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Given a simple polygon P in the plane, we present new algorithms and data structures for computing the weak visibility polygon from any query line segment in P. We build a data structure in O(n) time and O(n) space that can compute the…

Computational Geometry · Computer Science 2012-12-27 Danny Z. Chen , Haitao Wang

Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…

Graphics · Computer Science 2024-07-30 Peter Oliver , Eugene Zhang , Yue Zhang

In this paper, we characterize planar point sets that can be partitioned into disjoint polygons of arbitrarily specified sizes. We provide an algorithm to construct such a partition, if it exists, in polynomial time. We show that this…

Computational Geometry · Computer Science 2016-05-19 Ajit Arvind Diwan , Bodhayan Roy

Recovering high quality surfaces from noisy triangulated surfaces is a fundamental important problem in geometry processing. Sharp features including edges and corners can not be well preserved in most existing denoising methods except the…

Computational Geometry · Computer Science 2021-01-07 Zheng Liu , Rongjie Lai , Huayan Zhang , Chunlin Wu

We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider…

Data Structures and Algorithms · Computer Science 2014-12-15 Takehiro Ito , Hirotaka Ono , Yota Otachi

Most existing popular methods for learning graph embedding only consider fixed-order global structural features and lack structures hierarchical representation. To address this weakness, we propose a novel graph embedding algorithm named…

Machine Learning · Computer Science 2021-02-03 Xue Liu , Wei Wei , Xiangnan Feng , Xiaobo Cao , Dan Sun

We study a variant of a polygon partition problem, introduced by Chung, Iwama, Liao, and Ahn [ISAAC'25]. Given orthogonal unit vectors $\mathbf{u},\mathbf{v}\in \mathbb{R}^2$ and a polygon $P$ with $n$ vertices, we partition $P$ into…

Computational Geometry · Computer Science 2026-04-17 Jaehoon Chung

An ortho-polygon visibility representation of an $n$-vertex embedded graph $G$ (OPVR of $G$) is an embedding-preserving drawing of $G$ that maps every vertex to a distinct orthogonal polygon and each edge to a vertical or horizontal…

Computational Geometry · Computer Science 2017-05-17 Emilio Di Giacomo , Walter Didimo , William S. Evans , Giuseppe Liotta , Henk Meijer , Fabrizio Montecchiani , Stephen K. Wismath

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…

Data Structures and Algorithms · Computer Science 2015-02-19 Sampath Kannan , Claire Mathieu , Hang Zhou

A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was…

Discrete Mathematics · Computer Science 2017-04-04 Asahi Takaoka

In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…

General Mathematics · Mathematics 2011-10-21 Dhananjay P. Mehendale

Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…

Data Structures and Algorithms · Computer Science 2026-05-06 Arnaud Casteigts , Michelle Döring , Nils Morawietz

In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify…

Computational Geometry · Computer Science 2021-04-26 Ioannis Z. Emiris , Vissarion Fisikopoulos , Bernd Gärtner

Blind ptychography is a phase retrieval method using multiple coded diffraction patterns from different, overlapping parts of the unknown extended object illuminated with an unknown window function. The window function is also known as the…

Image and Video Processing · Electrical Eng. & Systems 2018-12-04 Albert Fannjiang

A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its…

Computational Geometry · Computer Science 2019-09-04 Therese Biedl , Giuseppe Liotta , Fabrizio Montecchiani

We give a quantum algorithm for a novel type of black-box problem: identifying a hidden $d$-regular base graph $G$ on $n$ vertices from oracle access to an obfuscated version of it, rather than traversing it. From $G$ we build the spired…

Quantum Physics · Physics 2026-05-13 Pawel Wocjan

The deck of a graph $G$ is the multiset of cards $\{G-v:v\in V(G)\}$. Myrvold (1992) showed that the degree sequence of a graph on $n\geq7$ vertices can be reconstructed from any deck missing one card. We prove that the degree sequence of a…

Combinatorics · Mathematics 2022-08-05 Carla Groenland , Tom Johnston , Andrey Kupavskii , Kitty Meeks , Alex Scott , Jane Tan

We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small tree-width, and applying dynamic…

Data Structures and Algorithms · Computer Science 2007-05-23 David Eppstein

Given a plane graph $G$ (i.e., a planar graph with a fixed planar embedding) and a simple cycle $C$ in $G$ whose vertices are mapped to a convex polygon, we consider the question whether this drawing can be extended to a planar…

Computational Geometry · Computer Science 2013-08-16 Tamara Mchedlidze , Martin Nöllenburg , Ignaz Rutter

We deal with the problem of reconstructing interfaces using complex geometrical optics solutions for the Maxwell system. The contributions are twofold. First, we justify the enclosure method for the impenetrable obstacle case avoiding any…

Analysis of PDEs · Mathematics 2013-10-25 Manas Kar , Mourad Sini