Periodic Reporting for period 4 - SUBMODULAR (The Power of Randomness and Continuity in Submodular Optimization)
Reporting period: 2024-05-01 to 2025-10-31
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.
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.
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.
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.
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.
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.