Balanced network flows. II. Simple augmentation algorithms
In previous papers, we discussed the fundamental theory of matching problems and algorithms in terms of a network flow model. In this paper, we present explicit augmentation procedures which apply to the wide range of capacitated matching problems and which are highly efficient for k‐factor problems...
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| Published in: | Networks Vol. 33; no. 1; pp. 29 - 41 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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New York
John Wiley & Sons, Inc
01.01.1999
John Wiley & Sons |
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| ISSN: | 0028-3045, 1097-0037 |
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| Abstract | In previous papers, we discussed the fundamental theory of matching problems and algorithms in terms of a network flow model. In this paper, we present explicit augmentation procedures which apply to the wide range of capacitated matching problems and which are highly efficient for k‐factor problems and the f‐factor problem. © 1999 John Wiley & Sons, Inc. Networks 33: 29–41, 1999 |
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| AbstractList | In previous papers, we discussed the fundamental theory of matching problems and algorithms in terms of a network flow model. In this paper, we present explicit augmentation procedures which apply to the wide range of capacitated matching problems and which are highly efficient for k‐factor problems and the f‐factor problem. © 1999 John Wiley & Sons, Inc. Networks 33: 29–41, 1999 |
| Author | Fremuth-Paeger, Christian Jungnickel, Dieter |
| Author_xml | – sequence: 1 givenname: Christian surname: Fremuth-Paeger fullname: Fremuth-Paeger, Christian organization: Lehrstuhl für Diskrete Mathematik, Optimierung und Operations Research, University of Augsburg, D-86135 Augsburg, Germany – sequence: 2 givenname: Dieter surname: Jungnickel fullname: Jungnickel, Dieter email: jungnickel@math.uni-augsburg.de organization: Lehrstuhl für Diskrete Mathematik, Optimierung und Operations Research, University of Augsburg, D-86135 Augsburg, Germany |
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| Issue | 1 |
| Keywords | First depth search Balancing Network flow Capacity Symmetric graph Heuristic method Graph theory Algorithm |
| Language | English |
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| Notes | ark:/67375/WNG-R21ZZ6PX-V ArticleID:NET2 The results of this paper form part of the first author's doctoral thesis which was written under the supervision of the second author. AMS subject classification: 05C70, 90B10, 90C35 istex:CEB476EF40B5E1749F8D4718E1C5CAE29EE0ABEC The results of this paper form part of the first author's doctoral thesis which was written under the supervision of the second author. AMS subject classification: 05C70, 90B10, 90C35 |
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| References | T. H. Corman, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, MIT Press, Cambridge, MA, 1990.. T. Kameda and I. Munro, An O(|V|*|E|) algorithm for maximum matching of graphs, Computing 12 1974, 91-98. R. P. Anstee, An algorithmic proof of Tutte's f-factor theorem, J Algor 6 1985, 112-131. L. R. Ford and D. R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, NJ, 1962. H. N. Gabow and R. E. Tarjan, A linear-time algorithm for a special case of disjoint set union, J Comput Syst Sci 30 1985, 209-221. R. E. Tarjan, Efficiency of a good but not linear set union algorithm, J ACM 22 1975, 215-225. V. V. Vazirani, A theory of alternating paths and blossoms for proving correctness of the O(√VE) general graph maximum matching algorithm, Combinatorica 14 1994, 71-109. W. Kocay and D. Stone, An algorithm for balanced flows, JCMCC 19 1995, 3-31. R. E. Tarjan, Data Structures and Network Algorithms, SIAM, Philadelphia, PA, 1983. C. Fremuth-Paeger and D. Jungnickel, Balanced network flows (I): A unifying framework for design and analysis of matching algorithms, Networks, to appear. 1996 1990. 1994; 14 1962 1974; 12 1983 1985; 30 1995; 19 1975; 22 1985; 6 Gabow (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB7) 1985; 30 Tarjan (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB12) 1983 Vazirani (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB13) 1994; 14 Corman (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB3) 1990. Kameda (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB8) 1974; 12 Kocay (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB9) 1995; 19 Tarjan (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB11) 1975; 22 Micali (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB10) Bergdolt (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB2) 1996 Anstee (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB1) 1985; 6 Fremuth-Paeger (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB5) Ford (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB4) 1962 Fremuth-Paeger (10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB6) |
