Related papers: Supermodular Maximization with Cardinality Constra…
We study the complexity of the maximum coverage problem, restricted to set systems of bounded VC-dimension. Our main result is a fixed-parameter tractable approximation scheme: an algorithm that outputs a $(1-\eps)$-approximation to the…
We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum…
Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large…
We consider the problem of maximizing a non-negative submodular function under the $b$-matching constraint, in the semi-streaming model. When the function is linear, monotone, and non-monotone, we obtain the approximation ratios of…
We study a clustering problem where the goal is to maximize the coverage of the input points by $k$ chosen centers. Specifically, given a set of $n$ points $P \subseteq \mathbb{R}^d$, the goal is to pick $k$ centers $C \subseteq…
Maximization of {\it non-submodular} functions appears in various scenarios, and many previous works studied it based on some measures that quantify the closeness to being submodular. On the other hand, many practical non-submodular…
Given a graph $G=(V,E)$ and an integer $k$, the Minimum Membership Dominating Set (MMDS) problem seeks to find a dominating set $S \subseteq V$ of $G$ such that for each $v \in V$, $|N[v] \cap S|$ is at most $k$. We investigate the…
Let $(L; \sqcap, \sqcup)$ be a finite lattice and let $n$ be a positive integer. A function $f : L^n \to \mathbb{R}$ is said to be submodular if $f(\tup{a} \sqcap \tup{b}) + f(\tup{a} \sqcup \tup{b}) \leq f(\tup{a}) + f(\tup{b})$ for all…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
We revisit the classic Maximum $k$-Coverage problem: Determine the largest number $t$ of elements that can be covered by choosing $k$ sets from a given family $\mathcal{F} = \{S_1,\dots, S_n\}$ of a size-$u$ universe. A notable special case…
We study the maximum cardinality matching problem in a standard distributed setting, where the nodes $V$ of a given $n$-node network graph $G=(V,E)$ communicate over the edges $E$ in synchronous rounds. More specifically, we consider the…
We consider the Hypergraph-$k$-cut problem. The input consists of a hypergraph $G=(V,E)$ with non-negative hyperedge-costs $c: E\rightarrow R_+$ and a positive integer $k$. The objective is to find a least-cost subset $F\subseteq E$ such…
We study the problem of differentially private constrained maximization of decomposable submodular functions. A submodular function is decomposable if it takes the form of a sum of submodular functions. The special case of maximizing a…
In this paper, we propose a randomized $\tilde{O}(\mu(G))$-round algorithm for the maximum cardinality matching problem in the CONGEST model, where $\mu(G)$ means the maximum size of a matching of the input graph $G$. The proposed algorithm…
Motivated by practical applications, recent works have considered maximization of sums of a submodular function $g$ and a linear function $\ell$. Almost all such works, to date, studied only the special case of this problem in which $g$ is…
We study algorithms for construction of composable coresets for the task of Determinant Maximization under partition constraint. Given a point set $V\subset \mathbb{R}^d$ that is partitioned into $s$ groups $V_1,\cdots, V_s$, and integers…
We study the problem of maximizing a monotone submodular function subject to a matroid constraint, and present for it a deterministic non-oblivious local search algorithm that has an approximation guarantee of $1 - 1/e - \varepsilon$ (for…
The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…
We investigate the performance of a deterministic GREEDY algorithm for the problem of maximizing functions under a partition matroid constraint. We consider non-monotone submodular functions and monotone subadditive functions. Even though…
We study the problem of ranking with submodular valuations. An instance of this problem consists of a ground set $[m]$, and a collection of $n$ monotone submodular set functions $f^1, \ldots, f^n$, where each $f^i: 2^{[m]} \to R_+$. An…