Grötschel, Martin
Overview
Works:  272 works in 695 publications in 4 languages and 5,282 library holdings 

Genres:  Conference papers and proceedings Handbooks and manuals 
Roles:  Author, Editor, Other 
Classifications:  QA402.5, 511.6 
Publication Timeline
.
Most widely held works by
Martin Grötschel
Geometric algorithms and combinatorial optimization by
Martin Grötschel(
Book
)
37 editions published between 1980 and 1994 in English and German and held by 617 WorldCat member libraries worldwide
Since the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and theorems presented here. For instance, the celebrated DyerFriezeKannan algorithm for approximating the volume of a convex body is based on the oracle model of convex bodies and uses the ellipsoid method as a preprocessing technique. The polynomial time equivalence of optimization, separation, and membership has become a commonly employed tool in the study of the complexity of combinatorial optimization problems and in the newly developing field of computational convexity. Implementations of the basis reduction algorithm can be found in various computer algebra software systems. On the other hand, several of the open problems discussed in the first edition are still unsolved. For example, there are still no combinatorial polynomial time algorithms known for minimizing a submodular function or finding a maximum clique in a perfect graph. Moreover, despite the success of the interior point methods for the solution of explicitly given linear programs there is still no method known that solves implicitly given linear programs, such as those described in this book, and that is both practically and theoretically efficient. In particular, it is not known how to adapt interior point methods to such linear programs
37 editions published between 1980 and 1994 in English and German and held by 617 WorldCat member libraries worldwide
Since the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and theorems presented here. For instance, the celebrated DyerFriezeKannan algorithm for approximating the volume of a convex body is based on the oracle model of convex bodies and uses the ellipsoid method as a preprocessing technique. The polynomial time equivalence of optimization, separation, and membership has become a commonly employed tool in the study of the complexity of combinatorial optimization problems and in the newly developing field of computational convexity. Implementations of the basis reduction algorithm can be found in various computer algebra software systems. On the other hand, several of the open problems discussed in the first edition are still unsolved. For example, there are still no combinatorial polynomial time algorithms known for minimizing a submodular function or finding a maximum clique in a perfect graph. Moreover, despite the success of the interior point methods for the solution of explicitly given linear programs there is still no method known that solves implicitly given linear programs, such as those described in this book, and that is both practically and theoretically efficient. In particular, it is not known how to adapt interior point methods to such linear programs
Handbook of combinatorics by
Ronald L Graham(
Book
)
14 editions published in 1995 in English and Italian and held by 523 WorldCat member libraries worldwide
14 editions published in 1995 in English and Italian and held by 523 WorldCat member libraries worldwide
Mathematical programming : the state of the art, Bonn 1982 by
A Bachem(
Book
)
20 editions published in 1983 in 3 languages and held by 371 WorldCat member libraries worldwide
About the XIth International Symposium on Mathematical Programming; Mathematical programming: the state of the Art  Bonn 1982; Scientific program
20 editions published in 1983 in 3 languages and held by 371 WorldCat member libraries worldwide
About the XIth International Symposium on Mathematical Programming; Mathematical programming: the state of the Art  Bonn 1982; Scientific program
Bonn Workshop on Combinatorial Optimization by
1980, Bonn) Workshop on Combinatorial Optimization (4(
Book
)
23 editions published between 1982 and 2011 in English and Dutch and held by 239 WorldCat member libraries worldwide
Bonn Workshop on Combinatorial Optimization
23 editions published between 1982 and 2011 in English and Dutch and held by 239 WorldCat member libraries worldwide
Bonn Workshop on Combinatorial Optimization
Online optimization of large scale systems by
Martin Grötschel(
Book
)
12 editions published between 2001 and 2011 in English and held by 182 WorldCat member libraries worldwide
Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. In online optimization the main issue is: incomplete data; and the scientific challenge: How well can an online algorithm perform? Can one guarantee solution quality, even without knowing all data in advance? In realtime optimization there is an additional requirement, decisions have to be computed very fast, fast in relation to the time frame of the instance we consider. Online and realtime optimization problems occur in all branches of optimization: linear, nonlinear, integer, stochastic. These areas have developed their own techniques but they are addressing the same issues: quality, stability, and robustness of the solutions. To fertilize this emerging topic of optimization theory and to foster cooperation between the different branches of optimization, the Deutsche Forschungsgemeinschaft (DFG) has supported a Priority Programme "Online Optimization of Large Systems". This volume contains "background articles" and "research articles". Background articles are intended to give an overview over the basic theory in the respective area and are accessible to graduate math students. Research articles summarize the progress in a project achieved in the Priority Programme
12 editions published between 2001 and 2011 in English and held by 182 WorldCat member libraries worldwide
Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. In online optimization the main issue is: incomplete data; and the scientific challenge: How well can an online algorithm perform? Can one guarantee solution quality, even without knowing all data in advance? In realtime optimization there is an additional requirement, decisions have to be computed very fast, fast in relation to the time frame of the instance we consider. Online and realtime optimization problems occur in all branches of optimization: linear, nonlinear, integer, stochastic. These areas have developed their own techniques but they are addressing the same issues: quality, stability, and robustness of the solutions. To fertilize this emerging topic of optimization theory and to foster cooperation between the different branches of optimization, the Deutsche Forschungsgemeinschaft (DFG) has supported a Priority Programme "Online Optimization of Large Systems". This volume contains "background articles" and "research articles". Background articles are intended to give an overview over the basic theory in the respective area and are accessible to graduate math students. Research articles summarize the progress in a project achieved in the Priority Programme
The sharpest cut : the impact of Manfred Padberg and his work by
Martin Grötschel(
Book
)
12 editions published in 2004 in English and held by 111 WorldCat member libraries worldwide
This title is written in honor of Manfred Padberg, who has made fundamental contributions to both the theoretical and computational sides of integer programming and combinatorial optimization. This outstanding collection presents recent results in these areas that are closely connected to Padberg's research. His deep commitment to the geometrical approach to combinatorial optimization can be felt throughout this volume; his search for increasingly better and computationally efficient cutting planes gave rise to its title. The peerreviewed papers contained here are based on invited lectures given at a workshop held in October 2001 to celebrate Padberg's 60th birthday. Grouped by topic (packing, stable sets, and perfect graphs; polyhedral combinatorics; general polytopes; semidefinite programming; computation), many of the papers set out to solve challenges set forth in Padberg's work. The book also shows how Padberg's ideas on cutting planes have influenced modern commercial optimization software
12 editions published in 2004 in English and held by 111 WorldCat member libraries worldwide
This title is written in honor of Manfred Padberg, who has made fundamental contributions to both the theoretical and computational sides of integer programming and combinatorial optimization. This outstanding collection presents recent results in these areas that are closely connected to Padberg's research. His deep commitment to the geometrical approach to combinatorial optimization can be felt throughout this volume; his search for increasingly better and computationally efficient cutting planes gave rise to its title. The peerreviewed papers contained here are based on invited lectures given at a workshop held in October 2001 to celebrate Padberg's 60th birthday. Grouped by topic (packing, stable sets, and perfect graphs; polyhedral combinatorics; general polytopes; semidefinite programming; computation), many of the papers set out to solve challenges set forth in Padberg's work. The book also shows how Padberg's ideas on cutting planes have influenced modern commercial optimization software
Produktionsfaktor Mathematik : wie Mathematik Technik und Wirtschaft bewegt by
Martin Grötschel(
Book
)
17 editions published between 2009 and 2010 in English and German and held by 110 WorldCat member libraries worldwide
Mathematics as a production factor or driving force for innovation? Those, who want to know and understand why mathematics is deeply involved in the design of products, the layout of production processes and supply chains will find this book an indispensable and rich source. Describing the interplay between mathematical and engineering sciences the book focusses on questions like  How can mathematics improve to the improvement of technological processes and products  What is happening already?  Where are the deficits?  What can we expect for the future? 19 articles written by mixed teams of authors of engineering, industry and mathematics offer a fascinating insight of the interaction between mathematics and engineering
17 editions published between 2009 and 2010 in English and German and held by 110 WorldCat member libraries worldwide
Mathematics as a production factor or driving force for innovation? Those, who want to know and understand why mathematics is deeply involved in the design of products, the layout of production processes and supply chains will find this book an indispensable and rich source. Describing the interplay between mathematical and engineering sciences the book focusses on questions like  How can mathematics improve to the improvement of technological processes and products  What is happening already?  Where are the deficits?  What can we expect for the future? 19 articles written by mixed teams of authors of engineering, industry and mathematics offer a fascinating insight of the interaction between mathematics and engineering
Building bridges : between mathematics and computer science by
Martin Grötschel(
Book
)
18 editions published between 2008 and 2011 in English and held by 93 WorldCat member libraries worldwide
"Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is Laszlo Lovasz, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovasz's 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers."Jacket
18 editions published between 2008 and 2011 in English and held by 93 WorldCat member libraries worldwide
"Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is Laszlo Lovasz, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovasz's 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers."Jacket
Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme by
Martin Grötschel(
Book
)
7 editions published in 1977 in German and Undetermined and held by 75 WorldCat member libraries worldwide
7 editions published in 1977 in German and Undetermined and held by 75 WorldCat member libraries worldwide
Handbook of combinatorics(
Book
)
8 editions published in 1995 in English and held by 48 WorldCat member libraries worldwide
8 editions published in 1995 in English and held by 48 WorldCat member libraries worldwide
Handbook of combinatorics(
Book
)
8 editions published between 1995 and 2006 in English and held by 32 WorldCat member libraries worldwide
8 editions published between 1995 and 2006 in English and held by 32 WorldCat member libraries worldwide
Handbook of combinatorics(
Book
)
2 editions published in 1995 in English and held by 25 WorldCat member libraries worldwide
2 editions published in 1995 in English and held by 25 WorldCat member libraries worldwide
Handbook of combinatorics(
Book
)
2 editions published in 1995 in English and held by 25 WorldCat member libraries worldwide
2 editions published in 1995 in English and held by 25 WorldCat member libraries worldwide
Matheonmathematics for key technologies(
Book
)
2 editions published in 2014 in English and held by 23 WorldCat member libraries worldwide
Mathematics: intellectual endeavor, production factor, key technology, key to key technologies? Mathematics is all of these! The last three of its facets have been the focus of the research and development in the Berlinbased DFG Research Center MATHEON in the last twelve years. Through these activities MATHEON has become an international trademark for carrying out creative, applicationdriven research in mathematics and for cooperating with industrial partners in the solution of complex problems in key technologies. Modern key technologies have become highly sophisticated, integrating aspects of engineering, computer, business and other sciences. Flexible mathematical models, as well as fast and accurate methods for numerical simulation and optimization open new possibilities to handle the indicated complexities, to react quickly, and to explore new options. Researchers in mathematical fields such as Optimization, Discrete Mathematics, Numerical Analysis, Scientific Computing, Applied Analysis and Stochastic Analysis have to work hand in hand with scientists and engineers to fully exploit this potential and to strengthen the transversal role of mathematics in the solution of the challenging problems in key technologies. This book presents in seven chapters the highlights of the research work carried out in the MATHEON application areas: Life Sciences, Networks, Production, Electronic and Photonic Devices, Finance, Visualization, and Education. The chapters summarize many of the contributions, put them in the context of current mathematical research activities and outline their impact in various key technologies. To make some of the results more easily accessible to the general public, a large number of "showcases" are presented that illustrate a few success stories
2 editions published in 2014 in English and held by 23 WorldCat member libraries worldwide
Mathematics: intellectual endeavor, production factor, key technology, key to key technologies? Mathematics is all of these! The last three of its facets have been the focus of the research and development in the Berlinbased DFG Research Center MATHEON in the last twelve years. Through these activities MATHEON has become an international trademark for carrying out creative, applicationdriven research in mathematics and for cooperating with industrial partners in the solution of complex problems in key technologies. Modern key technologies have become highly sophisticated, integrating aspects of engineering, computer, business and other sciences. Flexible mathematical models, as well as fast and accurate methods for numerical simulation and optimization open new possibilities to handle the indicated complexities, to react quickly, and to explore new options. Researchers in mathematical fields such as Optimization, Discrete Mathematics, Numerical Analysis, Scientific Computing, Applied Analysis and Stochastic Analysis have to work hand in hand with scientists and engineers to fully exploit this potential and to strengthen the transversal role of mathematics in the solution of the challenging problems in key technologies. This book presents in seven chapters the highlights of the research work carried out in the MATHEON application areas: Life Sciences, Networks, Production, Electronic and Photonic Devices, Finance, Visualization, and Education. The chapters summarize many of the contributions, put them in the context of current mathematical research activities and outline their impact in various key technologies. To make some of the results more easily accessible to the general public, a large number of "showcases" are presented that illustrate a few success stories
Packing Steiner Trees : polyhedral investigations by
Martin Grötschel(
Book
)
12 editions published between 1992 and 1994 in 3 languages and held by 21 WorldCat member libraries worldwide
We consider the Steiner tree packing problem from a polyhedral point of view and define an appropriate polyhedron, called the Steiner tree packing polyhedron. The goal of this paper is to (partially) describe this polyhedron by means of inequalities. It turns out that, under mild assumptions, each inequality that defines a facet for the (single) Steiner tree polyhedron can be lifted to a facetdefining inequality for the Steiner tree packing polyhedron. The main emphasis of this paper lies on the presentation of socalled joint inequalities that are valid and facet defining for this polyhedron. Inequalities of this kind involve at least two Steiner trees. The classes of inequalities we have found form the basis of a branch & cut algorithm. This algorithm is described in our companion paper [GMW92]."
