Grötschel, Martin
Overview
Works:  248 works in 551 publications in 4 languages and 4,347 library holdings 

Genres:  Conference proceedings Handbooks, manuals, etc 
Roles:  Author, Editor, Contributor 
Classifications:  QA402.5, 511.6 
Publication Timeline
.
Most widely held works by
Martin Grötschel
Geometric algorithms and combinatorial optimization
by
Martin Grötschel(
Book
)
32 editions published between 1980 and 2012 in English and German and held by 624 WorldCat member libraries worldwide
This book develops geometric techniques for proving the polynomial time solvability of problems in convexity theory, geometry, and, in particular, combinatorial optimization. It offers a unifying approach which is based on two fundamental geometric algorithms: the ellipsoid method for finding a point in a convex set and the basis reduction method for point lattices. This book is a continuation and extension of previous research of the authors for which they received the Fulkerson prize, awarded by the Mathematical Programming Society and the American Mathematical Society. The first edition of this book was received enthusiastically by the community of discrete mathematicians, combinatorial optimizers, operations researchers, and computer scientists. To quote just from a few reviews: "The book is written in a very grasping way, legible both for people who are interested in the most important results and for people who are interested in technical details and proofs." #manuscripta geodaetica#1
32 editions published between 1980 and 2012 in English and German and held by 624 WorldCat member libraries worldwide
This book develops geometric techniques for proving the polynomial time solvability of problems in convexity theory, geometry, and, in particular, combinatorial optimization. It offers a unifying approach which is based on two fundamental geometric algorithms: the ellipsoid method for finding a point in a convex set and the basis reduction method for point lattices. This book is a continuation and extension of previous research of the authors for which they received the Fulkerson prize, awarded by the Mathematical Programming Society and the American Mathematical Society. The first edition of this book was received enthusiastically by the community of discrete mathematicians, combinatorial optimizers, operations researchers, and computer scientists. To quote just from a few reviews: "The book is written in a very grasping way, legible both for people who are interested in the most important results and for people who are interested in technical details and proofs." #manuscripta geodaetica#1
Handbook of combinatorics
by
R. L Graham(
Book
)
10 editions published in 1995 in English and Italian and held by 519 WorldCat member libraries worldwide
10 editions published in 1995 in English and Italian and held by 519 WorldCat member libraries worldwide
Production factor mathematics
by
Martin Grötschel(
)
14 editions published in 2010 in English and held by 420 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 autho
14 editions published in 2010 in English and held by 420 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 autho
Building bridges between mathematics and computer science
by
Martin Grötschel(
)
16 editions published between 2008 and 2011 in English and held by 414 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 László Lovász, 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 Lovász'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
16 editions published between 2008 and 2011 in English and held by 414 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 László Lovász, 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 Lovász'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
Bonn Workshop on Combinatorial Optimization
by
1980, Bonn> Workshop on Combinatorial Optimization <4(
Book
)
19 editions published in 1982 in English and Dutch and held by 384 WorldCat member libraries worldwide
Bonn Workshop on Combinatorial Optimization
19 editions published in 1982 in English and Dutch and held by 384 WorldCat member libraries worldwide
Bonn Workshop on Combinatorial Optimization
Mathematical programming : the state of the art, Bonn 1982
by
A Bachem(
Book
)
12 editions published in 1983 in English and German and held by 366 WorldCat member libraries worldwide
About the XIth International Symposium on Mathematical Programming; Mathematical programming: the state of the Art  Bonn 1982; Scientific program
12 editions published in 1983 in English and German and held by 366 WorldCat member libraries worldwide
About the XIth International Symposium on Mathematical Programming; Mathematical programming: the state of the Art  Bonn 1982; Scientific program
Online optimization of large scale systems
by
Martin Grötschel(
Book
)
9 editions published between 2001 and 2010 in English and held by 196 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
9 editions published between 2001 and 2010 in English and held by 196 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
