Submodular Functions And Optimization

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Submodular Functions and Optimization

Satoru Fujishige
Submodular Functions and Optimization Book PDF

Author : Satoru Fujishige
Publisher : Elsevier
Page : 411 pages
File Size : 50,9 Mb
Release : 2005-07-26
Category : Mathematics
ISBN : 9780080461625

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Submodular Functions and Optimization by Satoru Fujishige Pdf

It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics. Self-contained exposition of the theory of submodular functions Selected up-to-date materials substantial to future developments Polyhedral description of Discrete Convex Analysis Full description of submodular function minimization algorithms Effective insertion of figures Useful in applied mathematics, operations research, computer science, and economics

Learning with Submodular Functions

Francis Bach
Learning with Submodular Functions Book PDF

Author : Francis Bach
Publisher : Unknown
Page : 258 pages
File Size : 51,7 Mb
Release : 2013-11
Category : Computers
ISBN : 1601987560

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Learning with Submodular Functions by Francis Bach Pdf

Learning with Submodular Functions presents the theory of submodular functions in a self-contained way from a convex analysis perspective, presenting tight links between certain polyhedra, combinatorial optimization and convex optimization problems.

Submodular Functions and Optimization

S. Fujishige
Submodular Functions and Optimization Book PDF

Author : S. Fujishige
Publisher : Elsevier
Page : 269 pages
File Size : 49,5 Mb
Release : 1991-01-24
Category : Mathematics
ISBN : 0080867871

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Submodular Functions and Optimization by S. Fujishige Pdf

The importance of submodular functions has been widely recognized in recent years in combinatorial optimization. This is the first book devoted to the exposition of the theory of submodular functions from an elementary technical level to an advanced one. A unifying view of the theory is shown by means of base polyhedra and duality for submodular and supermodular systems. Among the subjects treated are: neoflows (submodular flows, independent flows, polymatroidal flows), submodular analysis (submodular programs, duality, Lagrangian functions, principal partitions), nonlinear optimization with submodular constraints (lexicographically optimal bases, fair resource allocation). Special emphasis is placed on the constructive aspects of the theory, which lead to practical, efficient algorithms.

Tractability

Lucas Bordeaux,Youssef Hamadi,Pushmeet Kohli
Tractability Book PDF

Author : Lucas Bordeaux,Youssef Hamadi,Pushmeet Kohli
Publisher : Cambridge University Press
Page : 401 pages
File Size : 40,6 Mb
Release : 2014-02-06
Category : Computers
ISBN : 9781107025196

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Tractability by Lucas Bordeaux,Youssef Hamadi,Pushmeet Kohli Pdf

An overview of the techniques developed to circumvent computational intractability, a key challenge in many areas of computer science.

Submodular Functions and Electrical Networks

H. Narayanan
Submodular Functions and Electrical Networks Book PDF

Author : H. Narayanan
Publisher : Elsevier
Page : 682 pages
File Size : 49,9 Mb
Release : 1997-05
Category : Computers
ISBN : 9780444825230

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Submodular Functions and Electrical Networks by H. Narayanan Pdf

There is a strong case for electrical network topologists and submodular function theorists being aware of each other's fields. Presenting a topological approach to electrical network theory, this book demonstrates the strong links that exist between submodular functions and electrical networks. The book contains: . a detailed discussion of graphs, matroids, vector spaces and the algebra of generalized minors, relevant to network analysis (particularly to the construction of efficient circuit simulators) . a detailed discussion of submodular function theory in its own right; topics covered include, various operations, dualization, convolution and Dilworth truncation as well as the related notions of prinicpal partition and principal lattice of partitions. In order to make the book useful to a wide audience, the material on electrical networks and that on submodular functions is presented independently of each other. The hybrid rank problem, the bridge between (topological) electrical network theory and submodular functions, is covered in the final chapter. The emphasis in the book is on low complexity algorithms, particularly based on bipartite graphs. The book is intended for self-study and is recommended to designers of VLSI algorithms. More than 300 problems, almost all of them with solutions, are included at the end of each chapter.

Discrete Convex Analysis

Kazuo Murota
Discrete Convex Analysis Book PDF

Author : Kazuo Murota
Publisher : SIAM
Page : 411 pages
File Size : 53,9 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0898718503

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Discrete Convex Analysis by Kazuo Murota Pdf

Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis.

