Algorithms for some linear and fractional combinatorial optimization problems:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Stanford, Calif.
1992
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| Schriftenreihe: | Stanford University / Computer Science Department: Report STAN CS
1451 |
| Schlagwörter: | |
| Abstract: | Abstract: "Network flow problems are classical problems in combinatorial optimization. In this thesis we consider two network flow problems: the minimum arc cost sum flow problem and the minimum maximum arc cost flow problem. Both these problems consist in finding a feasible flow which minimizes a certain objective function. The first problem is to minimize the sum of the costs of flows along individual arcs. This problem is also called the minimum cost flow problem or the transshipment problem. The second problem is to minimize the maximum of the cost of flows along individual arcs We provide a tight analysis of the minimum-mean cycle canceling algorithm, which is a simple strongly polynomial algorithm solving the circulation version of the minimum arc cost sum flow problem. We also improve the upper bound of the dual maximum-mean cut canceling algorithm. The minimum maximum arc cost flow problem is closely related to the maximum mean-weight cut problem and the parametric flow problem. We analyze a very natural algorithm for the maximum mean-weight cut problem. Our analysis improves the best previously known upper bounds for all three problems mentioned here. The maximum mean-weight cut problem is an example of linear fractional combinatorial optimization We consider a generalization of the algorithm for the maximum mean-weight cut problem to this class of problems. The resulting scheme is called Newton's method, because it follows the pattern of Newton's root finding technique. We prove that Newton's method runs in a strongly polynomial number of iterations for any linear fractional combinatorial optimization problem. |
| Beschreibung: | Stanford, Calif., Univ., Diss. |
| Umfang: | VIII, 92 S. |
Internformat
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| 100 | 1 | |a Radzik, Tomasz |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algorithms for some linear and fractional combinatorial optimization problems |c by Tomasz Radzik |
| 264 | 1 | |a Stanford, Calif. |c 1992 | |
| 300 | |a VIII, 92 S. | ||
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| 490 | 1 | |a Stanford University / Computer Science Department: Report STAN CS |v 1451 | |
| 500 | |a Stanford, Calif., Univ., Diss. | ||
| 520 | 3 | |a Abstract: "Network flow problems are classical problems in combinatorial optimization. In this thesis we consider two network flow problems: the minimum arc cost sum flow problem and the minimum maximum arc cost flow problem. Both these problems consist in finding a feasible flow which minimizes a certain objective function. The first problem is to minimize the sum of the costs of flows along individual arcs. This problem is also called the minimum cost flow problem or the transshipment problem. The second problem is to minimize the maximum of the cost of flows along individual arcs | |
| 520 | 3 | |a We provide a tight analysis of the minimum-mean cycle canceling algorithm, which is a simple strongly polynomial algorithm solving the circulation version of the minimum arc cost sum flow problem. We also improve the upper bound of the dual maximum-mean cut canceling algorithm. The minimum maximum arc cost flow problem is closely related to the maximum mean-weight cut problem and the parametric flow problem. We analyze a very natural algorithm for the maximum mean-weight cut problem. Our analysis improves the best previously known upper bounds for all three problems mentioned here. The maximum mean-weight cut problem is an example of linear fractional combinatorial optimization | |
| 520 | 3 | |a We consider a generalization of the algorithm for the maximum mean-weight cut problem to this class of problems. The resulting scheme is called Newton's method, because it follows the pattern of Newton's root finding technique. We prove that Newton's method runs in a strongly polynomial number of iterations for any linear fractional combinatorial optimization problem. | |
| 650 | 4 | |a Combinatorial optimization | |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 810 | 2 | |a Computer Science Department: Report STAN CS |t Stanford University |v 1451 |w (DE-604)BV008928280 |9 1451 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-005952943 | |
Datensatz im Suchindex
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| illustrated | Not Illustrated |
| indexdate | 2024-12-20T09:30:20Z |
| institution | BVB |
| language | English |
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| physical | VIII, 92 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
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| series2 | Stanford University / Computer Science Department: Report STAN CS |
| spelling | Radzik, Tomasz Verfasser aut Algorithms for some linear and fractional combinatorial optimization problems by Tomasz Radzik Stanford, Calif. 1992 VIII, 92 S. txt rdacontent n rdamedia nc rdacarrier Stanford University / Computer Science Department: Report STAN CS 1451 Stanford, Calif., Univ., Diss. Abstract: "Network flow problems are classical problems in combinatorial optimization. In this thesis we consider two network flow problems: the minimum arc cost sum flow problem and the minimum maximum arc cost flow problem. Both these problems consist in finding a feasible flow which minimizes a certain objective function. The first problem is to minimize the sum of the costs of flows along individual arcs. This problem is also called the minimum cost flow problem or the transshipment problem. The second problem is to minimize the maximum of the cost of flows along individual arcs We provide a tight analysis of the minimum-mean cycle canceling algorithm, which is a simple strongly polynomial algorithm solving the circulation version of the minimum arc cost sum flow problem. We also improve the upper bound of the dual maximum-mean cut canceling algorithm. The minimum maximum arc cost flow problem is closely related to the maximum mean-weight cut problem and the parametric flow problem. We analyze a very natural algorithm for the maximum mean-weight cut problem. Our analysis improves the best previously known upper bounds for all three problems mentioned here. The maximum mean-weight cut problem is an example of linear fractional combinatorial optimization We consider a generalization of the algorithm for the maximum mean-weight cut problem to this class of problems. The resulting scheme is called Newton's method, because it follows the pattern of Newton's root finding technique. We prove that Newton's method runs in a strongly polynomial number of iterations for any linear fractional combinatorial optimization problem. Combinatorial optimization (DE-588)4113937-9 Hochschulschrift gnd-content Computer Science Department: Report STAN CS Stanford University 1451 (DE-604)BV008928280 1451 |
| spellingShingle | Radzik, Tomasz Algorithms for some linear and fractional combinatorial optimization problems Combinatorial optimization |
| subject_GND | (DE-588)4113937-9 |
| title | Algorithms for some linear and fractional combinatorial optimization problems |
| title_auth | Algorithms for some linear and fractional combinatorial optimization problems |
| title_exact_search | Algorithms for some linear and fractional combinatorial optimization problems |
| title_full | Algorithms for some linear and fractional combinatorial optimization problems by Tomasz Radzik |
| title_fullStr | Algorithms for some linear and fractional combinatorial optimization problems by Tomasz Radzik |
| title_full_unstemmed | Algorithms for some linear and fractional combinatorial optimization problems by Tomasz Radzik |
| title_short | Algorithms for some linear and fractional combinatorial optimization problems |
| title_sort | algorithms for some linear and fractional combinatorial optimization problems |
| topic | Combinatorial optimization |
| topic_facet | Combinatorial optimization Hochschulschrift |
| volume_link | (DE-604)BV008928280 |
| work_keys_str_mv | AT radziktomasz algorithmsforsomelinearandfractionalcombinatorialoptimizationproblems |