12 editions published between 1992 and 1994 in 3 languages and held by 21 WorldCat member libraries worldwide
We consider the Steiner tree packing problem from a polyhedral point of view and define an appropriate polyhedron, called the Steiner tree packing polyhedron. The goal of this paper is to (partially) describe this polyhedron by means of inequalities. It turns out that, under mild assumptions, each inequality that defines a facet for the (single) Steiner tree polyhedron can be lifted to a facetdefining inequality for the Steiner tree packing polyhedron. The main emphasis of this paper lies on the presentation of socalled joint inequalities that are valid and facet defining for this polyhedron. Inequalities of this kind involve at least two Steiner trees. The classes of inequalities we have found form the basis of a branch & cut algorithm. This algorithm is described in our companion paper [GMW92]."
Facets of combinatorial optimization : Festschrift for Martin Grötschel by
M Jünger(
Book
)
4 editions published in 2013 in English and held by 19 WorldCat member libraries worldwide
Martin Grötschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin Grötschel's doctoral descendant tree 19832012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 greatgrandchildren, and 2 greatgreatgrandchildren, a total of 139 doctoral descendants. This book starts with a personal tribute to Martin Grötschel by the editors (Part I), a contribution by his very special "predecessor" Manfred Padberg on "Facets and Rank of Integer Polyhedra" (Part II), and the doctoral descendant tree 19832012 (Part III). The core of this book (Part IV) contains 16 contributions, each of which is coauthored by at least one doctoral descendant. The sequence of the articles starts with contributions to the theory of mathematical optimization, including polyhedral combinatorics, extended formulations, mixedinteger convex optimization, superclasses of perfect graphs, efficient algorithms for subtreetelecenters, junctions in acyclic graphs, and preemptive restricted strip covering, as well as efficient approximation of nonpreemptive restricted strip covering. Combinations of new theoretical insights with algorithms and experiments deal with network design problems, combinatorial optimization problems with submodular objective functions, and more general mixedinteger nonlinear optimization problems. Applications include VLSI layout design, systems biology, wireless network design, meanrisk optimization, and gas network optimization. Computational studies include a semidefinite branch and cut approach for the max kcut problem, mixedinteger nonlinear optimal control, and mixedinteger linear optimization for scheduling and routing of flyin safari planes. The two closing articles are devoted to computational advances in general mixedinteger linear optimization, the first by scientists working in industry, the second by scientists working in academia. These articles reflect the "scientific facets" of Martin Grötschel who has set standards in theory, computation, and applications  P.4 of cover
4 editions published in 2013 in English and held by 19 WorldCat member libraries worldwide
Martin Grötschel is one of the most influential mathematicians of our time. He has received numerous honors and holds a number of key positions in the international mathematical community. He celebrated his 65th birthday on September 10, 2013. Martin Grötschel's doctoral descendant tree 19832012, i.e., the first 30 years, features 39 children, 74 grandchildren, 24 greatgrandchildren, and 2 greatgreatgrandchildren, a total of 139 doctoral descendants. This book starts with a personal tribute to Martin Grötschel by the editors (Part I), a contribution by his very special "predecessor" Manfred Padberg on "Facets and Rank of Integer Polyhedra" (Part II), and the doctoral descendant tree 19832012 (Part III). The core of this book (Part IV) contains 16 contributions, each of which is coauthored by at least one doctoral descendant. The sequence of the articles starts with contributions to the theory of mathematical optimization, including polyhedral combinatorics, extended formulations, mixedinteger convex optimization, superclasses of perfect graphs, efficient algorithms for subtreetelecenters, junctions in acyclic graphs, and preemptive restricted strip covering, as well as efficient approximation of nonpreemptive restricted strip covering. Combinations of new theoretical insights with algorithms and experiments deal with network design