The Power of Randomness and Continuity in Submodular Optimization

Informations projet

SUBMODULAR

N° de convention de subvention: 852780

DOI

10.3030/852780

Projet clôturé

Date de signature de la CE 8 Octobre 2019

Date de début 1 Novembre 2019

Date de fin 31 Octobre 2025

Financé au titre de

• EXCELLENT SCIENCE - European Research Council (ERC)

Coût total

€ 1 442 690,00

Contribution de l’UE

€ 1 442 690,00

Coordonné par

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Israel

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

Période du rapport: 2024-05-01 au 2025-10-31

Résumé du contexte et des objectifs généraux du projet

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.

Travail effectué depuis le début du projet jusqu’à la fin de la période considérée dans le rapport et principaux résultats atteints jusqu’à présent

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.

Progrès au-delà de l’état des connaissances et impact potentiel prévu (y compris l’impact socio-économique et les conséquences sociétales plus larges du projet jusqu’à présent)

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.

figure.jpg