Related papers: Graph-based time-space trade-offs for approximate …
We present an additive $\varepsilon n^{2}$-approximation algorithm for the Graph Edit Distance problem (GED) on graphs of VC dimension $d$ running in time $n^{O(d/\varepsilon^{2})}$. In particular, this recovers a previous result by Arora,…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
We consider the problem of searching for an unknown target vertex $t$ in a (possibly edge-weighted) graph. Each \emph{vertex-query} points to a vertex $v$ and the response either admits $v$ is the target or provides any neighbor $s\not=v$…
A distance-approximation algorithm for a graph property $\mathcal{P}$ in the adjacency-matrix model is given an approximation parameter $\epsilon \in (0,1)$ and query access to the adjacency matrix of a graph $G=(V,E)$. It is required to…
Temporal graphs are graphs where the edge set can change in each time step, and the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been…
Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Approximate nearest neighbor (ANN) search in high-dimensional metric spaces is a fundamental problem with many applications. Over the past decade, proximity graph (PG)-based indexes have demonstrated superior empirical performance over…
The greedy and nearest-neighbor TSP heuristics can both have $\log n$ approximation factors from optimal in worst case, even just for $n$ points in Euclidean space. In this note, we show that this approximation factor is only realized when…
We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional…
We provide new tradeoffs between approximation and running time for the decremental all-pairs shortest paths (APSP) problem. For undirected graphs with $m$ edges and $n$ nodes undergoing edge deletions, we provide four new approximate…
Some of the most fundamental and well-studied graph parameters are the Diameter (the largest shortest paths distance) and Radius (the smallest distance for which a "center" node can reach all other nodes). The natural and important…
Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…
Graph representation learning has drawn increasing attention in recent years, especially for learning the low dimensional embedding at both node and graph level for classification and recommendations tasks. To enable learning the…
We consider the problem of graph searching with prediction recently introduced by Banerjee et al. (2022). In this problem, an agent, starting at some vertex $r$ has to traverse a (potentially unknown) graph $G$ to find a hidden goal node…
We present a new data structure for the c-approximate near neighbor problem (ANN) in the Euclidean space. For n points in R^d, our algorithm achieves O(n^{\rho} + d log n) query time and O(n^{1 + \rho} + d log n) space, where \rho <=…
We provide an efficient reduction from the problem of querying approximate multiplicatively weighted farthest neighbors in a metric space to the unweighted problem. Combining our techniques with core-sets for approximate unweighted farthest…
In this article we prove that the minimum-degree greedy algorithm, with adversarial tie-breaking, is a $(2/3)$-approximation for the Maximum Independent Set problem on interval graphs. We show that this is tight, even on unit interval…
Neighborhood finders and nearest neighbor queries are fundamental parts of sampling based motion planning algorithms. Using different distance metrics or otherwise changing the definition of a neighborhood produces different algorithms with…
We present a framework for similarity search based on Locality-Sensitive Filtering (LSF), generalizing the Indyk-Motwani (STOC 1998) Locality-Sensitive Hashing (LSH) framework to support space-time tradeoffs. Given a family of filters,…