The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected componen...

Depth-First Search and Linear Graph Algorithms

We study two families of error-correcting codes defined in terms of very sparse matrices "MN" (MacKay-Neal (1995)) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties The decoding of both codes can be tackled with a practical sum-product algorithm We prove that these codes are "very good", in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit This result holds not only for the binary-symmetric channel but also for any channel with symmetric stationary ergodic noise We give experimental results for binary-symmetric channels and Gaussian channels demonstrating that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed, the performance of Gallager codes is almost as close to the Shannon limit as that of turbo codes

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Good error-correcting codes based on very sparse matrices

A survey is presented of current methods for decision tree classifier (DTC) designs and the various existing issues. After considering potential advantages of DTCs over single-state classifiers, the subjects of tree structure design, feature selection at each internal node, and decision and search strategies are discussed. The relation between decision trees and neutral networks (NN) is also discussed. >

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A survey of decision tree classifier methodology

The authors report the empirical performance of Gallager's low density parity check codes on Gaussian channels. They show that performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed the performance is almost as close to the Shannon limit as that of turbo codes.

Near Shannon limit performance of low density parity check codes

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

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A Dynamic Survey of Graph Labeling

This book provides a comprehensive description of the methodologies and the application areas, throughout the range of digital communication, in which individual signals and sets of signals with favorable correlation properties play a central role. The necessary mathematical background is presented to explain how these signals are generated, and to show how they satisfy the appropriate correlation constraints. All the known methods to obtain balanced binary sequences with two-valued autocorrelation, many of them only recently discovered, are presented in depth. The authors treat important application areas including: Code Division Multiple Access (CDMA) signals, such as those already in widespread use for cell-phone communication, and planned for universal adoption in the various approaches to 'third-generation'(3G) cell-phone use; systems for coded radar and sonar signals; communication signals to minimize mutual interference ('cross-talk') in multi-user environments; and pseudo-random sequence generation for secure authentication and for stream cipher cryptology.

Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar

A widely used method of efftcient search is examined in detail. This examination provides the opportunity to formulate its scope and methods in their full generality. In addL tion to a general exposition of the basic process, some important refinemertts are indicated. Examples are given which illustrate the salient features of this searching process.

Backtrack Programming

Publisher Summary This chapter explains the way of numbering a graph. The problem of numbering a graph is to assign integers to the nodes so as to achieve G(Г). The principal questions which arise in the theory of numbering the nodes of graphs revolve around the relationship between G(Г) and e, for example, identifying classes of graphs for which G(Г)= e and other classes for which G(Г)

How to number a graph

Perfect Codes in the Lee Metric and the Packing of Polyominoes

A generalized Barker sequence is a finite sequence \{a_{r}\} of complex numbers having absolute value 1 , and possessing a correlation function C(\tau) satisfying the constraint |C(\tau)| \leq 1, \tau \neq 0 . Classes of transformations leaving |C(\tau)| invariant are exhibited. Constructions for generalized Barker sequences of various lengths and alphabet sizes are given. Sextic Barker sequences are investigated and examples are given for all lengths through thirteen. No theoretical limit to the length of sextic sequences has been found.

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Solomon W. Golomb

Papers

Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar

Backtrack Programming

How to number a graph

Perfect Codes in the Lee Metric and the Packing of Polyominoes

Generalized Barker sequences