Related papers: Seeded Graph Matching via Large Neighborhood Stati…
The network alignment problem asks for the best correspondence between two given graphs, so that the largest possible number of edges are matched. This problem appears in many scientific problems (like the study of protein-protein…
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…
The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability…
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Graph-based algorithms have demonstrated state-of-the-art performance in the nearest neighbor search (NN-Search) problem. These empirical successes urge the need for theoretical results that guarantee the search quality and efficiency of…
Graph sparsification is a technique that approximates a given graph by a sparse graph with a subset of vertices and/or edges. The goal of an effective sparsification algorithm is to maintain specific graph properties relevant to the…
In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…
Spectral graph sparsification aims to find ultra-sparse subgraphs whose Laplacian matrix can well approximate the original Laplacian eigenvalues and eigenvectors. In recent years, spectral sparsification techniques have been extensively…
We aim to learn a sparse and connected graph from sparse data, where the number of observations K can be substantially smaller than the signal dimension N for signals x in R^N, and the underlying distribution is unknown. In this severely…
Building on work of Cai, F\"urer, and Immerman \cite{CFI92}, we show two hardness results for the Graph Isomorphism problem. First, we show that there are pairs of nonisomorphic $n$-vertex graphs $G$ and $H$ such that any sum-of-squares…
We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures.…
We study the complexity of proving that a sparse random regular graph on an odd number of vertices does not have a perfect matching, and related problems involving each vertex being matched some pre-specified number of times. We show that…
We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing…
For every integer $g$, isomorphism of graphs of Euler genus at most $g$ can be decided in linear time. This improves previously known algorithms whose time complexity is $n^{O(g)}$ (shown in early 1980's), and in fact, this is the first…
We consider the problem of learning the nearest neighbor graph of a dataset of n items. The metric is unknown, but we can query an oracle to obtain a noisy estimate of the distance between any pair of items. This framework applies to…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…
We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant degree regular graphs. We show that for $r$-regular graphs with $n$ nodes and girth at least $g$, the…
We study recovering a 1D order from a noisy, locally sampled pairwise comparison matrix under a tight query budget. We recast the task as reconstructing a sparse, noisy line graph and present, to our knowledge, the first method that…
We consider the following two algorithmic problems: given a graph $G$ and a subgraph $H\subseteq G$, decide whether $H$ is an isometric or a geodesically convex subgraph of $G$. It is relatively easy to see that the problems can be solved…