Combinatorial Optimization -- Eureka, You Shrink!

Michael Jünger,Gerhard Reinelt,Giovanni Rinaldi
Combinatorial Optimization Eureka You Shrink Book PDF

Author : Michael Jünger,Gerhard Reinelt,Giovanni Rinaldi
Publisher : Springer
Page : 214 pages
File Size : 49,7 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540364788

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Combinatorial Optimization -- Eureka, You Shrink! by Michael Jünger,Gerhard Reinelt,Giovanni Rinaldi Pdf

This book is dedicated to Jack Edmonds in appreciation of his ground breaking work that laid the foundations for a broad variety of subsequent results achieved in combinatorial optimization.The main part consists of 13 revised full papers on current topics in combinatorial optimization, presented at Aussois 2001, the Fifth Aussois Workshop on Combinatorial Optimization, March 5-9, 2001, and dedicated to Jack Edmonds.Additional highlights in this book are an account of an Aussois 2001 special session dedicated to Jack Edmonds including a speech given by William R. Pulleyblank as well as newly typeset versions of three up-to-now hardly accessible classical papers:- Submodular Functions, Matroids, and Certain Polyhedranbsp;nbsp; by Jack Edmonds- Matching: A Well-Solved Class of Integer Linear Programsnbsp;nbsp; by Jack Edmonds and Ellis L. Johnson- Theoretical Improvements in Algorithmic Efficiency for Network Flow Problemsnbsp;nbsp; by Jack Edmonds and Richard M. Karp.

Mathematical Programming The State of the Art

A. Bachem,M. Grötschel,B. Korte
Mathematical Programming The State of the Art Book PDF

Author : A. Bachem,M. Grötschel,B. Korte
Publisher : Springer Science & Business Media
Page : 662 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642688744

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Mathematical Programming The State of the Art by A. Bachem,M. Grötschel,B. Korte Pdf

In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.

Learning with Submodular Functions

Francis Bach,Now Publishers
Learning with Submodular Functions Book PDF

Author : Francis Bach,Now Publishers
Publisher : Unknown
Page : 228 pages
File Size : 41,9 Mb
Release : 2013
Category : Convex functions
ISBN : 1601987579

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Learning with Submodular Functions by Francis Bach,Now Publishers Pdf

Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the Lovász extension of submodular functions provides a useful set of regularization functions for supervised and unsupervised learning. In this monograph, we present the theory of submodular functions from a convex analysis perspective, presenting tight links between certain polyhedra, combinatorial optimization and convex optimization problems. In particular, we show how submodular function minimization is equivalent to solving a wide variety of convex optimization problems. This allows the derivation of new efficient algorithms for approximate and exact submodular function minimization with theoretical guarantees and good practical performance. By listing many examples of submodular functions, we review various applications to machine learning, such as clustering, experimental design, sensor placement, graphical model structure learning or subset selection, as well as a family of structured sparsity-inducing norms that can be derived and used from submodular functions.

Iterative Methods in Combinatorial Optimization

Lap Chi Lau,R. Ravi,Mohit Singh
Iterative Methods in Combinatorial Optimization Book PDF

Author : Lap Chi Lau,R. Ravi,Mohit Singh
Publisher : Cambridge University Press
Page : 255 pages
File Size : 52,5 Mb
Release : 2011-04-18
Category : Computers
ISBN : 9781139499392

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Iterative Methods in Combinatorial Optimization by Lap Chi Lau,R. Ravi,Mohit Singh Pdf

With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.

