Geometric Algorithms and Combinatorial Optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1993
|
| Edition: | Second Corrected Edition |
| Series: | Algorithms and Combinatorics
2 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 Nevertheless, we do not feel that the ongoing research has made this book outdated.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 Dyer-Frieze-Kannan 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 |
| Physical Description: | 1 Online-Ressource (XII, 362p. 23 illus) |
| ISBN: | 9783642782404 9783642782428 |
| ISSN: | 0937-5511 |
| DOI: | 10.1007/978-3-642-78240-4 |
Staff View
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| 500 | |a 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 Nevertheless, we do not feel that the ongoing research has made this book outdated.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 Dyer-Frieze-Kannan 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 | ||
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| illustrated | Not Illustrated |
| indexdate | 2025-02-24T09:01:07Z |
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| issn | 0937-5511 |
| language | English |
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| spelling | Grötschel, Martin Verfasser aut Geometric Algorithms and Combinatorial Optimization by Martin Grötschel, László Lovász, Alexander Schrijver Second Corrected Edition Berlin, Heidelberg Springer Berlin Heidelberg 1993 1 Online-Ressource (XII, 362p. 23 illus) txt rdacontent c rdamedia cr rdacarrier Algorithms and Combinatorics 2 0937-5511 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 Dyer-Frieze-Kannan 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 Mathematics Systems theory Combinatorics Mathematical optimization Economics Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Economic Theory Mathematik Wirtschaft Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Polynomialzeitalgorithmus (DE-588)4199652-5 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Polyedrische Kombinatorik (DE-588)4132100-5 gnd rswk-swf Kombinatorische Optimierung (DE-588)4031826-6 s Polyedrische Kombinatorik (DE-588)4132100-5 s Polynomialzeitalgorithmus (DE-588)4199652-5 s 1\p DE-604 Geometrie (DE-588)4020236-7 s 2\p DE-604 Algorithmische Geometrie (DE-588)4130267-9 s 3\p DE-604 Kombinatorische Geometrie (DE-588)4140733-7 s 4\p DE-604 Lovász, László Sonstige oth Schrijver, Alexander Sonstige oth https://doi.org/10.1007/978-3-642-78240-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Grötschel, Martin Geometric Algorithms and Combinatorial Optimization Mathematics Systems theory Combinatorics Mathematical optimization Economics Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Economic Theory Mathematik Wirtschaft Kombinatorische Geometrie (DE-588)4140733-7 gnd Polynomialzeitalgorithmus (DE-588)4199652-5 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Geometrie (DE-588)4020236-7 gnd Polyedrische Kombinatorik (DE-588)4132100-5 gnd |
| subject_GND | (DE-588)4140733-7 (DE-588)4199652-5 (DE-588)4031826-6 (DE-588)4130267-9 (DE-588)4020236-7 (DE-588)4132100-5 |
| title | Geometric Algorithms and Combinatorial Optimization |
| title_auth | Geometric Algorithms and Combinatorial Optimization |
| title_exact_search | Geometric Algorithms and Combinatorial Optimization |
| title_full | Geometric Algorithms and Combinatorial Optimization by Martin Grötschel, László Lovász, Alexander Schrijver |
| title_fullStr | Geometric Algorithms and Combinatorial Optimization by Martin Grötschel, László Lovász, Alexander Schrijver |
| title_full_unstemmed | Geometric Algorithms and Combinatorial Optimization by Martin Grötschel, László Lovász, Alexander Schrijver |
| title_short | Geometric Algorithms and Combinatorial Optimization |
| title_sort | geometric algorithms and combinatorial optimization |
| topic | Mathematics Systems theory Combinatorics Mathematical optimization Economics Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Economic Theory Mathematik Wirtschaft Kombinatorische Geometrie (DE-588)4140733-7 gnd Polynomialzeitalgorithmus (DE-588)4199652-5 gnd Kombinatorische Optimierung (DE-588)4031826-6 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Geometrie (DE-588)4020236-7 gnd Polyedrische Kombinatorik (DE-588)4132100-5 gnd |
| topic_facet | Mathematics Systems theory Combinatorics Mathematical optimization Economics Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Economic Theory Mathematik Wirtschaft Kombinatorische Geometrie Polynomialzeitalgorithmus Kombinatorische Optimierung Algorithmische Geometrie Geometrie Polyedrische Kombinatorik |
| url | https://doi.org/10.1007/978-3-642-78240-4 |
| work_keys_str_mv | AT grotschelmartin geometricalgorithmsandcombinatorialoptimization AT lovaszlaszlo geometricalgorithmsandcombinatorialoptimization AT schrijveralexander geometricalgorithmsandcombinatorialoptimization |