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In natural language processing (NLP), labeling on regions of text, such as words, sentences and paragraphs, is a basic task. In this paper, label is defined as map between mention of entity in a region on text and context of entity in a…

Computation and Language · Computer Science 2022-05-24 Takeshi Inagaki

We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross…

Data Structures and Algorithms · Computer Science 2017-09-20 David Eppstein , Siddharth Gupta

Label placement in maps is a very challenging task that is critical for the overall map quality. Most previous work focused on designing and implementing fully automatic solutions, but the resulting visual and aesthetic quality has not…

Computational Geometry · Computer Science 2019-10-22 Fabian Klute , Guangping Li , Raphael Löffler , Martin Nöllenburg , Manuela Schmidt

A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…

Computational Geometry · Computer Science 2012-03-28 Sergio Cabello , Bojan Mohar

Legible labels should not overlap with other labels and other marks in a chart. When a chart contains a large number of data points, manually positioning these labels for each data point in the chart is a tedious task. A labeling algorithm…

Graphics · Computer Science 2024-08-05 Chanwut Kittivorawong

The purpose of this note is to attach a name to a natural class of combinatorial problems and to point out that this class includes many important special cases. We also show that a simple problem of placing nonoverlapping labels on a…

Data Structures and Algorithms · Computer Science 2008-02-03 Donald E. Knuth , Arvind Raghunathan

In the Segment Intersection Graph Representation Problem, we want to represent the vertices of a graph as straight line segments in the plane such that two segments cross if and only if there is an edge between the corresponding vertices.…

Computational Geometry · Computer Science 2025-02-25 Simon D. Fink , Matthias Pfretzschner , Peter Stumpf

The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1…

Physics and Society · Physics 2011-08-25 Sang Hoon Lee , Petter Holme

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

Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…

Data Structures and Algorithms · Computer Science 2024-07-15 Erin Wolf Chambers , Elizabeth Munch , Sarah Percival , Xinyi Wang

A map graph is a graph admitting a representation in which vertices are nations on a spherical map and edges are shared curve segments or points between nations. We present an explicit fixed-parameter tractable algorithm for recognizing map…

Data Structures and Algorithms · Computer Science 2022-07-01 Patrizio Angelini , Michael A. Bekos , Giordano Da Lozzo , Martin Gronemann , Fabrizio Montecchiani , Alessandra Tappini

Boundary labeling is a well-known method for displaying short textual labels for a set of point features in a figure alongside the boundary of that figure. Labels and their corresponding points are connected via crossing-free leaders. We…

Computational Geometry · Computer Science 2024-09-06 Annika Bonerath , Martin Nöllenburg , Soeren Terziadis , Markus Wallinger , Jules Wulms

A map is an abstract visual representation of a region, taken from a given space, usually designed for final human consumption. Traditional cartography focuses on the mapping of Euclidean spaces by using some distance metric. In this paper…

Digital Libraries · Computer Science 2013-03-26 Valeria Fionda , Claudio Gutierrez , Giuseppe Pirró

Let $P$ and $Q$ be finite point sets of the same cardinality in $\mathbb{R}^2$, each labelled from $1$ to $n$. Two noncrossing geometric graphs $G_P$ and $G_Q$ spanning $P$ and $Q$, respectively, are called compatible if for every face $f$…

A map is a partition of the sphere into regions that are labeled as countries or holes. The vertices of a map graph are the countries of a map. There is an edge if and only if the countries are adjacent and meet in at least one point. For a…

Computational Geometry · Computer Science 2023-08-23 Franz J. Brandenburg

An important problem in multi-label classification is to capture label patterns or underlying structures that have an impact on such patterns. This paper addresses one such problem, namely how to exploit hierarchical structures over labels.…

Machine Learning · Computer Science 2015-04-17 Jinseok Nam , Johannes Fürnkranz

Let $\mathcal{A}$ be a set of positive numbers. A graph $G$ is called an $\mathcal{A}$-embeddable graph in $\mathbb{R}^d$ if the vertices of $G$ can be positioned in $\mathbb{R}^d$ so that the distance between endpoints of any edge is an…

Computational Complexity · Computer Science 2017-10-17 Mikhail Tikhomirov

A distance labeling scheme is an assignments of labels, that is binary strings, to all nodes of a graph, so that the distance between any two nodes can be computed from their labels and the labels are as short as possible. A major open…

Data Structures and Algorithms · Computer Science 2016-11-22 Paweł Gawrychowski , Przemysław Uznański

We present a novel approach to geolocalising panoramic images on a 2-D cartographic map based on learning a low dimensional embedded space, which allows a comparison between an image captured at a location and local neighbourhoods of the…

Computer Vision and Pattern Recognition · Computer Science 2020-07-22 Noe Samano , Mengjie Zhou , Andrew Calway

In this paper we focus on the map matching problem where the goal is to find a path through a planar graph such that the path through the vertices closely matches a given polygonal curve. The map matching problem is usually approached with…

Computational Geometry · Computer Science 2016-05-19 Tim Wylie , Binhai Zhu