Summary
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 and
academia, are NP-hard and it is expected that no polynomial-time algorithm exists to obtain an optimal solution for them. Nevertheless, they are
solved millions of times on a daily basis. Solving them would be unfeasible without the use of preprocessing techniques, which significantly reduce
running times and are often necessary to solve a problem. Explaining why these methods work in practice and designing new ones that come with
performance guarantees is a great challenge in Theoretical Computer Science. In the framework of Parameterized Complexity, they are modeled
through kernelization, which uses an additional measurement of the problem's structure (the parameter) to output a small equivalent instance that
can be quickly solved.
However, there will usually exist several optimal solutions, regardless of the optimality criterion, and drawing conclusions from a single one may be
misleading. Knowing more about the set of optimal solutions is thus necessary in many scenarios and can be formalized through enumeration
problems. 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 will
design and implement novel parameterized algorithms and kernels for enumeration problems, and build the lower-bound theory required to
separate problems between those that admit polynomial enumeration kernels and those that do not. The designed kernels will be some of the
earliest enumeration kernels, while the lower-bound theory will be a fundamental part of Parameterized Complexity, allowing researcher's to
identify problems that do not admit efficient preprocessing and focus their efforts on problems that do.
academia, are NP-hard and it is expected that no polynomial-time algorithm exists to obtain an optimal solution for them. Nevertheless, they are
solved millions of times on a daily basis. Solving them would be unfeasible without the use of preprocessing techniques, which significantly reduce
running times and are often necessary to solve a problem. Explaining why these methods work in practice and designing new ones that come with
performance guarantees is a great challenge in Theoretical Computer Science. In the framework of Parameterized Complexity, they are modeled
through kernelization, which uses an additional measurement of the problem's structure (the parameter) to output a small equivalent instance that
can be quickly solved.
However, there will usually exist several optimal solutions, regardless of the optimality criterion, and drawing conclusions from a single one may be
misleading. Knowing more about the set of optimal solutions is thus necessary in many scenarios and can be formalized through enumeration
problems. 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 will
design and implement novel parameterized algorithms and kernels for enumeration problems, and build the lower-bound theory required to
separate problems between those that admit polynomial enumeration kernels and those that do not. The designed kernels will be some of the
earliest enumeration kernels, while the lower-bound theory will be a fundamental part of Parameterized Complexity, allowing researcher's to
identify problems that do not admit efficient preprocessing and focus their efforts on problems that do.
Unfold all
/
Fold all
More information & hyperlinks
| Web resources: | https://cordis.europa.eu/project/id/101109317 |
| Start date: | 01-09-2024 |
| End date: | 07-07-2026 |
| Total budget - Public funding: | - 140 797,00 Euro |
Cordis data
Original description
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 are
solved millions of times on a daily basis. Solving them would be unfeasible without the use of preprocessing techniques, which significantly reduce
running times and are often necessary to solve a problem. Explaining why these methods work in practice and designing new ones that come with
performance guarantees is a great challenge in Theoretical Computer Science. In the framework of Parameterized Complexity, they are modeled
through kernelization, which uses an additional measurement of the problem's structure (the parameter) to output a small equivalent instance that
can be quickly solved.
However, there will usually exist several optimal solutions, regardless of the optimality criterion, and drawing conclusions from a single one may be
misleading. Knowing more about the set of optimal solutions is thus necessary in many scenarios and can be formalized through enumeration
problems. 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 will
design and implement novel parameterized algorithms and kernels for enumeration problems, and build the lower-bound theory required to
separate problems between those that admit polynomial enumeration kernels and those that do not. The designed kernels will be some of the
earliest enumeration kernels, while the lower-bound theory will be a fundamental part of Parameterized Complexity, allowing researcher's to
identify problems that do not admit efficient preprocessing and focus their efforts on problems that do.
Status
SIGNEDCall topic
HORIZON-MSCA-2022-PF-01-01Update Date
31-07-2023
Images
No images available.
Geographical location(s)
