Related papers: The Densest SWAMP problem: subhypergraphs with arb…
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on…
We consider a general decomposable convex optimization problem. By using right-hand side allocation technique, it can be transformed into a collection of small dimensional optimization problems. The master problem is a convex non-smooth…
This paper introduces the Simultaneous assignment problem. Let us given a graph with a weight and a capacity function on its edges, and a set of its subgraphs along with a degree upper bound function for each of them. We are also given a…
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…
Boob et al. [1] described an iterative peeling algorithm called Greedy++ for the Densest Subgraph Problem (DSG) and conjectured that it converges to an optimum solution. Chekuri, Quanrud, and Torres [2] extended the algorithm to general…
Finding the densest subgraph (DS) from a graph is a fundamental problem in graph databases. The DS obtained, which reveals closely related entities, has been found to be useful in various application domains such as e-commerce, social…
We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a…
With the introduction of the graph-theoretic time-inconsistent planning model due to Kleinberg and Oren, it has been possible to investigate the computational complexity of how a task designer best can support a present-biased agent in…
Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…
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 consider the problem of finding a subgraph of a given graph which maximizes a given function evaluated at its degree sequence. While the problem is intractable already for convex functions, we show that it can be solved in polynomial…
In this paper we derive a moment relaxation for large-scale nonsmooth optimization problems with graphical structure and spherical constraints. In contrast to classical moment relaxations for global polynomial optimization that suffer from…
The problem of finding the maximum-weight, planar subgraph of a finite, simple graph with nonnegative real edge weights is well known in industrial and electrical engineering, systems biology, sociology and finance. As the problem is known…
Densest subgraph discovery (DSD) is a fundamental problem in graph mining. It has been studied for decades, and is widely used in various areas, including network science, biological analysis, and graph databases. Given a graph G, DSD aims…
We give the first quasipolynomial upper bound $\phi n^{\text{polylog}(n)}$ for the smoothed complexity of the SWAP algorithm for local Graph Partitioning (also known as Bisection Width), where $n$ is the number of nodes in the graph and…
We consider the problem of maximizing submodular functions; while this problem is known to be NP-hard, several numerically efficient local search techniques with approximation guarantees are available. In this paper, we propose a novel…
We study the densest subgraph problem and give algorithms via multiplicative weights update and area convexity that converge in $O\left(\frac{\log m}{\epsilon^{2}}\right)$ and $O\left(\frac{\log m}{\epsilon}\right)$ iterations,…
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…
We consider the problem of inferring a matching hidden in a weighted random $k$-hypergraph. We assume that the hyperedges' weights are random and distributed according to two different densities conditioning on the fact that they belong to…
We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set…