Related papers: Simple, Fast, and Scalable Reachability Oracle

Graph Transformers, leveraging the global attention to capture long-range dependencies in graph structures, have significantly advanced graph machine learning, but face prohibitive computational complexity. Tokenized Graph Learning Models…

Integrating human expertise into machine learning systems often reduces the role of experts to labeling oracles, a paradigm that limits the amount of information exchanged and fails to capture the nuances of human judgment. We address this…

Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…

The graph exploration problem is to visit all the nodes of a connected graph by a mobile entity, e.g., a robot. The robot has no a priori knowledge of the topology of the graph or of its size. Cohen et al. \cite{Ilcinkas08} introduced label…

Listing triangles is a fundamental graph problem with many applications, and large graphs require fast algorithms. Vertex ordering allows the orientation of edges from lower to higher vertex indices, and state-of-the-art triangle listing…

Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…

Algorithms for reinforcement learning (RL) in large state spaces crucially rely on supervised learning subroutines to estimate objects such as value functions or transition probabilities. Since only the simplest supervised learning problems…

The Hopf formula for Hamilton-Jacobi reachability (HJR) analysis has been proposed to solve high-dimensional differential games, producing the set of initial states and corresponding controller required to reach (or avoid) a target despite…

Dynamic networks are a complex subject. Not only do they inherit the complexity of static networks (as a particular case); they are also sensitive to definitional subtleties that are a frequent source of confusion and incomparability of…

We propose an algorithm for finding overlapping community structure in very large networks. The algorithm is based on the label propagation technique of Raghavan, Albert, and Kumara, but is able to detect communities that overlap. Like the…

The problem of finding a path between two points while avoiding obstacles is critical in robotic path planning. We focus on the feasibility problem: determining whether such a path exists. We model the robot as a query-specific rectangular…

Skip graphs are a novel distributed data structure, based on skip lists, that provide the full functionality of a balanced tree in a distributed system where resources are stored in separate nodes that may fail at any time. They are…

Existing Graph Neural Networks (GNNs) follow the message-passing mechanism that conducts information interaction among nodes iteratively. While considerable progress has been made, such node interaction paradigms still have the following…

Learning with noisy labels in multimedia classification often combines external annotations and model predictions into a single reliability weight, even though the two sources can fail for different reasons. We instead estimate disentangled…

Numerous tasks in program analysis and synthesis reduce to deciding reachability in possibly infinite graphs such as those induced by Petri nets. However, the Petri net reachability problem has recently been shown to require non-elementary…

In this note we describe an application of low-high orders in fault-tolerant network design. Baswana et al. [DISC 2015] study the following reachability problem. We are given a flow graph $G = (V, A)$ with start vertex $s$, and a spanning…

Hierarchical topological representations can significantly reduce search times within mapping and localization algorithms. Although recent research has shown the potential for such approaches, limited consideration has been given to the…

While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological…

This paper proposes methods for reachability analysis of nonlinear systems in both open loop and closed loop with advanced controllers. The methods combine hybrid zonotopes, a construct called a state-update set, functional decomposition,…

The reachability problem asks to decide if there exists a path from one vertex to another in a digraph. In a grid digraph, the vertices are the points of a two-dimensional square grid, and an edge can occur between a vertex and its…