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This article introduces recursive relations allowing the calculation of the number of partitions with constraints on the minimum and/or on the maximum fragment size.

Nuclear Theory · Physics 2009-11-07 Pierre Desesquelles

In this paper, we describe geometrical constructions to obtain triangulations of connected sums of closed orientable triangulated 3-manifolds. Using these constructions, we show that it takes time polynomial in the number of tetrahedra to…

Geometric Topology · Mathematics 2009-09-29 Alexander Barchechat

Problems related to projections on closed convex cones are frequently encountered in optimization theory and related fields. To study these problems, various unifying ideas have been introduced, including asymmetric vector-valued norms and…

Optimization and Control · Mathematics 2022-04-11 Jani Jokela

A constant-workspace algorithm has read-only access to an input array and may use only O(1) additional words of $O(\log n)$ bits, where $n$ is the size of the input. We assume that a simple $n$-gon is given by the ordered sequence of its…

Computational Geometry · Computer Science 2013-06-14 Tetsuo Asano , Kevin Buchin , Maike Buchin , Matias Korman , Wolfgang Mulzer , Günter Rote , André Schulz

Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…

Soft Condensed Matter · Physics 2026-02-13 P. D. S. de Lima , R. De La Cour , K. Gaff , J. M. de Araújo , S. J. Cox , M. S. Ferreira , S. Hutzler

A construction is given for the recovery of a disjoint union of strictly convex smooth planar obstacles from travelling-time information. The obstacles are required to be such that no Euclidean line meets more than two of them.

Dynamical Systems · Mathematics 2020-10-12 Lyle Noakes , Luchezar Stoyanov

Let $G$ be a planar $3$-graph (i.e., a planar graph with vertex degree at most three) with $n$ vertices. We present the first $O(n^2)$-time algorithm that computes a planar orthogonal drawing of $G$ with the minimum number of bends in the…

Data Structures and Algorithms · Computer Science 2018-09-06 Walter Didimo , Giuseppe Liotta , Maurizio Patrignani

The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…

Numerical Analysis · Mathematics 2025-10-20 Vladimir Chelyshkov

We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor of optimal in…

Computational Geometry · Computer Science 2015-07-16 Michael J. Bannister , David Eppstein , Joseph A. Simons

For any positive integers $a$ and $b$, we enumerate all colored partitions made by noncrossing diagonals of a convex polygon into polygons whose number of sides is congruent to $b$ modulo $a$. For the number of such partitions made by a…

Combinatorics · Mathematics 2017-01-23 Daniel Birmajer , Juan B. Gil , Michael D. Weiner

In memory-constrained algorithms we have read-only access to the input, and the number of additional variables is limited. In this paper we introduce the compressed stack technique, a method that allows to transform algorithms whose space…

Computational Geometry · Computer Science 2014-06-26 Luis Barba , Matias Korman , Stefan Langerman , Kunikiko Sadakane , Rodrigo Silveira

Given an initial placement of a set of rectangles in the plane, we consider the problem of finding a disjoint placement of the rectangles that minimizes the area of the bounding box and preserves the orthogonal order i.e.\ maintains the…

Computational Geometry · Computer Science 2015-02-24 Sayan Bandyapadhyay , Santanu Bhowmick , Kasturi Varadarajan

Consider two axis-aligned rectilinear simple polygons in the domain consisting of axis-aligned rectilinear obstacles in the plane such that the bounding boxes, one for each obstacle and one for each polygon, are disjoint. We present an…

Computational Geometry · Computer Science 2021-06-29 Mincheol Kim , Hee-Kap Ahn

We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of…

Computational Geometry · Computer Science 2015-09-03 Jonathan Klawitter , Martin Nöllenburg , Torsten Ueckerdt

This paper presents a novel method to generate spatial constraints for motion planning in dynamic environments. Motion planning methods for autonomous driving and mobile robots typically need to rely on the spatial constraints imposed by a…

Robotics · Computer Science 2021-10-29 Han Hu , Peyman Yadmellat

Given a collection of N rectangles such that the side ratio of each one is a quadratic irrationality, we find all rectangles which can be tiled by rectangles similar to one of the given ones. It means that each possible shape can be used…

Combinatorics · Mathematics 2016-12-06 Fyodor Sharov

We study configuration spaces of linkages whose underlying graph are polygons with diagonal constrains, or more general, partial two-trees. We show that (with an appropriate definition) the oriented area is a Bott-Morse function on the…

Metric Geometry · Mathematics 2018-06-27 Gaiane Panina , Dirk Siersma

We show that every convex code realizable by compact sets in the plane admits a realization consisting of polygons, and analogously every open convex code in the plane can be realized by interiors of polygons. We give factorial-type bounds…

Combinatorics · Mathematics 2022-12-14 Boris Bukh , R. Amzi Jeffs

Graphic design is essential for visual communication with layouts being fundamental to composing attractive designs. Layout generation differs from pixel-level image synthesis and is unique in terms of the requirement of mutual relations…

Computer Vision and Pattern Recognition · Computer Science 2020-07-20 Hsin-Ying Lee , Lu Jiang , Irfan Essa , Phuong B Le , Haifeng Gong , Ming-Hsuan Yang , Weilong Yang

In a planar confluent orthogonal drawing (PCOD) of a directed graph (digraph) vertices are drawn as points in the plane and edges as orthogonal polylines starting with a vertical segment and ending with a horizontal segment. Edges may…

Computational Geometry · Computer Science 2022-09-01 Sabine Cornelsen , Gregor Diatzko