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Algorithms
Special Issues
Combinatorial Designs: Theory and Applications
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Combinatorial Designs: Theory and Applications

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (1 August 2022) | Viewed by 9036

Special Issue Editor

Dr. Natanael Karjanto

E-Mail Website
Guest Editor
Department of Mathematics, University College, Sungkyunkwan University, Natural Science Campus, Suwon 16419, Gyeonggi-do, Republic of Korea
Interests: nonlinear wave phenomena; partial differential equations; soliton theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear colleagues,

The study of combinatorial designs has attracted attention in recent decades thanks to a multidisciplinary effort from mathematicians, engineers, and computer scientists. The topic has a wide range of applications which include sports, educational, and social science issues. For example, an instructor is interested in forming teams of students for collaborative learning. How can we construct team formation, whereby for each week, each team member will meet new people as a new team is formed? Recall Kirkman’s schoolgirl problem from 1850: A schoolmistress has fifteen girl pupils, and she wishes to take them on a daily walk. The girls are to walk in five rows of three girls each. It is required that no two girls should walk in the same row more than once per week. How should the girls be arranged? Recall also the social golfer problem: Twenty golfers wish to play in foursomes for five days. Is it possible for each golfer to play no more than once with any other golfer? These are some examples where combinatorial designs play an essential role in proposing algorithms in finding potential solutions. In this Special Issue of Algorithms, we seek contributions from both young and established researchers on the topics in combinatorial designs. All types of contributions are welcome, including but not limited to modeling, theoretical and mathematical, computational, and experimental.

Dr. Natanael Karjanto
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • graph theory
  • team formation
  • orthogonal grouping
  • combinatorics
  • combinatorial designs
  • combinatorial optimization
  • projective linear group
  • Galois geometry
  • Kirkman triple system
  • social golfer problem
  • Steiner triple system
  • Steiner quadruple system
  • resolvable covering problem
  • Oberwolfach problem
  • isomorphism
  • pairwise balanced design (PBD)
  • symmetry breaking
  • constraint programming
  • balanced incomplete block design (BIBD)
  • resolvable balanced incomplete block design
  • dobble card game
  • progressive dinner party designs
  • speed networking events
  • sports competitions
  • cooperative learning strategy

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Published Papers (3 papers)

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Research

28 pages, 4194 KiB  
Article
Joining Constraint Satisfaction Problems and Configurable CAD Product Models: A Step-by-Step Implementation Guide
by Paul Christoph Gembarski
Algorithms 2022, 15(9), 318; https://doi.org/10.3390/a15090318 - 6 Sep 2022
Cited by 5 | Viewed by 2252
Abstract
In configuration design, the task is to compose a system out of a set of predefined, modu-lar building blocks assembled by defined interfaces. Product configuration systems, both with or without integration of geometric models, implement reasoning techniques to model and explore the resulting [...] Read more.
In configuration design, the task is to compose a system out of a set of predefined, modu-lar building blocks assembled by defined interfaces. Product configuration systems, both with or without integration of geometric models, implement reasoning techniques to model and explore the resulting solution spaces. Among others, the formulation of constraint satisfaction problems (CSP) is state of the art and the informational background in many proprietary configuration engine software packages. Basically, configuration design tasks can also be implemented in modern computer aided design (CAD) systems as these contain different techniques for knowledge-based product modeling but literature reports only little about detailed application examples, best practices or training materials. This article aims at bridging this gap and presents a step-by-step implementation guide for CSP-based CAD configurators for combinatorial designs with the example of Autodesk Inventor. Full article
(This article belongs to the Special Issue Combinatorial Designs: Theory and Applications)
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20 pages, 593 KiB  
Article
Properties and Recognition of Atom Graphs
by Geneviève Simonet and Anne Berry
Algorithms 2022, 15(8), 294; https://doi.org/10.3390/a15080294 - 19 Aug 2022
Viewed by 1748
Abstract
The atom graph of a connected graph is a graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all its atom trees. A graph G is an atom graph if [...] Read more.
The atom graph of a connected graph is a graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all its atom trees. A graph G is an atom graph if there is a graph whose atom graph is isomorphic to G. We study the class of atom graphs, which is also the class of atom graphs of chordal graphs, and the associated recognition problem. We prove that each atom graph is a perfect graph and give a characterization of atom graphs in terms of a spanning tree, inspired by the characterization of clique graphs of chordal graphs as expanded trees. We also characterize the chordal graphs having the same atom and clique graph, and solve the recognition problem of atom graphs of two graph classes. Full article
(This article belongs to the Special Issue Combinatorial Designs: Theory and Applications)
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12 pages, 10060 KiB  
Article
Temari Balls, Spheres, SphereHarmonic: From Japanese Folkcraft to Music
by Maria Mannone and Takashi Yoshino
Algorithms 2022, 15(8), 286; https://doi.org/10.3390/a15080286 - 14 Aug 2022
Viewed by 3687
Abstract
Temari balls are traditional Japanese toys and artworks. The variety of their geometries and tessellations can be investigated formally and computationally with the means of combinatorics. As a further step, we also propose a musical application of the core idea of Temari balls. [...] Read more.
Temari balls are traditional Japanese toys and artworks. The variety of their geometries and tessellations can be investigated formally and computationally with the means of combinatorics. As a further step, we also propose a musical application of the core idea of Temari balls. In fact, inspired by the classical idea of music of spheres and by the CubeHarmonic, a musical application of the Rubik’s cube, we present the concept of a new musical instrument, the SphereHarmonic. The mathematical (and musical) description of Temari balls lies in the wide background of interactions between art and combinatorics. Concerning the methods, we present the tools of permutations and tessellations we adopted here, and the core idea for the SphereHarmonic. As the results, we first describe a classification of structures according to the theory of groups. Then, we summarize the main passages implemented in our code, to make the SphereHarmonic play on a laptop. Our study explores an aspect of the deep connections between the mutually inspiring scientific and artistic thinking. Full article
(This article belongs to the Special Issue Combinatorial Designs: Theory and Applications)
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