Related papers: Monotone Submodular Multiway Partition
Streaming algorithms are generally judged by the quality of their solution, memory footprint, and computational complexity. In this paper, we study the problem of maximizing a monotone submodular function in the streaming setting with a…
We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. At one extreme, there is a trivial $2$-approximation for this problem that uses only $O(\log n)$ space, namely, count the number of…
The n-way number partitioning problem, a fundamental challenge in combinatorial optimization, has significant implications for applications such as fair division and machine scheduling. Despite these problems being NP-hard, many…
We consider the rank reduction problem for matroids: Given a matroid M and an integer k, find a minimum size subset of elements of M whose removal reduces the rank of M by at least k. When M is a graphical matroid this problem is the…
In hypergraphs, an edge that crosses a cut (i.e., a bipartition of nodes) can be split in several ways, depending on how many nodes are placed on each side of the cut. A cardinality-based splitting function assigns a nonnegative cost of…
Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less…
The two weighted graph problems Node Multiway Cut (NMC) and Subset Feedback Vertex Set (SFVS) both ask for a vertex set of minimum total weight, that for NMC disconnects a given set of terminals, and for SFVS intersects all cycles…
Let $V$ be a finite set of $n$ elements, $f: 2^V \rightarrow \mathbb{R}_+$ be a nonnegative monotone supermodular function, and $k$ be a positive integer no greater than $n$. This paper addresses the problem of maximizing $f(S)$ over all…
Exact subgraph matching is a fundamental graph operator that supports many graph analytics tasks, yet it remains computationally challenging due to its NP-completeness. Recent learning-based approaches accelerate query processing via…
We introduce and study the Doubly Balanced Connected graph Partitioning (DBCP) problem: Let $G=(V,E)$ be a connected graph with a weight (supply/demand) function $p:V\rightarrow \{-1,+1\}$ satisfying $p(V)=\sum_{j\in V} p(j)=0$. The…
Generally, a graph G, an independent set is a subset S of vertices in G such that no two vertices in S are adjacent (connected by an edge) and a vertex cover is a subset S of vertices such that each edge of G has at least one of its…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut…
We study the problem of maximizing a monotone submodular function subject to a matroid independence constraint. For more than a decade, a rich body of work has studied this problem. Initially, a tight approximation of $ (1-\frac{1}{e})$ was…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
We study the Requirement Cut problem, a generalization of numerous classical graph partitioning problems including Multicut, Multiway Cut, $k$-Cut, and Steiner Multicut among others. Given a graph with edge costs, terminal groups $(S_1,…
A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…
In this paper, we study the adaptive submodular cover problem under the worst-case setting. This problem generalizes many previously studied problems, namely, the pool-based active learning and the stochastic submodular set cover. The input…
Several large-scale machine learning tasks, such as data summarization, can be approached by maximizing functions that satisfy submodularity. These optimization problems often involve complex side constraints, imposed by the underlying…
In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…