Besser als Mathe Moderne angewandte Mathematik aus dem Matheon zum Mitmachen
by Katja Biermann(
)
7 editions published between 2010 and 2013 in German and held by 176 WorldCat member libraries worldwide
Wozu braucht man Mathematik?' Dieses Buch stellt unter Beweis, dass moderne Mathematik in fast sämtlichen Lebensbereichen eine wichtige Rolle spielt. Aktuelle Forschung wird durch unterhaltsame Aufgaben und ihre Lösungen anschaulich. Das Buch fordert zum aktiven Mitmachen auf und zeigt, dass Mathematik interessant ist und Freude bereiten kann. Für die Anstrengung des konzentrierten Nachdenkens werden die Leserinnen und Leser mit nützlichen und manchmal auch verblüffenden Ergebnissen belohnt. Das Buch basiert auf einer Auswahl der schönsten Aufgaben aus sechs Jahrgängen des mathematischen Advents
7 editions published between 2010 and 2013 in German and held by 176 WorldCat member libraries worldwide
Wozu braucht man Mathematik?' Dieses Buch stellt unter Beweis, dass moderne Mathematik in fast sämtlichen Lebensbereichen eine wichtige Rolle spielt. Aktuelle Forschung wird durch unterhaltsame Aufgaben und ihre Lösungen anschaulich. Das Buch fordert zum aktiven Mitmachen auf und zeigt, dass Mathematik interessant ist und Freude bereiten kann. Für die Anstrengung des konzentrierten Nachdenkens werden die Leserinnen und Leser mit nützlichen und manchmal auch verblüffenden Ergebnissen belohnt. Das Buch basiert auf einer Auswahl der schönsten Aufgaben aus sechs Jahrgängen des mathematischen Advents
The sharpest cut : the impact of Manfred Padberg and his work
by
Martin Grötschel(
Book
)
10 editions published in 2004 in English and held by 150 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
10 editions published in 2004 in English and held by 150 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
(
)
4 editions published in 2009 in German and English and held by 141 WorldCat member libraries worldwide
4 editions published in 2009 in German and English and held by 141 WorldCat member libraries worldwide
Handbook of combinatorics
(
Book
)
8 editions published in 1995 in English and held by 78 WorldCat member libraries worldwide
8 editions published in 1995 in English and held by 78 WorldCat member libraries worldwide
Handbook of combinatorics
(
Book
)
10 editions published between 1995 and 2006 in English and held by 72 WorldCat member libraries worldwide
10 editions published between 1995 and 2006 in English and held by 72 WorldCat member libraries worldwide
Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme
by
Martin Grötschel(
Book
)
4 editions published in 1977 in German and held by 62 WorldCat member libraries worldwide
4 editions published in 1977 in German and held by 62 WorldCat member libraries worldwide
Packing Steiner Trees : a cutting plane algorithm and computational results
by
Martin Grötschel(
Book
)
14 editions published between 1992 and 1994 in 3 languages and held by 29 WorldCat member libraries worldwide
Abstract: "In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem, a problem that arises, e.g., in VLSI routing. The separation problem for Steiner partition inequalities is NPhard in general. We show that it can be solved in polynomial time for those instances that come up in switchbox routing. Our algorithm uses dynamic programming techniques. These techniques are also applied to the much more complicated separation problem for alternating cycle inequalities. In this case we can compute in polynomial time, given some point y, a lower bound for the gap [alpha]  a[superscript T]y over all alternating cycle inequalities a[superscript T]x [> or =] [alpha]. This gives rise to a very effective separation heuristic. A byproduct of our algorithm is the solution of a combinatorial optimization problem that is interesting in its own right: Find a shortest path in a graph where the 'length' of a path is its usual length minus the length of its longest edge."
14 editions published between 1992 and 1994 in 3 languages and held by 29 WorldCat member libraries worldwide
Abstract: "In this paper we investigate separation problems for classes of inequalities valid for the polytope associated with the Steiner tree packing problem, a problem that arises, e.g., in VLSI routing. The separation problem for Steiner partition inequalities is NPhard in general. We show that it can be solved in polynomial time for those instances that come up in switchbox routing. Our algorithm uses dynamic programming techniques. These techniques are also applied to the much more complicated separation problem for alternating cycle inequalities. In this case we can compute in polynomial time, given some point y, a lower bound for the gap [alpha]  a[superscript T]y over all alternating cycle inequalities a[superscript T]x [> or =] [alpha]. This gives rise to a very effective separation heuristic. A byproduct of our algorithm is the solution of a combinatorial optimization problem that is interesting in its own right: Find a shortest path in a graph where the 'length' of a path is its usual length minus the length of its longest edge."
