(1977). Graph Theory with Applications. Journal of the Operational Research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.

https://link.springer.com/content/pdf/10.1057%2Fjors.1977.45.pdf

Graph theory with applications

From the Publisher:
This book presents the data structures and algorithms that underpin much of today's computer programming. The basis of this book is the material contained in the first six chapters of our earlier work, The Design and Analysis of Computer Algorithms. We have expanded that coverage and have added material on algorithms for external storage and memory management. As a consequence, this book should be suitable as a text for a first course on data structures and algorithms. The only prerequisite we assume is familiarity with some high-level programming language such as Pascal.

/pdf/data-structures-and-algorithms-1czw3cmuao.pdf

Data Structures and Algorithms

ly, this program guesses nondeterministically the correct permutation via permutation(Xs,Ys), and ordered checks that the permutation is actually ordered. Operationally, the behavior is as follows. A query involving sort is reduced to a query involving permutation and ordered. A failure-driven loop ensues. A permutation of the list is generated by permutation and tested by ordered. If the permuted list is not ordered, the execution backtracks to the permutation goal, which generates another permutation to be tested. Eventually an ordered permutation is generated and the computation terminates. Permutation sort is a highly inefficient sorting algorithm, requiring time super-exponential in the size of the list to be sorted. Pushing the tester into the generator, however, leads to a reasonable algorithm. The generator for permutation sort, permutation, selects an arbitrary element and recursively permutes the rest of the list. The tester, ordered, verifies that the first two elements of the permutation are in order, then recursively checks the rest. If we view the combined recursive permutation and ordered goals as a recursive sorting process, we have the basis for insertion sort, Program 3.21. To sort a list, sort the tail of the list and insert the head of the list into its correct place in the order. The arbitrary selection of an element has been replaced by choosing the first element. Another example of the advantage of intertwining generating and testing can be seen with programs solving the N queens problem. The N queens problem requires the placement of N pieces on an Nby-N rectangular board so that no two pieces are on the same line: horizontal, vertical, or diagonal. The original formulation called for 8 queens to be placed on a chessboard, and the criterion of not being on the same line corresponds to two queens not attacking each other under the rules of chess. Hence the problem's name. 253 Nondeterministic Programming

The art of Prolog

This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.

/pdf/low-density-parity-check-codes-based-on-finite-geometries-a-4hq963rleu.pdf

Low-density parity-check codes based on finite geometries: a rediscovery and new results

This paper addresses the control of a team of nonholonomic mobile robots navigating in a terrain with obstacles while maintaining a desired formation and changing formations when required, using graph theory. We model the team as a triple, (g, r, H), consisting of a group element g that describes the gross position of the lead robot, a set of shape variables r that describe the relative positions of robots, and a control graph H that describes the behaviors of the robots in the formation. Our framework enables the representation and enumeration of possible control graphs and the coordination of transitions between any two formations.

/pdf/modeling-and-control-of-formations-of-nonholonomic-mobile-3vgx71xgee.pdf

Modeling and control of formations of nonholonomic mobile robots

Introductory Graph Theory with ApplicationsGraph Theory with ApplicationsResearch Topics in Graph Theory and Its ApplicationsChemical Graph TheoryMathematical Foundations and Applications of Graph EntropyGraph Theory with Applications to Engineering and Computer ScienceGraphs Theory and ApplicationsQuantitative Graph TheoryApplied Graph TheoryChemical Graph TheoryA First Course in Graph TheoryGraph TheoryGraph Theory with ApplicationsGraph Theory with ApplicationsSpectra of GraphsFuzzy Graph Theory with Applications to Human TraffickingApplications of Graph TheoryChemical Applications of Graph TheoryRecent Advancements in Graph TheoryA Textbook of Graph TheoryGraph Theory and Its Engineering ApplicationsGraph Theory, Combinatorics, and ApplicationsAdvanced Graph Theory and CombinatoricsTopics in Intersection Graph TheoryGraph Theory with Applications to Engineering and Computer ScienceGraph Theory and Its Applications, Second EditionHandbook of Research on Advanced Applications of Graph Theory in Modern SocietyGraph Theory with Applications to Algorithms and Computer ScienceGraph TheoryGraph Theory with Algorithms and its ApplicationsGraph TheoryGraph Theory with ApplicationsGraph Theory ApplicationsHandbook of Graph TheoryGraph Theory and Its Applications to Problems of SocietyBasic Graph Theory with ApplicationsTen

N.R. Malik

Papers

Graph theory with applications to engineering and computer science