Computer algorithms

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Data Structures ◽  
Analysis Of Algorithms ◽  
Shortest Paths ◽  
Minimum Cut ◽  
Network Data ◽  
Computer Algorithms ◽  
Breadth First Search ◽  
Augmenting Path ◽  
Basic Concepts ◽  
Maximum Flows

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.

scholarly journals Cache-Oblivious Data Structures and Algorithms for Undirected Breadth-First Search and Shortest Paths

2004 ◽  
Vol 11 (2) ◽  
Author(s):  
Gerth Stølting Brodal ◽  
Rolf Fagerberg ◽  
Ulrich Meyer ◽  
Norbert Zeh
Keyword(s):  
Data Structures ◽  
Shortest Paths ◽  
Block Size ◽  
Priority Queue ◽  
Breadth First Search ◽  
Undirected Graphs ◽  
Performance Gap ◽  
Negative Edge ◽  
Data Structures And Algorithms ◽  
Cache Oblivious

We present improved cache-oblivious data structures and algorithms for breadth-first search (BFS) on undirected graphs and the single-source shortest path (SSSP) problem on undirected graphs with non-negative edge weights. For the SSSP problem, our result closes the performance gap between the currently best <em>cache-aware</em> algorithm and the <em>cache-oblivious</em> counterpart. Our cache-oblivious SSSP-algorithm takes nearly full advantage of block transfers for <em>dense</em> graphs. The algorithm relies on a new data structure, called <em>bucket heap</em>, which is the first cache-oblivious priority queue to efficiently support a weak D<small>ECREASE</small>K<small>EY</small> operation. For the BFS problem, we reduce the number of I/Os for <em>sparse</em> graphs by a factor of nearly sqrt{B}, where B is the cache-block size, nearly closing the performance gap between the currently best <em>cache-aware</em> and <em>cache-oblivious</em> algorithms.

Networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Biological Networks ◽  
Generative Models ◽  
The Internet ◽  
Network Data ◽  
Computer Algorithms ◽  
Graph Models ◽  
Random Graph Models ◽  
The Social ◽  
Spectral Algorithms ◽  
Wide Availability

The study of networks, including computer networks, social networks, and biological networks, has attracted enormous interest in recent years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyse network data on an unprecendented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social science. This book brings together the most important breakthroughts in each of these fields and presents them in a unified fashion, highlighting the strong interconnections between work in different areas. Topics covered include the measurement of networks; methods for analysing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms, including spectral algorithms and community detection; mathematical models of networks such as random graph models and generative models; and models of processes taking place on networks.

Indoor landmark-based path-finding utilising the expanded connectivity of an endpoint partition

2016 ◽  
Vol 45 (2) ◽  
pp. 233-252
Author(s):  
Pepijn Viaene ◽  
Alain De Wulf ◽  
Philippe De Maeyer
Keyword(s):  
Visual Information ◽  
Spatial Configuration ◽  
Shortest Paths ◽  
Minimal Amount ◽  
Path Finding ◽  
Breadth First Search ◽  
Length Increase ◽  
Efficient Communication ◽  
Indoor Wayfinding

Landmarks are ideal wayfinding tools to guide a person from A to B as they allow fast reasoning and efficient communication. However, very few path-finding algorithms start from the availability of landmarks to generate a path. In this paper, which focuses on indoor wayfinding, a landmark-based path-finding algorithm is presented in which the endpoint partition is proposed as spatial model of the environment. In this model, the indoor environment is divided into convex sub-shapes, called e-spaces, that are stable with respect to the visual information provided by a person’s surroundings (e.g. walls, landmarks). The algorithm itself implements a breadth-first search on a graph in which mutually visible e-spaces suited for wayfinding are connected. The results of a case study, in which the calculated paths were compared with their corresponding shortest paths, show that the proposed algorithm is a valuable alternative for Dijkstra’s shortest path algorithm. It is able to calculate a path with a minimal amount of actions that are linked to landmarks, while the path length increase is comparable to the increase observed when applying other path algorithms that adhere to natural wayfinding behaviour. However, the practicability of the proposed algorithm is highly dependent on the availability of landmarks and on the spatial configuration of the building.

