Algorithms for Optimization Problems On Structured
il y a 2 semaines
**Algorithms for optimization problems on structured digraphs**:
- Réf **ABG-124677**
- Sujet de Thèse- 18/06/2024- Contrat doctoral- LIMOS- Lieu de travail- Clermont-Ferrand - Auvergne-Rhône-Alpes - France- Intitulé du sujet- Algorithms for optimization problems on structured digraphs- Champs scientifiques- Informatique
- Mathématiques
- Mots clés- algorithms, graphs**Description du sujet**:
A large number of fundamental combinatorial optimization problems are NP-hard on directed graphs (digraphs). This includes the problems of Directed Feedback Vertex/Arc Set [3,4], Vertex/Arc Disjoint Paths [2], Path Cover [1,2], and many others. Improving known approximation or parameterized algorithms for these problems, when the input can be any digraph, remains a well-known and long-standing open problem. This motivates the study of these problems on classes of structured digraphs, where they remain NP-hard, but are likely to admit non-trivial approximation and parameterized algorithms, as in [1,2,3,4].
The objective of this doctoral thesis will be to explore the algorithmic side of fundamental optimization problems on digraphs. To this end, we will develop new algorithms and lower bounds for these problems on different classes of structured digraphs (tournaments, semi-complete digraphs, planar or triangulated digraphs, etc.). We will focus on two lines of research:
1. Approximation algorithms: the goal is to design polynomial-time algorithms to produce constant factor or O(log n) approximation solutions for inputs of size n.
2. Parameterized algorithms: the goal is to design algorithms that compute an exact solution of size at most k in time f(k)poly(n), where f is a function with (moderately) exponential growth of k and poly is a polynomial.
[1] M. Caceres, M. Cairo, B. Mumey, R. Rizzi, and A.I. Tomescu. Sparsifying, shrinking and splicing for minimum path cover in parameterized linear time. Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022, pp. 359-376.
[2] H. Fernau, F. Foucaud, K. Mann, U. Padariya and R. Rao. Parameterizing path partitions. Proceedings of the 13th International Conference on Algorithms and Complexity (CIAC 2023), Lecture Notes in Computer Science 13898:187-201, 2023.
[3] M. Kumar and D. Lokshtanov. Faster exact and parameterized algorithm for feedback vertex set in tournaments. Proceedings of the 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016, February 17-20, 2016. LIPIcs 47, pp. 49:1-49:13, 2016.
[4] D. Lokshtanov, P. Misra, J. Mukherjee, F. Panolan, G. Philip and S. Saurabh. 2-approximating Feedback Vertex Set in tournaments. ACM Transactions on Algorithms17(2): 11:1-11:14, 2021.
**Prise de fonction**:
- 01/10/2024**Nature du financement**:
- Contrat doctoral**Précisions sur le financement**:
- CNRS**Présentation établissement et labo d'accueil**:
- LIMOSThe Laboratory of Informatics, Modelling and Optimization of the Systems (LIMOS) is a Mixed Unit of Research (UMR 6158) in computing, and more generally in Sciences and Technologies of information and the Communication ( STIC).
The LIMOS is mainly connected with the Institute of the Sciences of the Information and their Interactions (INS2I) of the CNRS, and in a secondary way to the Institute of the Sciences of the Engineering and the Systems (INSIS). He has for academic supervision the Clermont Auvergne university and the graduate school of Mines of Saint-Etienne (EMSE), and as partner establishment the Engineer Institute SIGMA. The LIMOS is a member labex IMOBS3 and ClercVolc and federation of search in Environment FR 3467 (which groups 17 laboratories UCA and INRA of the site of Clermont-Ferrand). It is an associate member of the federation MODMAD (Mathematical MODELLING and Decision support, FED 4169) carried by University Jean Monnet of Saint-Etienne
The scientific positioning of the LIMOS is centered around the Computing, the Modelling and the Optimization of the Organizational and alive Systems. The main themes of search developed within the laboratory are:
Combinatorial optimization
Algorithmics, Graphs, Complexity
Team Metamodeling, Continuous Optimization and Applications (MOCA)
Data, Services, Intelligence
Network and Security
Modeling and Optimization of Manufacturing Systems
Service Design and Planning
**Site web**:
The recruited person must hold a master's degree in computer science or mathematics (or related area) at the starting date, and have prior knowledge in graph theory and algorithms. Good knowledge in structural graph theory, directed graphs, approximation algorithms, and/or parameterized algorithms is a plus.
Working level of English (written and spoken) is necessary.
The PhD will have a duration of 3 years and will be performed at the LIMOS laboratory (located in Aubière, in the outskirts of Clermont-Ferrand).
The contract will start ideally on October 1st 2024, but a later starting date is also possible.
The net salary is about 1
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