Facets of combinatorial optimization Festschrift for Martin Grötschel
by
M Jünger(
Book
)
3 editions published in 2013 in English and held by 21 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
3 editions published in 2013 in English and held by 21 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 of transportation systems
by
Ralf Borndörfer(
Book
)
5 editions published in 1998 in English and held by 12 WorldCat member libraries worldwide
Abstract: "The world has experienced two hundred years of unprecedented advances in vehicle technology, transport system development, and traffic network extension. Technical progress continues but seems to have reached some limits. Congestion, pollution, and increasing costs have created, in some parts of the world, a climate of hostility against transportation technology. Mobility, however, is still increasing. What can be done? There is no panacea. Interdisciplinary cooperation is necessary, and we are going to argue in this paper that Mathematics can contribute significantly to the solution of some of the problems. We propose to employ methods developed in the Theory of Optimization to make better use of resources and existing technology. One way of optimization is better planning. We will point out that Discrete Mathematics provides a suitable framework for planning decisions within transportation systems. The mathematical approach leads to a better understanding of problems. Precise and quantitative models, and advanced mathematical tools allow for provable and reproducible conclusions. Modern computing equipment is suited to put such methods into practice. At present, mathematical methods contribute, in particular, to the solution of various problems of operational planning. We report about encouraging results achieved so far."
5 editions published in 1998 in English and held by 12 WorldCat member libraries worldwide
Abstract: "The world has experienced two hundred years of unprecedented advances in vehicle technology, transport system development, and traffic network extension. Technical progress continues but seems to have reached some limits. Congestion, pollution, and increasing costs have created, in some parts of the world, a climate of hostility against transportation technology. Mobility, however, is still increasing. What can be done? There is no panacea. Interdisciplinary cooperation is necessary, and we are going to argue in this paper that Mathematics can contribute significantly to the solution of some of the problems. We propose to employ methods developed in the Theory of Optimization to make better use of resources and existing technology. One way of optimization is better planning. We will point out that Discrete Mathematics provides a suitable framework for planning decisions within transportation systems. The mathematical approach leads to a better understanding of problems. Precise and quantitative models, and advanced mathematical tools allow for provable and reproducible conclusions. Modern computing equipment is suited to put such methods into practice. At present, mathematical methods contribute, in particular, to the solution of various problems of operational planning. We report about encouraging results achieved so far."
Produktionsfaktor Mathematik (acatech DISKUTIERT) (German Edition)
by
Martin Grötschel(
)
1 edition published in 2008 in German and held by 12 WorldCat member libraries worldwide
Mathematik trägt immer stärker zur Produktentwicklung und Produktionssicherheit, zur Wertschöpfung und Ressourcenschonung bei. Das Buch erörtert in verschiedenen ingenieurwissenschaftlichen Themenfeldern das Verhältnis von Mathematik und Technikwissenschaften, den Beitrag der Mathematik zur industriellen Wertschöpfung und die Schlüsselrolle der Mathematik bei der Beherrschung komplexer Systeme. Gleichzeitig schlagen die Autoren Maßnahmen zur Verbesserung der Interaktion zwischen Mathematik und Technikwissenschaften, Forschung und Industrie vor
1 edition published in 2008 in German and held by 12 WorldCat member libraries worldwide
Mathematik trägt immer stärker zur Produktentwicklung und Produktionssicherheit, zur Wertschöpfung und Ressourcenschonung bei. Das Buch erörtert in verschiedenen ingenieurwissenschaftlichen Themenfeldern das Verhältnis von Mathematik und Technikwissenschaften, den Beitrag der Mathematik zur industriellen Wertschöpfung und die Schlüsselrolle der Mathematik bei der Beherrschung komplexer Systeme. Gleichzeitig schlagen die Autoren Maßnahmen zur Verbesserung der Interaktion zwischen Mathematik und Technikwissenschaften, Forschung und Industrie vor
Combinatorics in statistical physics
by
C. D Godsil(
Book
)
6 editions published in 1991 in German and English and held by 11 WorldCat member libraries worldwide
6 editions published in 1991 in German and English and held by 11 WorldCat member libraries worldwide
Solving the asymmetric travelling salesman problem with time windows by branchandcut
by Norbert Ascheuer(
Book
)
5 editions published in 1999 in English and held by 11 WorldCat member libraries worldwide
Abstract: "Many optimization problems have several equivalent mathematical models. It is often not apparent which of these models is most suitable for practical computation, in particular, when a certain application with a specific range of instance sizes is in focus. Our paper addresses the Asymmetric Travelling Salesman Problem with time windows (ATSPTW) from such a point of view. The realworld application we aim at is the control of a stacker crane in a warehouse. We have implemented codes based on three alternative integer programming formulations of the ATSPTW and more than ten heuristics. Computational results for realworld instances with up to 233 nodes are reported, showing that a new model presented in a companion paper outperforms the other two models we considered  at least for our special application  and that the heuristics provide acceptable solutions."