scholarly journals The Number of Moves of the Largest Disc in Shortest Paths on Hanoi Graphs

10.37236/4252 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Simon Aumann ◽  
Katharina A.M. Götz ◽  
Andreas M. Hinz ◽  
Ciril Petr
Keyword(s):  
Shortest Paths ◽  
General Setting ◽  
Optimal Number ◽  
Numerical Results ◽  
Breadth First Search ◽  
Tower Of Hanoi ◽  
Optimal Paths ◽  
Widespread Interest ◽  
Binary Strings

In contrast to the widespread interest in the Frame-Stewart conjecture (FSC) about the optimal number of moves in the classical Tower of Hanoi task with more than three pegs, this is the first study of the question of investigating shortest paths in Hanoi graphs $H_p^n$ in a more general setting. Here $p$ stands for the number of pegs and $n$ for the number of discs in the Tower of Hanoi interpretation of these graphs. The analysis depends crucially on the number of largest disc moves (LDMs). The patterns of these LDMs will be coded as binary strings of length $p-1$ assigned to each pair of starting and goal states individually. This will be approached both analytically and numerically. The main theoretical achievement is the existence, at least for all $n\geqslant p(p-2)$, of optimal paths where $p-1$ LDMs are necessary. Numerical results, obtained by an algorithm based on a modified breadth-first search making use of symmetries of the graphs, lead to a couple of conjectures about some cases not covered by our ascertained results. These, in turn, may shed some light on the notoriously open FSC.

Maximum Flows by Incremental Breadth-First Search

2011 ◽  
pp. 457-468 ◽  
Author(s):  
Andrew V. Goldberg ◽  
Sagi Hed ◽  
Haim Kaplan ◽  
Robert E. Tarjan ◽  
Renato F. Werneck
Keyword(s):  
Breadth First Search ◽  
Maximum Flows

Network Data Characteristics

2011 ◽  
pp. 104-122
Author(s):  
Yu Wang
Keyword(s):  
Real World ◽  
Random Variables ◽  
Network Data ◽  
Traffic Data ◽  
Real World Data ◽  
Additional Information ◽  
Data Points ◽  
Key Features ◽  
Basic Concepts ◽  
Data Elements

Data represents the natural phenomena of our real world. Data is constructed by rows and columns; usually rows represent the observations and columns represent the variables. Observations, also called subjects, records, or data points, represent a phenomenon in the real world and variables, as also known as data elements or data fields, represent the characteristics of observations in data. Variables take different values for different observations, which can make observations independent of each other. Figure 4.1 illustrates a section of TCP/IP traffic data, in which the rows are individual network traffics, and the columns, separated by a space, are characteristics of the traffics. In this example, the first column is a session index of each connection and the second column is the date when the connection occurred. In this chapter, we will discuss some fundamental key features of variables and network data. We will present detailed discussions on variable characteristics and distributions in Sections Random Variables and Variables Distributions, and describe network data modules in Section Network Data Modules. The material covered in this chapter will help readers who do not have a solid background in this area gain an understanding of the basic concepts of variables and data. Additional information can be found from Introduction to the Practice of Statistics by Moore and McCabe (1998).

scholarly journals Preface

2019 ◽  
Vol 28 (4) ◽  
pp. 483-484
Author(s):  
Hsien-Kuei Hwang ◽  
Ralph Neininger ◽  
Marek Zaionc
Keyword(s):  
Data Structures ◽  
Analysis Of Algorithms ◽  
Probabilistic Methods ◽  
Algorithms And Data Structures ◽  
Special Issue ◽  
Rich Variety ◽  
Cost Distribution ◽  
Discrete Structures ◽  
Measure Of Performance ◽  
The Cost

This special issue is devoted to the Mathematical Analysis of Algorithms, which aims to predict the performance of fundamental algorithms and data structures in general use in Computer Science. The simplest measure of performance is the expected value of a cost function under natural models of randomness for the data, and finer properties of the cost distribution provide a deeper understanding of the complexity. Research in this area, which is intimately connected to combinatorics and random discrete structures, uses a rich variety of combinatorial, analytic and probabilistic methods.

Sign in / Sign up

Export Citation Format

Share Document