prof. Dag Haugland.
- 2021. The unsuitable neighbourhood inequalities for the fixed cardinality stable set polytope. Paper 87, pages 107-116. In:
- 2021. Graphs and Combinatorial Optimization: from Theory to Applications - CTW2020 Proceedings. Springer. 240 pages. ISBN: 978-3-030-63071-3.
- 2018. The matching relaxation for a class of generalized set partitioning problems. Discrete Applied Mathematics. 253: 153-166. doi: 10.1016/j.dam.2018.05.033
- 2016. Combinatorial relaxation bounds and preprocessing for berth allocation problems.
I deeply admire Federico Ardila, a mathematician and professor at both Universidad de Los Andes and San Francisco State University. His essay "Todos Cuentan" (Notices of the AMS, 2016) is an inspiring expression of his pedagogical and transformative efforts.
I humbly believe in his approach to tackle the underrepresentation problems in mathematics and science. His ideas build on the following foundational axioms.
Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Axiom 4. Every student deserves to be treated with dignity and respect.