5 editions published in 1999 in English and held by 11 WorldCat member libraries worldwide
Abstract: "Many optimization problems have several equivalent mathematical models. It is often not apparent which of these models is most suitable for practical computation, in particular, when a certain application with a specific range of instance sizes is in focus. Our paper addresses the Asymmetric Travelling Salesman Problem with time windows (ATSPTW) from such a point of view. The realworld application we aim at is the control of a stacker crane in a warehouse. We have implemented codes based on three alternative integer programming formulations of the ATSPTW and more than ten heuristics. Computational results for realworld instances with up to 233 nodes are reported, showing that a new model presented in a companion paper outperforms the other two models we considered  at least for our special application  and that the heuristics provide acceptable solutions."
Online dispatching of automobile service units in realtime
by
Martin Grötschel(
Book
)
4 editions published in 2002 in English and held by 11 WorldCat member libraries worldwide
Abstract: "Combinatorial online optimization is an area with lots of applications and potential for significant progress, both in theory and in practice. In this short note we sketch the ADAC problem, a typical largescale online optimization problem, discuss some theoretical and practical issues coming up, and explain, very briefly, how we approach this problem mathematically. Online problems are a battlefield of heuristics with many strong claims about their solution quality. We indicate that a stronger problem orientation and the use of a little more mathematics may yield."
4 editions published in 2002 in English and held by 11 WorldCat member libraries worldwide
Abstract: "Combinatorial online optimization is an area with lots of applications and potential for significant progress, both in theory and in practice. In this short note we sketch the ADAC problem, a typical largescale online optimization problem, discuss some theoretical and practical issues coming up, and explain, very briefly, how we approach this problem mathematically. Online problems are a battlefield of heuristics with many strong claims about their solution quality. We indicate that a stronger problem orientation and the use of a little more mathematics may yield."
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Kids  General  Special 
Related Identities
 Lovász, László 1948 Honoree Editor
 Bachem, A. Author Editor
 Korte, B. H. (Bernhard H.) 1938 Author Editor
 Graham, Ronald L. 1935 Editor
 Schrijver, A.
 Mehrmann, V. L. (Volker Ludwig) 1955 Editor
 Lucas, Klaus
 Katona, G.
 Bonn Workshop on Combinatorial Optimization (1980)
 Rambau, Jörg Editor
Associated Subjects
Algorithms Combinations Combinatorial analysis Combinatorial geometry Combinatorial optimization Computational complexity Computer algorithms Computer science Computer scienceMathematics Discrete groups Economics Electronic data processing Engineering Engineering mathematics Factors of production Geometry of numbers Information theory Integer programming Mathematical optimization Mathematics Number theory Operations research Polyhedra Production (Economic theory) Production controlMathematical models Production functions (Economic theory) Programming (Mathematics) Realtime data processing ScienceMathematics Statistical physics Steiner systems TransportationPlanning Traveling salesman problem Trees (Graph theory)