Related papers: Finding planted cliques using gradient descent
This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
We study the computational complexity of two related problems: recovering a planted $q$-coloring in $G(n,1/2)$, and finding efficiently verifiable witnesses of non-$q$-colorability (a.k.a. refutations) in $G(n,1/2)$. Our main results show…
Planted dense cycles are a type of latent structure that appears in many applications, such as small-world networks in social sciences and sequence assembly in computational biology. We consider a model where a dense cycle with expected…
In this article we use the modular decomposition technique for exact solving the weighted maximum clique problem. Our algorithm takes the modular decomposition tree from the paper of Tedder et. al. and finds solution recursively. Also, we…
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
Researchers currently use a number of approaches to predict and substantiate information-computation gaps in high-dimensional statistical estimation problems. A prominent approach is to characterize the limits of restricted models of…
We study finding and listing $k$-cliques in a graph, for constant $k\geq 3$, a fundamental problem of both theoretical and practical importance. Our main contribution is a new output-sensitive algorithm for listing $k$-cliques in graphs,…
In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or,…
In this paper, we study the problems of detection and recovery of hidden submatrices with elevated means inside a large Gaussian random matrix. We consider two different structures for the planted submatrices. In the first model, the…
Clique partitioning is a fundamental network clustering task, with applications in a wide range of computational sciences. It involves identifying an optimal partition of the nodes for a real-valued weighted graph according to the edge…
Listing dense subgraphs in large graphs plays a key task in varieties of network analysis applications like community detection. Clique, as the densest model, has been widely investigated. However, in practice, communities rarely form as…
We give a lower bound of $\tilde{\Omega}(\sqrt{n})$ for the degree-4 Sum-of-Squares SDP relaxation for the planted clique problem. Specifically, we show that on an Erd\"os-R\'enyi graph $G(n,\tfrac{1}{2})$, with high probability there is a…
The problem of finding the largest induced balanced bipartite subgraph in a given graph is NP-hard. This problem is closely related to the problem of finding the smallest Odd Cycle Transversal. In this work, we consider the following model…
Many natural computational problems, including e.g. Max Weight Independent Set, Feedback Vertex Set, or Vertex Planarization, can be unified under an umbrella of finding the largest sparse induced subgraph, that satisfies some property…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
Finding cliques in a graph has several applications for its pattern matching ability. $k$-clique problem, a special case of clique problem, determines whether an arbitrary graph contains a clique of size $k$, has already been addressed in…
The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…
Finding large cliques or cliques missing a few edges is a fundamental algorithmic task in the study of real-world graphs, with applications in community detection, pattern recognition, and clustering. A number of effective…
We consider the task of detecting a hidden bipartite subgraph in a given random graph. This is formulated as a hypothesis testing problem, under the null hypothesis, the graph is a realization of an Erd\H{o}s-R\'{e}nyi random graph over $n$…