Related papers: Finding Planted Cycles in a Random Graph
We study the planted clique problem in which a clique of size k is planted in an Erdos-Renyi graph G(n,1/2) and one is interested in recovering this planted clique. It is widely believed that it exhibits a statistical-computational gap when…
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…
We investigate the problem of identifying planted cliques in random geometric graphs, focusing on two distinct algorithmic approaches: the first based on vertex degrees (VD) and the other on common neighbors (CN). We analyze the performance…
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…
We study the planted clique problem in which a clique of size k is planted in an Erd\H{o}s-R\'enyi graph G(n, 1/2), and one is interested in either detecting or recovering this planted clique. This problem is interesting because it is…
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 give a polynomial-time algorithm that finds a planted clique of size $k \ge \sqrt{n \log n}$ in the semirandom model, improving the state-of-the-art $\sqrt{n} (\log n)^2$ bound. This $\textit{semirandom planted clique problem}$ concerns…
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…
Suppose a graph $G$ is stochastically created by uniformly sampling vertices along a line segment and connecting each pair of vertices with a probability that is a known decreasing function of their distance. We ask if it is possible to…
In the planted partition problem, the $n$ vertices of a random graph are partitioned into $k$ "clusters," and edges between vertices in the same cluster and different clusters are included with constant probability $p$ and $q$, respectively…
We study a planted clique model introduced by Feige where a complete graph of size $c\cdot n$ is planted uniformly at random in an arbitrary $n$-vertex graph. We give a simple deterministic algorithm that, in almost linear time, recovers a…
Hypergraph data are often projected onto a weighted graph by constructing an adjacency matrix whose $(i,j)$ entry counts the number of hyperedges containing both nodes $i$ and $j$. This reduction is computationally convenient, but it can…
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…
We study graph matching between two correlated networks in the almost fully seeded regime, where all but a vanishing fraction of vertex correspondences are revealed. Concretely, we consider the correlated stochastic block model and assume…
We design new polynomial-time algorithms for recovering planted cliques in the semi-random graph model introduced by Feige and Kilian 2001. The previous best algorithms for this model succeed if the planted clique has size at least…
We consider a variant of the planted clique problem where we are allowed unbounded computational time but can only investigate a small part of the graph by adaptive edge queries. We determine (up to logarithmic factors) the number of…
We study the problem of efficiently recovering the matching between an unlabelled collection of $n$ points in $\mathbb{R}^d$ and a small random perturbation of those points. We consider a model where the initial points are i.i.d. standard…
The problem of finding large cliques in random graphs and its "planted" variant, where one wants to recover a clique of size $\omega \gg \log{(n)}$ added to an \Erdos-\Renyi graph $G \sim G(n,\frac{1}{2})$, have been intensely studied.…
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…
We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices, so as to minimize the maximum stretch of any edge, subject to the constraint that the…