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Tree-width and path-width are well-known graph parameters. Many NP-hard graph problems allow polynomial-time solutions, when restricted to graphs of bounded tree-width or bounded path-width. In this work, we study the behavior of tree-width…
Retrieving targeted pathways in biological knowledge bases, particularly when incorporating wet-lab experimental data, remains a challenging task and often requires downstream analyses and specialized expertise. In this paper, we frame this…
With the increasing integration of robots into human life, their role in architectural spaces where people spend most of their time has become more prominent. While motion capabilities and accurate localization for automated robots have…
The Reeb graph of a scalar function defined on a domain gives a topologically meaningful summary of that domain. Reeb graphs have been shown in the past decade to be of great importance in geometric processing, image processing, computer…
Representations are crucial for a robot to learn effective navigation policies. Recent work has shown that mid-level perceptual abstractions, such as depth estimates or 2D semantic segmentation, lead to more effective policies when provided…
Scene graphs enhance 3D mapping capabilities in robotics by understanding the relationships between different spatial elements, such as rooms and objects. Recent research extends scene graphs to hierarchical layers, adding and leveraging…
We present an optimal partially-persistent external-memory search tree with amortized I/O bounds matching those achieved by the non-persistent $B^{\varepsilon}$-tree by Brodal and Fagerberg [SODA 2003]. In a partially-persistent data…
In spatially embedded networks such as transportation and power grids, understanding how edge removals affect connectivity is crucial for robustness analysis. This paper studies a planar graph dismantling problem under an edge-budget…
Many disciplines of science and engineering deal with problems related to compositions, ranging from chemical compositions in materials science to portfolio compositions in economics. They exist in non-Euclidean simplex spaces, causing many…
The treewidth is a structural parameter that measures the tree-likeness of a graph. Many algorithmic and combinatorial results are expressed in terms of the treewidth. In this paper, we study the treewidth of outer $k$-planar graphs, that…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
Deep declarative networks and other recent related works have shown how to differentiate the solution map of a (continuous) parametrized optimization problem, opening up the possibility of embedding mathematical optimization problems into…
We present a data structure that can maintain a simple planar graph under edge contractions in linear total time. The data structure supports adjacency queries and provides access to neighbor lists in $O(1)$ time. Moreover, it can report…
The capability of autonomous exploration in complex, unknown environments is important in many robotic applications. While recent research on autonomous exploration have achieved much progress, there are still limitations, e.g., existing…
As the sizes of graphs grow rapidly, currently many real-world graphs can hardly be loaded in the main memory. It becomes a hot topic to compute depth-first search (DFS) results, i.e., depth-first order or DFS-Tree, on semi-external memory…
This paper introduces a method to extract a hierarchical tree representation from 3D unorganized polygonal data. The proposed approach first extracts a graph representation of the surface, which serves as the foundation for structural…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
As data are increasingly modeled as graphs for expressing complex relationships, the tree pattern query on graph-structured data becomes an important type of queries in real-world applications. Most practical query languages, such as XQuery…
Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…
In the age of big data, sorting is an indispensable operation for DBMSes and similar systems. Having data sorted can help produce query plans with significantly lower run times. It also can provide other benefits like having non-blocking…