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

We investigate the complexity of producing aesthetically pleasing drawings of binary trees, drawings that are as narrow as possible. The notion of what is aesthetically pleasing is embodied in several constraints on the placement of nodes, relative to other nodes. Among the results we give are: (1) There is no obvious "principle of optimality" that can be applied, since globally narrow, aesthetic placements of trees may require wider than necessary subtrees. (2) A previously suggested heuristic can produce drawings on n-node trees that are ?(n) times as wide as necessary. (3) The problem can be reduced in polynomial time to linear programming; hence, if the coordinates assigned to the nodes are continuous variables, then the problem can be solved in polynomial time. (4) If the placement is restricted to the integral lattice then the problem is NP-hard, as is its approximation to within a factor of about 4 per cent.

https://www.reingold.co/tree-complexity.pdf

The complexity of drawing trees nicely

Determining the majority

The es tab l i shment of lower bounds on the number of comparisons necessary to solve various combinator ia l problems is considered. Some of the new results are : (a) given two finite sets of real numbers , A and B, where n = max ( I A I , I B I ), O(n. log n) comparisons are required to determine if A = B, even when comparisons are allowed between l inear functions of the numbers ; and (b) the maximum of a set of n real numbers cannot be computed in fewer than n 1 comparisons if comparisons of only l inear funct ions of the numbers are permitted, but the maximum can be computed in Ilog2n] comparisons if comparisons are allowed between exponential funct ions of the numbers ,

On the Optimality of Some Set Algorithms

Given a set of $n$ elements each of which is either red or blue, it is known that in the worst case $n-\nu(n)$ pairwise equal/not equal color comparisons are necessary and sufficient to determine the majority color, where $\nu(n)$ is the number of 1-bits in the binary representation of $n$. We prove that $\frac{2n}{3} - \sqrt\frac{8n}{9\pi} + O(\log n)$ such comparisons are necessary and sufficient in the average case.

The Average-Case Complexity of Determining the Majority

We consider the problem of constructing multiple description scalar quantizers and describing the achievable rate-distortion tuples in that setting. We model this as a combinatorial optimization problem of number arrangements in a matrix. This approach gives a general technique for deriving lower bounds on the distortion at given channel rates. This technique is constructive, thus allowing an algorithm that gives an upper bound. For the case of two communication channels with equal rates, the bounds coincide, thus giving the precise lowest achievable distortion at fixed rates. The bounds are within a small constant for a higher number of channels. To the best of our knowledge, this is the first result involving systems with more than two communication channels.

Edward M. Reingold

Papers

The complexity of drawing trees nicely

Determining the majority

On the Optimality of Some Set Algorithms

The Average-Case Complexity of Determining the Majority

Index assignment for multichannel communication under failure