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Given an embedded planar acyclic digraph G, we define the problem of "acyclic hamiltonian path completion with crossing minimization (Acyclic-HPCCM)" to be the problem of determining an hamiltonian path completion set of edges such that,…
Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…
Dijkstra's algorithm is the standard method for computing shortest paths on arbitrary graphs. However, it is slow for large graphs, taking at least linear time. It has been long known that for real world road networks, creating a hierarchy…
This paper presents a hierarchical planning algorithm for racing with multiple opponents. The two-stage approach consists of a high-level behavioral planning step and a low-level optimization step. By combining discrete and continuous…
In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a "travel time" value, are…
The construction of online vectorized High-Definition (HD) maps is critical for downstream prediction and planning. Recent efforts have built strong baselines for this task, however, shapes and relations of instances in urban road systems…
Given multiple videos of the same task, procedure learning addresses identifying the key-steps and determining their order to perform the task. For this purpose, existing approaches use the signal generated from a pair of videos. This makes…
This paper addresses path set planning that yields important applications in robot manipulation and navigation such as path generation for deformable object keypoints and swarms. A path set refers to the collection of finite agent paths to…
The absence of the efficient methods for the design of the information sources impact network does not allow defining the influence of the information sources on one another accurately and detecting the primary sources of the information…
An Horizontal Visibility Graph (for short, HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between…
Stress models are a promising approach for graph drawing. They minimize the weighted sum of the squared errors of the Euclidean and desired distances for each node pair. The desired distance typically uses the graph-theoretic distances…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
Practical global path planning is critical for commercializing cleaning robots working in semi-structured environments. In the literature, global path planning methods for free space usually focus on path length and neglect the traffic rule…
This paper studies real-world road networks from an algorithmic perspective, focusing on empirical studies that yield useful properties of road networks that can be exploited in the design of fast algorithms that deal with geographic data.…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
$\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important problems defined on finite metric spaces, and provide efficient new algorithms and approximation schemes for these problems on inputs given as graph shortest path…
We study a multimodal journey planning scenario consisting of a public transit network and a transfer graph which represents a secondary transportation mode (e.g., walking, cycling, e-scooter). The objective is to compute Pareto-optimal…
How efficiently can we find an unknown graph using distance or shortest path queries between its vertices? Let $G = (V,E)$ be an unweighted, connected graph of bounded degree. The edge set $E$ is initially unknown, and the graph can be…
This paper proposes a geodesic-distance-based feature that encodes global information for improved video segmentation algorithms. The feature is a joint histogram of intensity and geodesic distances, where the geodesic distances are…
Geometric methods for solving open-world off-road navigation tasks, by learning occupancy and metric maps, provide good generalization but can be brittle in outdoor environments that violate their assumptions (e.g., tall grass).…