problems, combinatorial optimization problems with submodular objective functions, and more general mixedinteger nonlinear optimization problems. Applications include VLSI layout design, systems biology, wireless network design, meanrisk optimization, and gas network optimization. Computational studies include a semidefinite branch and cut approach for the max kcut problem, mixedinteger nonlinear optimal control, and mixedinteger linear optimization for scheduling and routing of flyin safari planes. The two closing articles are devoted to computational advances in general mixedinteger linear optimization, the first by scientists working in industry, the second by scientists working in academia. These articles reflect the "scientific facets" of Martin Grötschel who has set standards in theory, computation, and applications  P.4 of cover
Optimization stories by International Symposium on Mathematical Programming(
Book
)
4 editions published in 2012 in English and held by 17 WorldCat member libraries worldwide
4 editions published in 2012 in English and held by 17 WorldCat member libraries worldwide
Polynomial inequalities representing polyhedra(
)
2 editions published between 2003 and 2004 in English and held by 14 WorldCat member libraries worldwide
Our main result is that every dimensional polytope can be described by at most polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an dimensional pointed polyhedral cone we prove the bound and for arbitrary polyhedra we get a constructible representation by polynomial inequalities
2 editions published between 2003 and 2004 in English and held by 14 WorldCat member libraries worldwide
Our main result is that every dimensional polytope can be described by at most polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an dimensional pointed polyhedral cone we prove the bound and for arbitrary polyhedra we get a constructible representation by polynomial inequalities
Order picking in an automatic warehouse : solving online asymmetric TSPs by Norbert Ascheuer(
Book
)
5 editions published between 1998 and 2000 in English and held by 14 WorldCat member libraries worldwide
Traveling Salesman Problem, OnlineAlgorithm, Automatic Storage System
5 editions published between 1998 and 2000 in English and held by 14 WorldCat member libraries worldwide
Traveling Salesman Problem, OnlineAlgorithm, Automatic Storage System
Design of broadband virtual private networks : model and heuristics for the BWiN by
Andreas Bley(
Book
)
5 editions published between 1998 and 2000 in English and held by 14 WorldCat member libraries worldwide
Telecommunication Network Design, Survivable Networks, Network Capacity Planning, OSPF Routing, Shortest Path Routing, Heuristics
5 editions published between 1998 and 2000 in English and held by 14 WorldCat member libraries worldwide
Telecommunication Network Design, Survivable Networks, Network Capacity Planning, OSPF Routing, Shortest Path Routing, Heuristics
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Related Identities
 Lovász, László 1948 Other Honoree Author Editor
 Bachem, A. Other Author Editor
 Korte, B. H. (Bernhard H.) 1938 Other Author Editor
 Schrijver, A.
 Graham, Ronald L. 1935 Other Author Editor
 Mehrmann, V. L. (Volker Ludwig) 1955 Editor
 Lucas, Klaus
 Katona, G. Editor
 Rambau, Jörg Editor
 Krumke, Sven O. Editor
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Associated Subjects
Algorithms Broadband communication systems Business mathematics Combinations Combinatorial analysis Combinatorial geometry Combinatorial optimization Computational complexity Computer science Computer scienceMathematics Discrete groups Economics Electronic data processing Engineering Engineering mathematics Factors of production Geometry of numbers Information theory Integer programming Life sciencesMathematics Lovász, László, Mathematical optimization Mathematics MathematicsIndustrial applications Number theory Operations research Packet switching (Data transmission) Polyhedra Production (Economic theory) Production controlMathematical models Production functions (Economic theory) Programming (Mathematics) ScienceMathematics Steiner systems Traveling salesman problem
Alternative Names
Groetschel, Martin
Grötschel, M.
Grötschel, M. 1948
Grötschel, M. (Martin)
Martin Grötschel deutscher Mathematiker
Martin Grötschel Duits wiskundige
Martin Grötschel German mathematician
Martin Grötschel matemático alemán
Martin Grötschel tysk matematikar
Martin Grötschel tysk matematiker
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