Related papers: Verifying Graph Algorithms in Separation Logic: A …
Simultaneous localization and mapping (SLAM) is a critical capability in autonomous navigation, but memory and computational limits make long-term application of common SLAM techniques impractical; a robot must be able to determine what…
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…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
This paper presents GraphFederator, a novel approach to construct joint representations of multi-party graphs and supports privacy-preserving visual analysis of graphs. Inspired by the concept of federated learning, we reformulate the…
A graph is called $P_t$-free} if it does not contain a $t$-vertex path as an induced subgraph. While $P_4$-free graphs are exactly cographs, the structure of $P_t$-free graphs for $t \geq 5$ remains little understood. On one hand, classic…
The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…
In these lecture notes, we first recall the connection between graph neural networks, Weisfeiler-Lehman tests and logics such as first-order logic and graded modal logic. We then present a modal logic in which counting modalities appear in…
In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability.…
One exact and two heuristic algorithms for determining the generators, orbits and order of the graph automorphism group are presented. A basic tool of these algorithms is the well-known individualization and refinement procedure. A search…
Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…
Most automated program verifiers for separation logic use either symbolic execution or verification condition generation to extract proof obligations, which are then handed over to an SMT solver. Existing verification algorithms are…
Graph partition is a fundamental problem of parallel computing for big graph data. Many graph partition algorithms have been proposed to solve the problem in various applications, such as matrix computations and PageRank, etc., but none has…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…
For fixed integers $r,\ell \geq 0$, a graph $G$ is called an {\em $(r,\ell)$-graph} if the vertex set $V(G)$ can be partitioned into $r$ independent sets and $\ell$ cliques. This brings us to the following natural parameterized questions:…
Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance…
In this paper, we demonstrate that considering experiments in a graph-theoretic manner allows us to exploit automorphisms of the graph to reduce the number of evaluations of candidate designs for those experiments, and thus find optimal…
Graph Transformers (GTs) have made remarkable achievements in graph-level tasks. However, most existing works regard graph structures as a form of guidance or bias for enhancing node representations, which focuses on node-central…
Our starting point is the observation that if graphs in a class C have low descriptive complexity in first order logic, then the isomorphism problem for C is solvable by a fast parallel algorithm (essentially, by a simple combinatorial…