Project description
Advanced algorithms to optimally resolve knapsack-type problems
The knapsack problem belongs to a class of mathematical problems famous for pushing the limits of computing. The EU-funded TIPEA project aims to resolve challenging integer programming problems related to a list of knapsack-type problems including the subset sum and the partition of numbers. Combining efficient algorithmic tools and studies on structural theory and conditional lower bounds will allow researchers to derive the best possible algorithms for these widespread computing problems. The new algorithms could also prove useful in the study of polynomial-time problems.
Objective
This project aims to resolve challenging integer programming problems in exact and approximate settings, with a focus on Knapsack-type problems (such as Subset Sum, Partition, and Knapsack). To this end, we will develop a unified approach of algorithm design as a combination of algorithmic tools, structural theory, and conditional lower bounds. Specific tasks include:
- utilizing recent advances in efficient algorithms, since although Knapsack-type algorithms are NP-hard their main challenges ask for polynomial improvements in running time,
- leveraging structural results from additive combinatorics for the design of algorithms for problems of additive nature, such as Knapsack-type problems, and
- using and expanding fine-grained complexity theory to explain the limits of algorithms by proving conditional lower bounds based on plausible conjectures.
In particular, our combination of modern algorithmic techniques and structural results on the one hand, and conditional lower bounds on the other hand, allows us to aim at best-possible algorithms (conditional on plausible conjectures). We also plan to transfer techniques in the other direction (from integer programming to efficient algorithms), by using the insights of practical integer programming solvers to obtain highly-efficient implementations for selected polynomial-time problems.
Designing best-possible algorithms for one of the Knapsack-type problems will already be groundbreaking, and complete resolution of our goals would be dramatic algorithmic progress with consequences in computer science, optimization, and operations research.
Fields of science
Programme(s)
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Funding Scheme
ERC-STG - Starting GrantHost institution
66123 Saarbrucken
Germany