English
Related papers

Related papers: On Embeddability of Buses in Point Sets

200 papers

An effective way to reduce clutter in a graph drawing that has (many) crossings is to group edges that travel in parallel into \emph{bundles}. Each edge can participate in many such bundles. Any crossing in this bundled graph occurs between…

Computational Geometry · Computer Science 2022-09-23 Steven Chaplick , Thomas C. van Dijk , Myroslav Kryven , Ji-won Park , Alexander Ravsky , Alexander Wolff

The line coverage problem involves finding efficient routes for the coverage of linear features by one or more resource-constrained robots. Linear features model environments like road networks, power lines, and oil and gas pipelines. Two…

Robotics · Computer Science 2024-01-02 Saurav Agarwal , Srinivas Akella

Determining whether two STRIPS planning instances are isomorphic is the simplest form of comparison between planning instances. It is also a particular case of the problem concerned with finding an isomorphism between a planning instance…

Artificial Intelligence · Computer Science 2024-06-25 Arnaud Lequen , Martin C. Cooper , Frédéric Maris

This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…

Combinatorics · Mathematics 2007-05-23 Sostenes Lins

The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a…

Data Structures and Algorithms · Computer Science 2024-04-10 Stefano Ardizzoni , Luca Consolini , Mattia Laurini , Marco Locatelli

We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…

Discrete Mathematics · Computer Science 2012-11-06 Ajit Diwan , Soumitra Pal , Abhiram Ranade

Abstract. The Set Intersection Problem (SIP) is the problem of finding a point in the intersection of convex sets. This problem is typically solved by the method of alternating projections. To accelerate the convergence, the idea of using…

Optimization and Control · Mathematics 2015-02-17 C. H. Jeffrey Pang

We introduce the $k$-Plane Insertion into Plane drawing ($k$-PIP) problem: given a plane drawing of a planar graph $G$ and a set $F$ of edges, insert the edges in $F$ into the drawing such that the resulting drawing is $k$-plane. In this…

Computational Geometry · Computer Science 2024-09-09 Julia Katheder , Philipp Kindermann , Fabian Klute , Irene Parada , Ignaz Rutter

The problem of computing induced subgraphs that satisfy some specified restrictions arises in various applications of graph algorithms and has been well studied. In this paper, we consider the following Balanced Connected Subgraph (shortly,…

Discrete Mathematics · Computer Science 2018-09-25 Sujoy Bhore , Sourav Chakraborty , Satyabrata Jana , Joseph S. B. Mitchell , Supantha Pandit , Sasanka Roy

We investigate an algebraic problem related to the determination of the fundamental group of a class of spaces of configurations on surfaces. The configuration spaces are spaces of points grouped into colors. Whether two points are allowed…

Algebraic Topology · Mathematics 2017-11-15 Marcel Bökstedt

Given a set R of red points and a set B of blue points in the plane, the Red-Blue point separation problem asks if there are at most k lines that separate R from B, that is, each cell induced by the lines of the solution is either empty or…

Data Structures and Algorithms · Computer Science 2020-05-14 Neeldhara Misra , Harshil Mittal , Aditi Sethia

In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…

Machine Learning · Statistics 2021-12-07 Vladimir Kostic , Saverio Salzo , Massimilano Pontil

In this paper we consider a colouring version of the general position problem. The \emph{$\gp $-chromatic number} is the smallest number of colours needed to colour the vertices of the graph such that each colour class has the…

Combinatorics · Mathematics 2025-09-11 Ullas Chandran S. V. , Gabriele Di Stefano , Haritha S. , Elias John Thomas , James Tuite

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

This study examines the computational complexity of the decision problem modeled on the smartphone game Bus Out. The objective of the game is to load all the passengers in a queue onto appropriate buses using a limited number of bus parking…

Computational Complexity · Computer Science 2025-05-15 Takehiro Ishibashi , Ryo Yoshinaka , Ayumi Shinohara

This paper focuses on exact approaches for the Colored Bin Packing Problem (CBPP), a generalization of the classical one-dimensional Bin Packing Problem in which each item has, in addition to its length, a color, and no two items of the…

Optimization and Control · Mathematics 2023-05-25 Yulle G. F. Borges , Rafael C. S. Schouery , Flávio K. Miyazawa

We present a centralized algorithm for labeled, disk-shaped Multi-Robot Path Planning (MPP) in a continuous planar workspace with polygonal boundaries. Our method automatically transform the continuous problem into a discrete, graph-based…

Robotics · Computer Science 2022-07-20 Liang He , Zherong Pan , Kiril Solovey , Biao Jia , Dinesh Manocha

The embedding-based representation learning is commonly used in deep learning recommendation models to map the raw sparse features to dense vectors. The traditional embedding manner that assigns a uniform size to all features has two…

Machine Learning · Computer Science 2021-03-12 Siyi Liu , Chen Gao , Yihong Chen , Depeng Jin , Yong Li

The C-Planarity problem asks for a drawing of a $\textit{clustered graph}$, i.e., a graph whose vertices belong to properly nested clusters, in which each cluster is represented by a simple closed region with no edge-edge crossings, no…

Data Structures and Algorithms · Computer Science 2018-03-16 Giordano Da Lozzo , David Eppstein , Michael T. Goodrich , Siddharth Gupta

Let $S$ be a point set in the plane such that each of its elements is colored either red or blue. A matching of $S$ with rectangles is any set of pairwise-disjoint axis-aligned rectangles such that each rectangle contains exactly two points…

Computational Geometry · Computer Science 2014-01-06 L. E. Caraballo , C. Ochoa , P. Pérez-Lantero , J. Rojas-Ledesma