The Power of Randomness and Continuity in Submodular Optimization

Project Information

SUBMODULAR

Grant agreement ID: 852780

DOI

10.3030/852780

Project closed

EC signature date 8 October 2019

Start date 1 November 2019

End date 31 October 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 442 690,00

EU contribution

€ 1 442 690,00

Coordinated by

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Israel

Periodic Reporting for period 4 - SUBMODULAR (The Power of Randomness and Continuity in Submodular Optimization)

Reporting period: 2024-05-01 to 2025-10-31

Summary of the context and overall objectives of the project

This research project deals with the theoretical foundations of submodular maximization in particular and submodular optimization in general.
Submodular optimization affects many aspects of our daily lives, and has found applications ranging from pollution detection, the spread of influence in social networks, and even reduction of gang violence.
Thus, it is no surprise that optimization problems with a submodular objective have been the focus of intense theoretical and practical research for more than a decade.
The overarching goal of this research is to enrich the algorithmic toolkit and devise new algorithmic approaches that can be broadly applied to fundamental problems in submodular and combinatorial optimization.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The study of new methods for designing and analyzing combinatorial algorithms for submodular maximization problems, as well as continuous and randomized methods for submodular maximization, have been performed.
Two examples includes the maximization of a submodular function given a knapsack constraint (a classic optimization problem which has found numerous practical applications throughout the years) and the use of a Poisson process for submodular maximization over a matroid independence constraint.
Moreover, problems relating to submodularity and other ascepts, e.g. fault tolerance and clustering, ordering, resource allocation, online, and other computational settings have also been studied.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

We plan to study how randomness and continuous approaches can be used for submodular maximization and more broadly applied to fundamental problems in combinatorial optimization.
The ultimate goal is to present such new algorithmic approaches that will enable us to resolve basic problems in the area and provide new algorithmic foundations to submodular optimization.

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