相关论文: On the Paley RIP and Paley graph extractor

A classical branch of graph algorithms is graph transversals, where one seeks a minimum-weight subset of nodes in a node-weighted graph $G$ which intersects all copies of subgraphs~$F$ from a fixed family $\mathcal F$. Many such graph…

We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and…

Given a matrix $A$ with $n$ rows, a number $k<n$, and $0<\delta < 1$, $A$ is $(k,\delta)$-RIP (Restricted Isometry Property) if, for any vector $x \in \mathbb{R}^n$, with at most $k$ non-zero co-ordinates, $$(1-\delta) \|x\|_2 \leq \|A…

Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and…

We introduce a simple yet effective sampling-based planner that is tailored for bottleneck pathfinding: Given an implicitly-defined cost map $\mathcal{M}:\mathbb{R}^d\rightarrow \mathbb{R}$, which assigns to every point in space a real…

Restricted isometry property (RIP), essentially stating that the linear measurements are approximately norm-preserving, plays a crucial role in studying low-rank matrix recovery problem. However, RIP fails in the robust setting, when a…

Knowledge graph (KG) embedding methods which map entities and relations to unique embeddings in the KG have shown promising results on many reasoning tasks. However, the same embedding dimension for both dense entities and sparse entities…

Subgraph isomorphism is a fundamental problem in graph analysis that seeks to find all instances of a pattern graph within a larger data graph while preserving structural relationships. This NP-complete problem is central to domains such as…

We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the…

Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…

Graph Representation Learning (GRL) methods opened new avenues for addressing complex, real-world problems represented by graphs. However, many graphs used in these applications comprise millions of nodes and billions of edges and are…

Given an unknown $n \times n$ matrix $A$ having non-negative entries, the \emph{inner product} (IP) oracle takes as inputs a specified row (or a column) of $A$ and a vector $v \in \mathbb{R}^{n}$, and returns their inner product. A…

A recent trend in parameterized algorithms is the application of polytope tools (specifically, LP-branching) to FPT algorithms (e.g., Cygan et al., 2011; Narayanaswamy et al., 2012). However, although interesting results have been achieved,…

The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…

Graph-based retrieval-augmented generation (GraphRAG) exploits structured knowledge to support knowledge-intensive reasoning. However, most existing methods treat graphs as intermediate artifacts, and the few subgraph-based retrieval…

Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…

Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open…

A path system $\mathcal{P}$ in a graph $G=(V,E)$ is said to be irreducible if there does not exist a partition $V= A\sqcup B$ such that $\mathcal{P}$ restricts to a path system on both $G[A]$ and $G[B]$. In this paper, we construct an…

Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…

We study a generalization of the classic Global Min-Cut problem, called Global Label Min-Cut (or sometimes Global Hedge Min-Cut): the edges of the input (multi)graph are labeled (or partitioned into color classes or hedges), and removing…