Related papers: Recovery thresholds in the sparse planted matching…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
Threshold graphs are recursive deterministic network models that have been proposed for describing certain economic and social interactions. One drawback of this graph family is that it has limited generative attachment rules. To mitigate…
Graph matching aims to find the latent vertex correspondence between two edge-correlated graphs and has found numerous applications across different fields. In this paper, we study a seeded graph matching problem, which assumes that a set…
In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In…
In the field of signal processing, phase transition phenomena have recently attracted great attention. Donoho's work established the signal recovery threshold using indicators such as restricted isotropy (RIP) and incoherence and proved…
In recent years, unfolding iterative algorithms as neural networks has become an empirical success in solving sparse recovery problems. However, its theoretical understanding is still immature, which prevents us from fully utilizing the…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
Motivated by applications in domains such as social networks and computational biology, we study the problem of community recovery in graphs with locality. In this problem, pairwise noisy measurements of whether two nodes are in the same…
We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…
Many inference problems in structured prediction can be modeled as maximizing a score function on a space of labels, where graphs are a natural representation to decompose the total score into a sum of unary (nodes) and pairwise (edges)…
Using edge weights is essential for modeling real-world systems where links possess relevant information, and preserving this information in low-dimensional representations is relevant for classification and prediction tasks. This paper…
The decision problem of perfect matchings in uniform hypergraphs is famously an NP-complete problem. It has been shown by Keevash--Knox--Mycroft [STOC, 2013] that for every $\varepsilon>0$, such decision problem restricted to $k$-uniform…
The planted densest subgraph detection problem refers to the task of testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on $n$ vertices. Under…
The goal of phase-only compressed sensing is to recover a structured signal $\mathbf{x}$ from the phases $\mathbf{z} = {\rm sign}(\mathbf{\Phi}\mathbf{x})$ under some complex-valued sensing matrix $\mathbf{\Phi}$. Exact reconstruction of…
In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
This paper introduces the \emph{$d$-distance matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges and an integer $d\in\mathbb Z_+$. The goal is to find a maximum…
The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…
We give a quasipolynomial time algorithm for the graph matching problem (also known as noisy or robust graph isomorphism) on correlated random graphs. Specifically, for every $\gamma>0$, we give a $n^{O(\log n)}$ time algorithm that given a…
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…