| References_xml | – reference: W. Kocay and D. Stone, An algorithm for balanced flows, JCMCC 19 1995, 3-31. – reference: H. N. Gabow and R. E. Tarjan, A linear-time algorithm for a special case of disjoint set union, J Comput Syst Sci 30 1985, 209-221. – reference: T. Kameda and I. Munro, An O(|V|*|E|) algorithm for maximum matching of graphs, Computing 12 1974, 91-98. – reference: R. E. Tarjan, Data Structures and Network Algorithms, SIAM, Philadelphia, PA, 1983. – reference: R. P. Anstee, An algorithmic proof of Tutte's f-factor theorem, J Algor 6 1985, 112-131. – reference: L. R. Ford and D. R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, NJ, 1962. – reference: C. Fremuth-Paeger and D. Jungnickel, Balanced network flows (I): A unifying framework for design and analysis of matching algorithms, Networks, to appear. – reference: T. H. Corman, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, MIT Press, Cambridge, MA, 1990.. – reference: V. V. Vazirani, A theory of alternating paths and blossoms for proving correctness of the O(√VE) general graph maximum matching algorithm, Combinatorica 14 1994, 71-109. – reference: R. E. Tarjan, Efficiency of a good but not linear set union algorithm, J ACM 22 1975, 215-225. – year: 1996 – volume: 19 start-page: 3 year: 1995 end-page: 31 article-title: An algorithm for balanced flows publication-title: JCMCC – start-page: 17 end-page: 27 – volume: 22 start-page: 215 year: 1975 end-page: 225 article-title: Efficiency of a good but not linear set union algorithm publication-title: J ACM – year: 1983 – year: 1962 – volume: 12 start-page: 91 year: 1974 end-page: 98 article-title: An O(|V|*|E|) algorithm for maximum matching of graphs publication-title: Computing – article-title: Balanced network flows (I): A unifying framework for design and analysis of matching algorithms publication-title: Networks – volume: 30 start-page: 209 year: 1985 end-page: 221 article-title: A linear‐time algorithm for a special case of disjoint set union publication-title: J Comput Syst Sci – year: 1990. – volume: 14 start-page: 71 year: 1994 end-page: 109 article-title: A theory of alternating paths and blossoms for proving correctness of the O(√ ) general graph maximum matching algorithm publication-title: Combinatorica – volume: 6 start-page: 112 year: 1985 end-page: 131 article-title: An algorithmic proof of Tutte's f‐factor theorem publication-title: J Algor – year: 1996 ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB2 – volume: 12 start-page: 91 year: 1974 ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB8 publication-title: Computing doi: 10.1007/BF02239502 – volume: 6 start-page: 112 year: 1985 ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB1 publication-title: J Algor doi: 10.1016/0196-6774(85)90022-7 – volume: 22 start-page: 215 year: 1975 ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB11 publication-title: J ACM doi: 10.1145/321879.321884 – volume-title: Flows in Networks year: 1962 ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB4 – volume-title: Data Structures and Network Algorithms year: 1983 ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB12 doi: 10.1137/1.9781611970265 – volume: 19 start-page: 3 year: 1995 ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB9 publication-title: JCMCC – ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB5 publication-title: Networks – volume: 30 start-page: 209 year: 1985 ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB7 publication-title: J Comput Syst Sci doi: 10.1016/0022-0000(85)90014-5 – ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB6 – volume: 14 start-page: 71 year: 1994 ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB13 publication-title: Combinatorica doi: 10.1007/BF01305952 – ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB10 – volume-title: Introduction to Algorithms year: 1990. ident: 10.1002/(SICI)1097-0037(199901)33:1<29::AID-NET2>3.0.CO;2-U-BIB3 |
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| SubjectTerms | antisymmetrical digraphs Applied sciences augmenting a matching balanced flow networks capacitated matching problems Exact sciences and technology Flows in networks. Combinatorial problems matching heuristics network flows Operational research and scientific management Operational research. Management science skew-symmetric graphs |
| Title | Balanced network flows. II. Simple augmentation algorithms |
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