From the Publisher:
With this text, you gain an understanding of the fundamental concepts of algorithms, the very heart of computer science. It introduces the basic data structures and programming techniques often used in efficient algorithms. Covers use of lists, push-down stacks, queues, trees, and graphs. Later chapters go into sorting, searching and graphing algorithms, the string-matching algorithms, and the Schonhage-Strassen integer-multiplication algorithm. Provides numerous graded exercises at the end of each chapter.


0201000296B04062001

The Design and Analysis of Computer Algorithms

There is no other package around that satisfies all the following requirements: •Ability to handle large graphs efficiently •Embeddable into higher level environments (like R [6] or Python [7]) •Ability to be used for quick prototyping of new algorithms (impossible with “click & play” interfaces) •Platform-independent and open source igraph aims to satisfy all these requirements while possibly remaining easy to use in interactive mode as well.

The igraph software package for complex network research

We present VOSviewer, a freely available computer program that we have developed for constructing and viewing bibliometric maps. Unlike most computer programs that are used for bibliometric mapping, VOSviewer pays special attention to the graphical representation of bibliometric maps. The functionality of VOSviewer is especially useful for displaying large bibliometric maps in an easy-to-interpret way. The paper consists of three parts. In the first part, an overview of VOSviewer’s functionality for displaying bibliometric maps is provided. In the second part, the technical implementation of specific parts of the program is discussed. Finally, in the third part, VOSviewer’s ability to handle large maps is demonstrated by using the program to construct and display a co-citation map of 5,000 major scientific journals.

/pdf/software-survey-vosviewer-a-computer-program-for-505jc6bwmd.pdf

Software survey: VOSviewer, a computer program for bibliometric mapping.

SUMMARY We present a modification of the spring-embedder model of Eades [ Congresses Numerantium, 42, 149–160, (1984)] for drawing undirected graphs with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptuallyintuitive, and efficient algorithm.

/pdf/graph-drawing-by-force-directed-placement-1a6bl10a4a.pdf

Graph drawing by force-directed placement

We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs) We provide software for accessing and managing the Collection, from MATLAB™, Mathematica™, Fortran, and C, as well as an online search capability Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task

The university of Florida sparse matrix collection

Bresenham's algorithm minimizes error in drawing lines on integer grid points; leap year calculations, surprisingly, are a generalization. We compare the two calculations, explicate the pattern, and discuss the connection of the leap year/line pattern with integer division and Euclid's algorithm for computing the greatest common divisor.

/pdf/line-drawing-leap-years-and-euclid-3me7ya0op3.pdf

Line drawing, leap years, and Euclid

It is shown that when a graph is represented as a binary connection matrix, the problems of finding the shortest path between two nodes of a graph, of determining whether the graph has a cycle, and of determining if a graph is strongly connected each require at leastO(n
2) operations. Thus the presently known best algorithms are optimal to within a multiplicative constant.

On the time required to detect cycles and connectivity in graphs

We consider self-organizing data structures when the number of data accesses is unknown. We show that certain general rearrangement rules can be modified to reduce significantly the number of data moves, without affecting the asymptotic cost of a data access. As a special case, explicit formulae are given for the expected cost of a data access and the expected number of data moves for the modified move-to-front rules for linear lists and binary trees. Since a data move usually costs at least as much as a data access, the modified rule eventually leads to a savings in total cost (the sum of data accesses and moves).

Stochastic rearrangement rules for self-organizing data structures

This note is concerned with the number of binary comparisons required to compute the maximum or the median of sets of numbers. The new results are: (a) the maximum of a set of n integers cannot be computed in fewer than n-1 comparisons if comparisons of only linear functions of the integers are permitted, but the maximum can be computed in log2 n comparisons if comparisons can be made between exponential functions of the integers and (b) the median of a set of n integers can be computed using only 2n comparisons if comparisons between polynomial functions of the integers are permitted.

Edward M. Reingold

Papers

Line drawing, leap years, and Euclid

On the time required to detect cycles and connectivity in graphs

Stochastic rearrangement rules for self-organizing data structures

Computing the maximum and the median

Combinatorial Algorithms: Theory and Practice.