Newton's method for fractional combinatorial optimization:
Abstract: "We consider Newton's method for the linear fractional combinatorial optimization. First we show a strongly polynomial bound on the number of iterations for the general case. Then we consider the transshipment problem when the maximum arc cost is being minimized. This problem can...
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Stanford, Calif.
1992
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| Series: | Stanford University / Computer Science Department: Report STAN CS
1406 |
| Subjects: | |
| Summary: | Abstract: "We consider Newton's method for the linear fractional combinatorial optimization. First we show a strongly polynomial bound on the number of iterations for the general case. Then we consider the transshipment problem when the maximum arc cost is being minimized. This problem can be reduced to the maximum mean-weight cut problem, which is a special case of the linear fractional combinatorial optimization. We prove that Newton's method runs in O(m) iterations for the maximum mean-weight cut problem. One iteration is dominated by the maximum flow computation, so the overall running time is Õ(m²n). The previous fastest algorithm is based on Meggido's parametric search method and runs in Õ(n³m) time." |
| Physical Description: | 20 S. |
Staff View
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| 490 | 1 | |a Stanford University / Computer Science Department: Report STAN CS |v 1406 | |
| 520 | 3 | |a Abstract: "We consider Newton's method for the linear fractional combinatorial optimization. First we show a strongly polynomial bound on the number of iterations for the general case. Then we consider the transshipment problem when the maximum arc cost is being minimized. This problem can be reduced to the maximum mean-weight cut problem, which is a special case of the linear fractional combinatorial optimization. We prove that Newton's method runs in O(m) iterations for the maximum mean-weight cut problem. One iteration is dominated by the maximum flow computation, so the overall running time is Õ(m²n). The previous fastest algorithm is based on Meggido's parametric search method and runs in Õ(n³m) time." | |
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| 650 | 4 | |a Combinatorial optimization |x Data processing | |
| 650 | 4 | |a Newton-Raphson method |x Data processing | |
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Record in the Search Index
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| author | Radzik, Tomasz |
| author_facet | Radzik, Tomasz |
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| author_variant | t r tr |
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| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)27036483 (DE-599)BVBBV008993180 |
| dewey-full | 511/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:28:08Z |
| institution | BVB |
| language | English |
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| physical | 20 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
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| series2 | Stanford University / Computer Science Department: Report STAN CS |
| spelling | Radzik, Tomasz Verfasser aut Newton's method for fractional combinatorial optimization by Thomas Radzik Stanford, Calif. 1992 20 S. txt rdacontent n rdamedia nc rdacarrier Stanford University / Computer Science Department: Report STAN CS 1406 Abstract: "We consider Newton's method for the linear fractional combinatorial optimization. First we show a strongly polynomial bound on the number of iterations for the general case. Then we consider the transshipment problem when the maximum arc cost is being minimized. This problem can be reduced to the maximum mean-weight cut problem, which is a special case of the linear fractional combinatorial optimization. We prove that Newton's method runs in O(m) iterations for the maximum mean-weight cut problem. One iteration is dominated by the maximum flow computation, so the overall running time is Õ(m²n). The previous fastest algorithm is based on Meggido's parametric search method and runs in Õ(n³m) time." Datenverarbeitung Combinatorial optimization Data processing Newton-Raphson method Data processing Computer Science Department: Report STAN CS Stanford University 1406 (DE-604)BV008928280 1406 |
| spellingShingle | Radzik, Tomasz Newton's method for fractional combinatorial optimization Datenverarbeitung Combinatorial optimization Data processing Newton-Raphson method Data processing |
| title | Newton's method for fractional combinatorial optimization |
| title_auth | Newton's method for fractional combinatorial optimization |
| title_exact_search | Newton's method for fractional combinatorial optimization |
| title_full | Newton's method for fractional combinatorial optimization by Thomas Radzik |
| title_fullStr | Newton's method for fractional combinatorial optimization by Thomas Radzik |
| title_full_unstemmed | Newton's method for fractional combinatorial optimization by Thomas Radzik |
| title_short | Newton's method for fractional combinatorial optimization |
| title_sort | newton s method for fractional combinatorial optimization |
| topic | Datenverarbeitung Combinatorial optimization Data processing Newton-Raphson method Data processing |
| topic_facet | Datenverarbeitung Combinatorial optimization Data processing Newton-Raphson method Data processing |
| volume_link | (DE-604)BV008928280 |
| work_keys_str_mv | AT radziktomasz newtonsmethodforfractionalcombinatorialoptimization |