Related papers: Finding planted cliques using gradient descent
We present a parallel k-clique listing algorithm with improved work bounds (for the same depth) in sparse graphs with low degeneracy or arboricity. We achieve this by introducing and analyzing a new pruning criterion for a backtracking…
We study efficient algorithms for recovering cliques in dense random intersection graphs (RIGs). In this model, $d = n^{\Omega(1)}$ cliques of size approximately $k$ are randomly planted by choosing the vertices to participate in each…
We are given a graph $G$ with $n$ vertices, where a random subset of $k$ vertices has been made into a clique, and the remaining edges are chosen independently with probability $\tfrac12$. This random graph model is denoted…
In this paper, we study the Planted Clique problem in a semi-random model. Our model is inspired from the Feige-Kilian model [16] which has been studied in many other works [8,11,17,26,35,38] for a variety of graph problems. Our algorithm…
The planted clique problem is well-studied in the context of observing, explaining, and predicting interesting computational phenomena associated with statistical problems. When equating computational efficiency with the existence of…
We study computational limitations in \emph{multi-plant} average-case inference problems, in which $t$ disjoint planted structures of size $k$ are embedded in a random background on $n$ elements. A natural parameter in this setting is the…
Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size t is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best…
We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear…
We introduce a framework for proving lower bounds on computational problems over distributions against algorithms that can be implemented using access to a statistical query oracle. For such algorithms, access to the input distribution is…
We consider the problem of identifying the densest k-node subgraph in a given graph. We write this problem as an instance of rank-constrained cardinality minimization and then relax using the nuclear and 11 norms. Although the original…
This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a…
We consider the k-disjoint-clique problem. The input is an undirected graph G in which the nodes represent data items, and edges indicate a similarity between the corresponding items. The problem is to find within the graph k disjoint…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
We consider two closely related problems: planted clustering and submatrix localization. The planted clustering problem assumes that a random graph is generated based on some underlying clusters of the nodes; the task is to recover these…
In this paper, we study the problem of finding a collection of planted cycles in an \ER random graph $G \sim \mathcal{G}(n, \lambda/n)$, in analogy to the famous Planted Clique Problem. When the cycles are planted on a uniformly random…
In many high-dimensional problems, like sparse-PCA, planted clique, or clustering, the best known algorithms with polynomial time complexity fail to reach the statistical performance provably achievable by algorithms free of computational…
Consider an Erd\"os-Renyi random graph in which each edge is present independently with probability 1/2, except for a subset $\sC_N$ of the vertices that form a clique (a completely connected subgraph). We consider the problem of…
Over-parametrization was a crucial ingredient for recent developments in inference and machine-learning fields. However a good theory explaining this success is still lacking. In this paper we study a very simple case of mismatched…
While the reliable use of some NP-complete problem in tandem with the assumption that P is not equal to NP has eluded cryptographers due to lack of results showing average-case hardness, one alternative which has been explored is reliance…
This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be…