The Power of Randomness and Continuity in Submodular Optimization

Projektinformationen

SUBMODULAR

ID Finanzhilfevereinbarung: 852780

DOI

10.3030/852780

Projekt abgeschlossen

EK-Unterschriftsdatum 8 Oktober 2019

Startdatum 1 November 2019

Enddatum 31 Oktober 2025

Finanziert unter

• EXCELLENT SCIENCE - European Research Council (ERC)

Gesamtkosten

€ 1 442 690,00

EU-Beitrag

€ 1 442 690,00

Koordiniert durch

TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY
Israel

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

Berichtszeitraum: 2024-05-01 bis 2025-10-31

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

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.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

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.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

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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