A Genetic Algorithm Based Approach for Solving the Minimum Dominating Set of Queens Problem

In the field of computing, combinatorics, and related areas, researchers have formulated several techniques for the Minimum Dominating Set of Queens Problem (MDSQP) pertaining to the typical chessboard based puzzles. However, literature shows that limited research has been carried out to solve theMDSQP using bioinspired algorithms. To fill this gap, this paper proposes a simple and effective solution based on genetic algorithms to solve this classical problem. We report results which demonstrate that near optimal solutions have been determined by the GA for different board sizes ranging from 8 × 8 to 11 × 11

Relation-algebraic modeling and solution of chessboard independence and domination problems

AbstractWe describe a simple computing technique for solving independence and domination problems on rectangular chessboards. It rests upon relational modeling and uses the BDD-based specific purpose computer algebra system RelView for the evaluation of the relation-algebraic expressions that specify the problems’ solutions and the visualization of the computed results. The technique described in the paper is very flexible and especially appropriate for experimentation. It can easily be applied to other chessboard problems

Toroidal Queens Graphs Over Finite Fields

For each positive integer n, the toroidal queens graph may be described as a graph with vertex set Zn × Zn where every vertex is adjacent to those vertices in the directions (1, 0), (0, 1), (1, 1), (1,−1) from it. We here extend this idea, examining graphs with vertex set F × F, where F is a finite field, and any four directions are used to define adjacency. The automorphism groups and isomorphism classes of such graphs are found

Eigenschaften kleinster dominierender Mengen und Dominanzzahlen von Damengraphen

Motiviert durch ein klassisches Schachproblem wird die Frage nach der Mächtigkeit einer kleinsten dominierenden Menge bzw. kleinsten unabhängigen dominierenden Menge des Damengraphen Q_n untersucht. Im Damengraph korrespondiert jeder Knoten zu einem Feld auf dem (n x n)-Schachbrett und zwei Knoten sind genau dann benachbart, wenn die zugehörigen Felder in derselben Zeile, Spalte oder Diagonale liegen. Im Detail wird gezeigt, dass jede p-Überdeckung von Q_n mit n>=19 beide langen Diagonalen durch zwei Eckfelder besetzt und daher diese Voraussetzung in der bekannten Charakterisierung mittels besetzter Diagonalen nicht einschränkend ist. Die Klasse der p-Überdeckungen wird zu orthodoxen Überdeckungen verallgemeinert und deren Relevanz durch Angabe entsprechender kleinster dominierender Mengen nachgewiesen. Für n=6(mod 8) mit n>=96 wird gezeigt, dass keine nicht-orthodoxe Überdeckung D von Q_n mit |D|=n/2 existiert. Zusammen mit einer hergeleiteten notwendigen Bedingung für die Existenz einer orthodoxen Überdeckung der Größe n/2 wird so in vielen Fällen die untere Schranke auf n/2 + 1 verschärft, was den Beweis einiger neuer Dominanzzahlen ermöglicht. Durch Angabe konkreter dominierender Mengen der Mächtigkeit (n+1)/2 werden Dominanzzahlen für folgende Instanzen bewiesen: n=43, 55, 83, 99, 107, 133, 137, 141, 143, 145, 149, 153, 157, 161, 163, 165, 169, 173, 177, 181, 183, 185, 189, 193, 197, 213 und 221. Durch Angabe konkreter unabhängiger dominierender Mengen der Mächtigkeit (n+1)/2 werden Dominanzzahlen für folgende Instanzen bewiesen: n=117, 121, 129, 141, 145, 157, 161, 165, 177, 185 und 189. Weiter wird ein Computerbeweis dafür erbracht, dass die Dominanzzahl folgender Instanzen n/2 + 1 beträgt: n=102, 110, 118, 126, 134, 142, 150, 158, 166, 174, 182, 190, 198, 214 und 222

Reports to the President

A compilation of annual reports for the 1982-1983 academic year, including a report from the President of the Massachusetts Institute of Technology, as well as reports from the academic and administrative units of the Institute. The reports outline the year's goals, accomplishments, honors and awards, and future plans

Energetic Phenomena on the Sun: The Solar Maximum Mission Flare Workshop. Proceedings

The general objectives of the conference were as follows: (1) Synthesize flare studies after three years of Solar Maximum Mission (SSM) data analysis. Encourage a broader participation in the SMM data analysis and combine this more fully with theory and other data sources-data obtained with other spacecraft such as the HINOTORI, p78-1, and ISEE-3 spacecrafts, and with the Very Large Array (VLA) and many other ground-based instruments. Many coordinated data sets, unprecedented in their breadth of coverage and multiplicity of sources, had been obtained within the structure of the Solar Maximum Year (SMY). (2) Stimulate joint studies, and publication in the general scientific literature. The intended primary benefit was for informal collaborations to be started or broadened at the Workshops with subsequent publications. (3) Provide a special publication resulting from the Workshop

Publications of Goddard Space Flight Center, 1964. Volume I - Space sciences

This publication is a collection of articles, papers, talks, and reports generated by the scientific and engineering staff of Goddard Space Flight Center in the year 1964. Many of these articles were originally published in scientific or engineering Journals or as official NASA technical publications, while other are documents of a more informal nature. All are reprinted here as nearly verbatim as typography and format will permit. These articles are grouped into broad subject categories, but no detailed subdivision has been made. Within each category, the articles are arranged alphabetically by author. An overall author index is given in the back of the volume. The years 1963, 1964, and 1965 are being published as whole-year issues, and the resulting size dictates the use of two volumes; the first volume is titled Space Sciences, and the second Space Technology. It is anticipated, however, that future issues will be quarterly single volumes