Related papers: Monotone comparative statics for submodular functi…

Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…

Compounding submodular monotone (i.e. 2-alternating) set functions on a finite set preserves this property, as shown in 2010. A natural generalization to k-alternating functions was presented in 2018, however hardly readable because of page…

We introduce a notion of substitutability for correspondences and establish a monotone comparative static result, unifying results such as the inverse isotonicity of M-matrices, Berry, Gandhi and Haile's identification of demand systems,…

We define a new class of set functions that in addition to being monotone and subadditive, also admit a very limited form of submodularity defined over a permutation of the ground set. We refer to this permutation as a submodular order.…

Recently MV18 identified and initiated work on the new problem of understanding structural relationships between the lattices of solutions of two "nearby" instances of stable matching. They also gave an application of their work to finding…

Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with…

Submodular functions are well-studied in combinatorial optimization, game theory and economics. The natural diminishing returns property makes them suitable for many applications. We study an extension of monotone submodular functions,…

We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…

In this article we introduce a new matroid invariant, a combinatorial analog of the topological zeta function of a polynomial. More specifically we associate to any ranked, atomic meet-semilattice L a rational function Z(L,s), in such a way…

Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal…

The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose…

Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary…

In this work, we study the problem of monotone non-submodular maximization with partition matroid constraint. Although a generalization of this problem has been studied in literature, our work focuses on leveraging properties of partition…

Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints,…

Streaming submodular maximization is a natural model for the task of selecting a representative subset from a large-scale dataset. If datapoints have sensitive attributes such as gender or race, it becomes important to enforce fairness to…

The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint…

We consider the problem of minimising functions represented as a difference of lattice submodular functions. We propose analogues to the SupSub, SubSup and ModMod routines for lattice submodular functions. We show that our…

Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…

In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…