相关论文: Improved Inapproximability For Submodular Maximiza…

Symmetric submodular functions are an important family of submodular functions capturing many interesting cases including cut functions of graphs and hypergraphs. Maximization of such functions subject to various constraints receives little…

We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a…

Submodular maximization under various constraints is a fundamental problem studied continuously, in both computer science and operations research, since the late $1970$'s. A central technique in this field is to approximately optimize the…

Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum…

We consider the problem of maximizing a nonnegative (possibly non-monotone) submodular set function with or without constraints. Feige et al. [FOCS'07] showed a 2/5-approximation for the unconstrained problem and also proved that no…

We study a combinatorial problem called Minimum Maximal Matching, where we are asked to find in a general graph the smallest that can not be extended. We show that this problem is hard to approximate with a constant smaller than 2, assuming…

In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature, on specialized…

We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique…

This paper presents a polynomial-time $1/2$-approximation algorithm for maximizing nonnegative $k$-submodular functions. This improves upon the previous $\max\{1/3, 1/(1+a)\}$-approximation by Ward and \v{Z}ivn\'y~(SODA'14), where…

In this work, we present a new algorithm for maximizing a non-monotone submodular function subject to a general constraint. Our algorithm finds an approximate fractional solution for maximizing the multilinear extension of the function over…

Monotone submodular maximization with a knapsack constraint is NP-hard. Various approximation algorithms have been devised to address this optimization problem. In this paper, we revisit the widely known modified greedy algorithm. First, we…

In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…

Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…

In this paper, the author puts forward a variation of Feige's Hypothesis, which claims that it is hard on average refuting Unbalanced Max 3-XOR under biased assignments on a natural distribution. Under this hypothesis, the author…

Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…

Non-monotone constrained submodular maximization plays a crucial role in various machine learning applications. However, existing algorithms often struggle with a trade-off between approximation guarantees and practical efficiency. The…

We consider the problem of maximizing a monotone submodular function subject to a knapsack constraint. Our main contribution is an algorithm that achieves a nearly-optimal, $1 - 1/e - \epsilon$ approximation, using…

A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function…

We study the problem of maximizing constrained non-monotone submodular functions and provide approximation algorithms that improve existing algorithms in terms of either the approximation factor or simplicity. Our algorithms combine…