Grötschel, MartinOverview
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Most widely held works by
Martin Grötschel
Geometric algorithms and combinatorial optimization
by Martin Grötschel
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31 editions published between 1981 and 2012 in English and German and held by 596 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 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. The ellipsoid method was used by Khachiyan to show the polynomial time solvability of linear programming. The basis reduction method yields a polynomial time procedure for certain diophantine approximation problems. A combination of these techniques makes it possible to show the polynomial time solvability of many questions concerning poyhedra  for instance, of linear programming problems having possibly exponentially many inequalities. Utilizing results from polyhedral combinatorics, it provides short proofs of the poynomial time solvability of many combinatiorial optimization problems. For a number of these problems, the geometric algorithms discussed in this book are the only techniques known to derive polynomial time solvability. 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
Handbook of combinatorics
by Ronald L Graham
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9 editions published in 1995 in English and held by 508 WorldCat member libraries worldwide
Building bridges between mathematics and computer science
by Martin Grötschel
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14 editions published between 2008 and 2011 in English and held by 395 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 Augus
Production factor mathematics
by Martin Grötschel
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13 editions published in 2010 in English and held by 395 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
Mathematical programming : the state of the art, Bonn 1982
by A Bachem
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10 editions published in 1983 in English and held by 348 WorldCat member libraries worldwide
Bonn Workshop on Combinatorial Optimization
by 1980, Bonn) Workshop on Combinatorial Optimization (4
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19 editions published between 1982 and 2011 in English and Dutch and held by 345 WorldCat member libraries worldwide Bonn Workshop on Combinatorial Optimization
Online optimization of large scale systems
by Martin Grötschel
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9 editions published between 2001 and 2010 in English and held by 184 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
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8 editions published in 2004 in English and held by 141 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
Besser als Mathe Moderne angewandte Mathematik aus dem Matheon zum Mitmachen
by Katja Biermann
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7 editions published between 2010 and 2013 in German and held by 136 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
Produktionsfaktor Mathematik wie Mathematik Technik und Wirtschaft bewegt
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4 editions published in 2009 in German and English and held by 124 WorldCat member libraries worldwide
Handbook of combinatorics
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11 editions published between 1995 and 2006 in English and held by 73 WorldCat member libraries worldwide
Handbook of combinatorics
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5 editions published in 1995 in English and held by 72 WorldCat member libraries worldwide
Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme
by Martin Grötschel
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4 editions published in 1977 in German and held by 60 WorldCat member libraries worldwide
Packing Steiner Trees : polyhedral investigations
by Martin Grötschel
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14 editions published between 1992 and 1998 in 3 languages and held by 25 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
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3 editions published in 2013 in English and held by 15 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
Models for line planning in public transport
by Ralf Borndörfer
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5 editions published between 2004 and 2008 in English and Undetermined and held by 13 WorldCat member libraries worldwide The line planning problem is one of the fundamental problems in strategic planning of public and rail transport. It consists of finding lines and corresponding frequencies in a public transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize its operating cost; the passengers request short travel times. We propose two new multicommodity flow models for line planning. Their main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically
Polynomial inequalities representing polyhedra
by Hartwig Bosse
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5 editions published between 2003 and 2004 in English and held by 13 WorldCat member libraries worldwide Our main result is that every ndimensional polytope can be described by at most 2n  1 polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an ndimensional pointed polyhedral cone we prove the bound 2n  2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities
Public transport to the fORe!
by Ralf Borndörfer
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3 editions published in 2005 in English and held by 12 WorldCat member libraries worldwide Abstract: "Can OR methods help the public transport industry to break even? How would you build a public transport system? For example, have a look at Berlin. The BVG, Berlin's public transport company, maintains a network of 2,423 km, operates 197 lines with 3,286 stops, using 1,554 busses, 1,391 subway cars, and 599 trams from 12 depots, and has 13,409 employees [7]. The BVG currently transports about 800 million passengers per year and covers about 40% of the total nonpedestrian traffic volume of the city [18]. Does Berlin have a 'reasonable' public transportation network? Does the BVG run a 'good' transportation system? Is it 'efficient'? These are difficult questions. In fact, politicians, transportation managers, customers, taxpayers, etc., frequently employ judgements such as "good" and "efficient", but nobody can give a definition what this exactly means. Since almost every public transportation system in the world is in the red, the cheapest system is no public transportation at all. On the other hand, the most convenient system for the passenger  a stop in front of every house with direct connections to everywhere  is much to expensive. What is the right compromise? Operations Research has no good answer either  so far. But OR can improve aspects of public transportation significantly, as we want to demonstrate in the following."
Optimization of transportation systems
by Ralf Borndörfer
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4 editions published in 1998 in English and held by 11 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."
Planning problems in public transit
by Ralf Borndörfer
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4 editions published in 2009 in English and held by 11 WorldCat member libraries worldwide Every day, millions of people are transported by buses, trains, and airplanes in Germany. Public transit (PT) is of major importance for the quality of life of individuals as well as the productivity of entire regions. Quality and efficiency of PT systems depend on the political framework (staterun, market oriented) and the suitability of the infrastructure (railway tracks, airport locations), the existing level of service (timetable, flight schedule), the use of adequate technologies (information, control, and booking systems), and the best possible deployment of equipment and resources (energy, vehicles, crews). The decision, planning, and optimization problems arising in this context are often gigantic and ±scream" for mathematical support because of their complexity. This article sketches the state and the relevance of mathematics in planning and operating public transit, describes today's challenges, and suggests a number of innovative actions. The current contribution of mathematics to public transit is  depending on the transportation mode  of varying depth. Air traffic is already well supported by mathematics. Bus traffic made significant advances in recent years, while rail traffic still bears significant opportunities for improvements. In all areas of public transit, the existing potentials are far from being exhausted. For some PT problems, such as vehicle and crew scheduling in bus and air traffic, excellent mathematical tools are not only available, but used in many places. In other areas, such as rolling stock rostering in rail traffic, the performance of the existing mathematical algorithms is not yet sufficient. Some topics are essentially untouched from a mathematical point of view; e.g., there are (except for air traffic) no network design or fare planning models of practical relevance more
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Algorithms 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 Local transitPlanningMathematical models Mathematical optimization Mathematics Number theory Operations research Polyhedra Production (Economic theory) Production controlMathematical models Production functions (Economic theory) Programming (Mathematics) ScienceMathematics Steiner systems Strategic planning Transportation TransportationComputer simulation TransportationPlanning Traveling salesman problem Trees (Graph theory)

Alternative Names
Groetschel, Martin
Grötschel, M.
Grötschel, M. 1948
Grötschel, M. (Martin)
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