PACKENUM · PArameterized Complexity and Kernelization for ENUMeration
Horizon Europe — Marie Skłodowska-Curie Actions
- Duration
- 2024-07-08 → 2026-07-07
- EU contribution
- €140,797
- Participants
- 2
- Scheme
- HORIZON-TMA-MSCA-PF-EF
Lines connect the coordinator with its partners.
Results in brief
PArameterized Complexity and Kernelization for ENUMeration
Preprocessing is a ubiquitous technique in algorithm design, aimed at reducing complex problem instances to simpler ones that can be solved more efficiently. While it is a core tool when dealing with optimization problems, preprocessing has not seen the same level of success on enumeration problems, where the goal is now to generate all viable solutions instead of only one. These problems naturally appear in various fields, including network design, data mining, and bioinformatics. Despite the practical importance of these problems, the theoretical understanding of preprocessing for enumeration is still in its early stages. To remedy this situation, the PACKENUM project (“PArameterized Complexity and Kernelization for ENUMeration”) was established to investigate preprocessing for enumeration problems under the lens of parameterized complexity theory. In this setting, preprocessing is modeled through the kernelization algorithms (or kernels), which transforms a given instance into an equivalent but smaller one whose size depends only on a chosen parameter, providing formal performance guarantees for the preprocessing algorithm; Intuitively, the smaller the output size, the better the kernel, with polynomial-sized kernels being defined as the efficient ones. Overall, PACKENUM goals were to develop a coherent theoretical foundation for enumerative kernelization and to provide concrete algorithmic advances. Its impact is to be materialized by both providing new examples of enumeration kernels and setting new research directions on the subject for the parameterized complexity and enumeration algorithms communities.
Data: CORDIS, © European Union
Project objective
Algorithms play crucial roles in many aspects of the lives of billions of people worldwide. Many of the problems we wish to solve, in industry andacademia, are NP-hard and it is expected that no polynomial-time algorithm exists to obtain an optimal solution for them. Nevertheless, they aresolved millions of times on a daily basis. Solving them would be unfeasible without the use of preprocessing techniques, which significantly reducerunning times and are often necessary to solve a problem. Explaining why these methods work in practice and designing new ones that come withperformance guarantees is a great challenge in Theoretical Computer Science. In the framework of Parameterized Complexity, they are modeledthrough kernelization, which uses an additional measurement of the problem's structure (the parameter) to output a small equivalent instance thatcan be quickly solved.However, there will usually exist several optimal solutions, regardless of the optimality criterion, and drawing conclusions from a single one may bemisleading. Knowing more about the set of optimal solutions is thus necessary in many scenarios and can be formalized through enumerationproblems. Unlike decision problems, very little is known about preprocessing for enumeration problems. In the recently defined enumeration kernel,solutions to the reduced instance are used to partition and efficiently list the solution set of the input. Through this project, the researcher willdesign and implement novel parameterized algorithms and kernels for enumeration problems, and build the lower-bound theory required toseparate problems between those that admit polynomial enumeration kernels and those that do not. The designed kernels will be some of theearliest enumeration kernels, while the lower-bound theory will be a fundamental part of Parameterized Complexity, allowing researcher's toidentify problems that do not admit efficient preprocessing and focus their efforts on problems that do.
Original text from CORDIS.
Participants
Links
- View on CORDIS
- DOI: 10.3030/101109317
- https://ec.europa.eu/research/participants/documents/downloadPublic?documentIds=080166e516b0653b&appId=PPGMS
Data: CORDIS, © European Union