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Jeudi 16 Avril
| Heure: |
10:30 - 12:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
Approximation Schemes for Planar Graph Connectivity Problems |
| Description: |
Meike Neuwohner The k-Edge-Connected Subgraph problem and the k-Connectivity Augmentation problem are among the most basic Network Design problems and, consequently, have been heavily studied. Due to their approximation hardness, the gold standard in terms of approximation guarantee are
strong constant factors. Interestingly, this approximation hardness does not carry over to planar graphs. In particular, the 2-Edge-Connected Subgraph problem admits a PTAS on planar graphs. However, the used techniques are very different from the celebrated Bakers framework, which is a standard way to design PTASs for planar graphs. The main obstacle of using Bakers technique in its classical form is that it requires a certain locality of the problem. However, k-edge/vertex-connectivity are global properties. We present a novel, and arguably clean, way to extend Bakers framework to deal with larger connectivity requirements. Based on this, we obtain a PTAS for the k-Edge-Connected Subgraph problem and its vertex analog, even with costs, as long as the max-to-min cost ratio is bounded by a constant. Moreover, together with further insights, we obtain a PTAS for the k-Connectivity Augmentation problem in the same cost setting. We complement this with an NP-hardness result for planar augmentation, showing that all our results are essentially tight.
This is joint work with Vera Traub and Rico Zenklusen. |
Jeudi 7 Mai
| Heure: |
10:30 - 12:00 |
| Lieu: |
Bâtiment Hypatia, "Salle Tour Eiffel", étage 4 |
| Résumé: |
Optimizing Networks Across the Device-Edge-Cloud Continuum |
| Description: |
Alberto Ceselli Modern networked systems are no longer confined to centralized infrastructures, but span a continuum from cloud data centers to edge nodes and individual end devices. In this setting, optimally placing and orchestrating virtualized services becomes a critical and complex optimization problem.
In this talk, I present a set of recent contributions addressing this class of problems, characterized by: (a) hard decisions on service placement and orchestration of modular applications, (b) scarce and heterogeneous resources, and (c) multi-layer network graphs.
I highlight key challenges arising in this context, formulate the underlying combinatorial optimization problems, present solution approaches based on mixed integer programming and decomposition methods, and outline directions for future research. |
Jeudi 21 Mai
| Heure: |
10:30 - 12:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
Integer programs with bounded subdeterminants: solving structured cases |
| Description: |
Stefan Kober It is a notorious open question whether integer programs (IPs), with an integer constraint matrix M whose subdeterminants are all bounded by a constant in absolute value, can be solved in polynomial time. We give an overview on recent progress towards this question and the rich combinatorial structures hidden within. Further, we show how to solve such IPs if the constraint matrix fulfills certain further structural conditions.
This talk is based on the following papers:
Aprile, M., Fiorini, S., Joret, G., Kober, S., Seweryn, M. T., Weltge, S., & Yuditsky, Y. Integer programs with nearly totally unimodular matrices: the cographic case. [SODA 2025]
Fiorini, S., Kober, S., Seweryn, M. T., Shantanam, A., & Yuditsky, Y. Face covers and rooted minors in bounded genus graphs. [preprint 2025]
Kober, S. Totally ?-Modular IPs with Two Non-zeros in Most Rows. [IPCO 2025] |
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