On a routing problem
01 Jan 1958-Quarterly of Applied Mathematics (American Mathematical Society (AMS))-Vol. 16, Iss: 1, pp 87-90
TL;DR: Given a set of N cities, with every two linked by a road, and the times required to traverse these roads, the functional equation technique of dynamic programming and approximation in policy space yield an iterative algorithm which converges after at most (N-1) iterations.
Abstract: : Given a set of N cities, with every two linked by a road, and the times required to traverse these roads, we wish to determine the path from one given city to another given city which minimizes the travel time. The times are not directly proportional to the distances due to varying quality of roads, and v varying quantities of traffic. The functional equation technique of dynamic programming, combined with approximation in policy space, yield an iterative algorithm which converges after at most (N-1) iterations.
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Book•
25 Apr 2008
TL;DR: Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field.
Abstract: Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.
4,905 citations
Cites methods from "On a routing problem"
...Berthomieu and Menasche [48] have used these data structures for the analysis of time Petri nets and Bellman [40] exploited these structures for constraint graphs....
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Book•
01 Jan 1996
TL;DR: This book familiarizes readers with important problems, algorithms, and impossibility results in the area, and teaches readers how to reason carefully about distributed algorithms-to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures.
Abstract: In Distributed Algorithms, Nancy Lynch provides a blueprint for designing, implementing, and analyzing distributed algorithms. She directs her book at a wide audience, including students, programmers, system designers, and researchers.
Distributed Algorithms contains the most significant algorithms and impossibility results in the area, all in a simple automata-theoretic setting. The algorithms are proved correct, and their complexity is analyzed according to precisely defined complexity measures. The problems covered include resource allocation, communication, consensus among distributed processes, data consistency, deadlock detection, leader election, global snapshots, and many others.
The material is organized according to the system model-first by the timing model and then by the interprocess communication mechanism. The material on system models is isolated in separate chapters for easy reference.
The presentation is completely rigorous, yet is intuitive enough for immediate comprehension. This book familiarizes readers with important problems, algorithms, and impossibility results in the area: readers can then recognize the problems when they arise in practice, apply the algorithms to solve them, and use the impossibility results to determine whether problems are unsolvable. The book also provides readers with the basic mathematical tools for designing new algorithms and proving new impossibility results. In addition, it teaches readers how to reason carefully about distributed algorithms-to model them formally, devise precise specifications for their required behavior, prove their correctness, and evaluate their performance with realistic measures.
Table of Contents
1 Introduction
2 Modelling I; Synchronous Network Model
3 Leader Election in a Synchronous Ring
4 Algorithms in General Synchronous Networks
5 Distributed Consensus with Link Failures
6 Distributed Consensus with Process Failures
7 More Consensus Problems
8 Modelling II: Asynchronous System Model
9 Modelling III: Asynchronous Shared Memory Model
10 Mutual Exclusion
11 Resource Allocation
12 Consensus
13 Atomic Objects
14 Modelling IV: Asynchronous Network Model
15 Basic Asynchronous Network Algorithms
16 Synchronizers
17 Shared Memory versus Networks
18 Logical Time
19 Global Snapshots and Stable Properties
20 Network Resource Allocation
21 Asynchronous Networks with Process Failures
22 Data Link Protocols
23 Partially Synchronous System Models
24 Mutual Exclusion with Partial Synchrony
25 Consensus with Partial Synchrony
4,340 citations
06 Jun 2010
TL;DR: A model for processing large graphs that has been designed for efficient, scalable and fault-tolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier.
Abstract: Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs - in some cases billions of vertices, trillions of edges - poses challenges to their efficient processing. In this paper we present a computational model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertex-centric approach is flexible enough to express a broad set of algorithms. The model has been designed for efficient, scalable and fault-tolerant implementation on clusters of thousands of commodity computers, and its implied synchronicity makes reasoning about programs easier. Distribution-related details are hidden behind an abstract API. The result is a framework for processing large graphs that is expressive and easy to program.
3,840 citations
Book•
05 Aug 2002
TL;DR: Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science, and it will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.
Abstract: The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.
1,938 citations
Cites methods from "On a routing problem"
...This algorithm originates from the papers [102] by Bellman, [245] by Ford and [572] by Moore....
[...]
TL;DR: AntNet is a distributed, mobile agents based Monte Carlo system that was inspired by recent work on the ant colony metaphor for solving optimization problems, and showed superior performance under all the experimental conditions with respect to its competitors.
Abstract: This paper introduces AntNet, a novel approach to the adaptive learning of routing tables in communications networks. AntNet is a distributed, mobile agents based Monte Carlo system that was inspired by recent work on the ant colony metaphor for solving optimization problems. AntNet's agents concurrently explore the network and exchange collected information. The communication among the agents is indirect and asynchronous, mediated by the network itself. This form of communication is typical of social insects and is called stigmergy. We compare our algorithm with six state-of-the-art routing algorithms coming from the telecommunications and machine learning fields. The algorithms' performance is evaluated over a set of realistic testbeds. We run many experiments over real and artificial IP datagram networks with increasing number of nodes and under several paradigmatic spatial and temporal traffic distributions. Results are very encouraging. AntNet showed superior performance under all the experimental conditions with respect to its competitors. We analyze the main characteristics of the algorithm and try to explain the reasons for its superiority.
1,712 citations
References
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Book•
[...]
21 Oct 1957
TL;DR: The more the authors study the information processing aspects of the mind, the more perplexed and impressed they become, and it will be a very long time before they understand these processes sufficiently to reproduce them.
Abstract: From the Publisher:
An introduction to the mathematical theory of multistage decision processes, this text takes a functional equation approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, strategies behind multistage games, and Markovian decision processes. Each chapter concludes with a problem set that Eric V. Denardo of Yale University, in his informative new introduction, calls a rich lode of applications and research topics. 1957 edition. 37 figures.
14,187 citations
TL;DR: The text of an invited address before the annual summer meeting of the American Mathematical Society at Laramie, Wyoming, September 2, 1954 is given in this article, where the contents are chiefly of an expository nature on the theory of dynamic programming.
Abstract: : The paper is the text of an invited address before the annual summer meeting of the American Mathematical Society at Laramie, Wyoming, September 2, 1954. The contents are chiefly of an expository nature on the theory of dynamic programming.
988 citations