Geometric optimization and computational complexity:
Our purpose here is to study problems involving geometric optimization, namely, questions of the type: Is there at least a minimum or at most a maximum number of certain geometric figures, that are within certain distances of other figures (objects). We are also concerned with the optimization of th...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Ithaca, NY
1984
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| Schriftenreihe: | Cornell University <Ithaca, NY> / Dep. of Computer Science: Technical report
629. |
| Schlagworte: | |
| Zusammenfassung: | Our purpose here is to study problems involving geometric optimization, namely, questions of the type: Is there at least a minimum or at most a maximum number of certain geometric figures, that are within certain distances of other figures (objects). We are also concerned with the optimization of the size of these geometric figures. These problems arise as geometric reductions from various classes of location-allocation optimization problems and are inherently not pure combinatorial. Our primary aim, then, is to discover techniques of dealing with such geometric optimization problems, while adapting to these problems the older combinatorial design and analysis methods The task of classifying problems accurately in the polynomial hierarchy is one of increasing importance. To solve an optimization problem deterministically it seems that one must solve both an Necessary conditions for the existence of mazima and minima in optimization problems are generally tied to the question of solvability of an equation or a system of equations. In calculus these equations are algebraic. By generating the minimal polynomial whose root over the field of rational numbers is the solution of the geometric optimization problem on the real (Euclidean) plane, we are able to prove the non-solvability of certain geometric optimization problems by radicals. The algebraic degree of the optimizing solution, which is the degree of the irreducible minimal polynomial for the problem, correlates with the inherent difficulty of constructing the solution and provides an algebraic complexity measure for these geometric optimization problems |
| Beschreibung: | Zugl.: Ithaca, NY, Univ., Diss. |
| Beschreibung: | VII, 87 S. Ill. |
Internformat
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| 490 | 1 | |a Cornell University <Ithaca, NY> / Dep. of Computer Science: Technical report |v 629. | |
| 500 | |a Zugl.: Ithaca, NY, Univ., Diss. | ||
| 520 | 3 | |a Our purpose here is to study problems involving geometric optimization, namely, questions of the type: Is there at least a minimum or at most a maximum number of certain geometric figures, that are within certain distances of other figures (objects). We are also concerned with the optimization of the size of these geometric figures. These problems arise as geometric reductions from various classes of location-allocation optimization problems and are inherently not pure combinatorial. Our primary aim, then, is to discover techniques of dealing with such geometric optimization problems, while adapting to these problems the older combinatorial design and analysis methods | |
| 520 | 3 | |a The task of classifying problems accurately in the polynomial hierarchy is one of increasing importance. To solve an optimization problem deterministically it seems that one must solve both an | |
| 520 | 3 | |a Necessary conditions for the existence of mazima and minima in optimization problems are generally tied to the question of solvability of an equation or a system of equations. In calculus these equations are algebraic. By generating the minimal polynomial whose root over the field of rational numbers is the solution of the geometric optimization problem on the real (Euclidean) plane, we are able to prove the non-solvability of certain geometric optimization problems by radicals. The algebraic degree of the optimizing solution, which is the degree of the irreducible minimal polynomial for the problem, correlates with the inherent difficulty of constructing the solution and provides an algebraic complexity measure for these geometric optimization problems | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Mathematical optimization | |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 810 | 2 | |a Dep. of Computer Science: Technical report |t Cornell University <Ithaca, NY> |v 629. |w (DE-604)BV006185504 |9 629 | |
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| discipline | Informatik Mathematik |
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| id | DE-604.BV006527893 |
| illustrated | Illustrated |
| indexdate | 2025-01-10T17:09:13Z |
| institution | BVB |
| language | English |
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| physical | VII, 87 S. Ill. |
| publishDate | 1984 |
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| series2 | Cornell University <Ithaca, NY> / Dep. of Computer Science: Technical report |
| spelling | Bajaj, Chanderjit Verfasser aut Geometric optimization and computational complexity Ithaca, NY 1984 VII, 87 S. Ill. txt rdacontent n rdamedia nc rdacarrier Cornell University <Ithaca, NY> / Dep. of Computer Science: Technical report 629. Zugl.: Ithaca, NY, Univ., Diss. Our purpose here is to study problems involving geometric optimization, namely, questions of the type: Is there at least a minimum or at most a maximum number of certain geometric figures, that are within certain distances of other figures (objects). We are also concerned with the optimization of the size of these geometric figures. These problems arise as geometric reductions from various classes of location-allocation optimization problems and are inherently not pure combinatorial. Our primary aim, then, is to discover techniques of dealing with such geometric optimization problems, while adapting to these problems the older combinatorial design and analysis methods The task of classifying problems accurately in the polynomial hierarchy is one of increasing importance. To solve an optimization problem deterministically it seems that one must solve both an Necessary conditions for the existence of mazima and minima in optimization problems are generally tied to the question of solvability of an equation or a system of equations. In calculus these equations are algebraic. By generating the minimal polynomial whose root over the field of rational numbers is the solution of the geometric optimization problem on the real (Euclidean) plane, we are able to prove the non-solvability of certain geometric optimization problems by radicals. The algebraic degree of the optimizing solution, which is the degree of the irreducible minimal polynomial for the problem, correlates with the inherent difficulty of constructing the solution and provides an algebraic complexity measure for these geometric optimization problems Computational complexity Mathematical optimization (DE-588)4113937-9 Hochschulschrift gnd-content Dep. of Computer Science: Technical report Cornell University <Ithaca, NY> 629. (DE-604)BV006185504 629 |
| spellingShingle | Bajaj, Chanderjit Geometric optimization and computational complexity Computational complexity Mathematical optimization |
| subject_GND | (DE-588)4113937-9 |
| title | Geometric optimization and computational complexity |
| title_auth | Geometric optimization and computational complexity |
| title_exact_search | Geometric optimization and computational complexity |
| title_full | Geometric optimization and computational complexity |
| title_fullStr | Geometric optimization and computational complexity |
| title_full_unstemmed | Geometric optimization and computational complexity |
| title_short | Geometric optimization and computational complexity |
| title_sort | geometric optimization and computational complexity |
| topic | Computational complexity Mathematical optimization |
| topic_facet | Computational complexity Mathematical optimization Hochschulschrift |
| volume_link | (DE-604)BV006185504 |
| work_keys_str_mv | AT bajajchanderjit geometricoptimizationandcomputationalcomplexity |