Submodularity in Dynamics and Control of Networked Systems

Andrew Clark,Basel Alomair,Linda Bushnell,Radha Poovendran
Submodularity in Dynamics and Control of Networked Systems Book PDF

Author : Andrew Clark,Basel Alomair,Linda Bushnell,Radha Poovendran
Publisher : Springer
Page : 210 pages
File Size : 53,6 Mb
Release : 2015-12-21
Category : Technology & Engineering
ISBN : 9783319269771

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Submodularity in Dynamics and Control of Networked Systems by Andrew Clark,Basel Alomair,Linda Bushnell,Radha Poovendran Pdf

This book presents a framework for the control of networked systems utilizing submodular optimization techniques. The main focus is on selecting input nodes for the control of networked systems, an inherently discrete optimization problem with applications in power system stability, social influence dynamics, and the control of vehicle formations. The first part of the book is devoted to background information on submodular functions, matroids, and submodular optimization, and presents algorithms for distributed submodular optimization that are scalable to large networked systems. In turn, the second part develops a unifying submodular optimization approach to controlling networked systems based on multiple performance and controllability criteria. Techniques are introduced for selecting input nodes to ensure smooth convergence, synchronization, and robustness to environmental and adversarial noise. Submodular optimization is the first unifying approach towards guaranteeing both performance and controllability with provable optimality bounds in static as well as time-varying networks. Throughout the text, the submodular framework is illustrated with the help of numerical examples and application-based case studies in biological, energy and vehicular systems. The book effectively combines two areas of growing interest, and will be especially useful for researchers in control theory, applied mathematics, networking or machine learning with experience in submodular optimization but who are less familiar with the problems and tools available for networked systems (or vice versa). It will also benefit graduate students, offering consistent terminology and notation that greatly reduces the initial effort associated with beginning a course of study in a new area.

Internet and Network Economics

Christos Papadimitriou,Shuzhong Zhang
Internet and Network Economics Book PDF

Author : Christos Papadimitriou,Shuzhong Zhang
Publisher : Springer
Page : 734 pages
File Size : 51,5 Mb
Release : 2008-12-11
Category : Computers
ISBN : 9783540921851

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Internet and Network Economics by Christos Papadimitriou,Shuzhong Zhang Pdf

This book constitutes the refereed proceedings of the 4th International Workshop on Internet and Network Economics, WINE 2008, held in Shanghai, China, in December 2008. The 68 revised full papers presented together with 10 invited talks were carefully reviewed and selected from 126 submissions. The papers are organized in topical sections on market equilibrium, congestion games, information markets, nash equilibrium, network games, solution concepts, algorithms and optimization, mechanism design, equilibrium, online advertisement, sponsored search auctions, and voting problems.

Integer Programming and Combinatorial Optimization

Jon Lee,Jens Vygen
Integer Programming and Combinatorial Optimization Book PDF

Author : Jon Lee,Jens Vygen
Publisher : Springer
Page : 418 pages
File Size : 42,6 Mb
Release : 2014-05-17
Category : Computers
ISBN : 9783319075570

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Integer Programming and Combinatorial Optimization by Jon Lee,Jens Vygen Pdf

This book constitutes the refereed proceedings of the 17th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2014, held in Bonn, Germany, in June 2014. The 34 full papers presented were carefully reviewed and selected from 143 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.

A First Course in Combinatorial Optimization

Jon Lee
A First Course in Combinatorial Optimization Book PDF

Author : Jon Lee
Publisher : Cambridge University Press
Page : 232 pages
File Size : 44,9 Mb
Release : 2004-02-09
Category : Business & Economics
ISBN : 0521010128

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A First Course in Combinatorial Optimization by Jon Lee Pdf

A First Course in Combinatorial Optimization is a text for a one-semester introductory graduate-level course for students of operations research, mathematics, and computer science. It is a self-contained treatment of the subject, requiring only some mathematical maturity. Topics include: linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Central to the exposition is the polyhedral viewpoint, which is the key principle underlying the successful integer-programming approach to combinatorial-optimization problems. Another key unifying topic is matroids. The author does not dwell on data structures and implementation details, preferring to focus on the key mathematical ideas that lead to useful models and algorithms. Problems and exercises are included throughout as well as references for further study.

Internet and Network Economics

Amin Saberi
Internet and Network Economics Book PDF

Author : Amin Saberi
Publisher : Springer
Page : 580 pages
File Size : 44,6 Mb
Release : 2010-12-06
Category : Computers
ISBN : 9783642175725

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Internet and Network Economics by Amin Saberi Pdf

This book constitutes the refereed proceedings of the 6th International Workshop on Internet and Network Economics, WINE 2010, held in Stanford, USA, in December 2010. The 52 revised full papers presented were carefully reviewed and selected from 95 submissions. The papers are organized in 33 regular papers and 19 short papers.