Related papers: Hierarchical Overlap Graph
Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…
We study the top-k set similarity search problem using semantic overlap. While vanilla overlap requires exact matches between set elements, semantic overlap allows elements that are syntactically different but semantically related to…
This paper details a new algorithm to solve the shortest path problem in valued graphs. Its complexity is $O(D \log v)$ where $D$ is the graph diameter and $v$ its number of vertices. This complexity has to be compared to the one of the…
Many real-world data can be represented as heterogeneous graphs with different types of nodes and connections. Heterogeneous graph neural network model aims to embed nodes or subgraphs into low-dimensional vector space for various…
For a graph G with real weights assigned to the vertices (edges), the MAX H-SUBGRAPH problem is to find an H-subgraph of G with maximum total weight, if one exists. The all-pairs MAX H-SUBGRAPH problem is to find for every pair of vertices…
THIS IS A CORRECTED VERSION INCLUDING AN APPENDED CORRIGENDUM. Best match graphs arise naturally as the first processing intermediate in algorithms for orthology detection. Let $T$ be a phylogenetic (gene) tree $T$ and $\sigma$ an…
Hypergraph clustering is a basic algorithmic primitive for analyzing complex datasets and systems characterized by multiway interactions, such as group email conversations, groups of co-purchased retail products, and co-authorship data.…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
A $k$-matching cover of a graph $G$ is a union of $k$ matchings of $G$ which covers $V(G)$. A matching cover of $G$ is optimal if it consists of the fewest matchings of $G$. In this paper, we present an algorithm for finding an optimal…
The girth of a graph is the length of its shortest cycle. We give an algorithm that computes in O(n(log n)^3) time and O(n) space the (weighted) girth of an n-vertex planar digraph with arbitrary real edge weights. This is an improvement of…
Connectivity is a central notion of graph theory and plays an important role in graph algorithm design and applications. With emerging new applications in networks, a new type of graph connectivity problem has been getting more…
We define and study analogs of probabilistic tree embedding and tree cover for directed graphs. We define the notion of a DAG cover of a general directed graph $G$: a small collection $D_1,\dots D_g$ of DAGs so that for all pairs of…
Hierarchical abstractions are a methodology for solving large-scale graph problems in various disciplines. Coarsening is one such approach: it generates a pyramid of graphs whereby the one in the next level is a structural summary of the…
Given a graph of which the n vertices form a regular two-dimensional grid, and in which each (possibly weighted and/or directed) edge connects a vertex to one of its eight neighbours, the following can be done in O(scan(n)) I/Os, provided M…
We show that the shortest $s$-$t$ path problem has the overlap-gap property in (i) sparse $\mathbf{G}(n,p)$ graphs and (ii) complete graphs with i.i.d. Exponential edge weights. Furthermore, we demonstrate that in sparse $\mathbf{G}(n,p)$…
We present a data stream algorithm for estimating the size of the maximum matching of a low arboricity graph. Recall that a graph has arboricity $\alpha$ if its edges can be partitioned into at most $\alpha$ forests and that a planar graph…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
Standard Retrieval-Augmented Generation (RAG) relies on chunk-based retrieval, whereas GraphRAG advances this approach by graph-based knowledge representation. However, existing graph-based RAG approaches are constrained by binary…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
There exist many orthogonal graph drawing algorithms that minimize edge crossings or edge bends, however they produce unsatisfactory drawings in many practical cases. In this paper we present a grid-based algorithm for drawing orthogonal…