Minimum cut bases in undirected networks
Given an undirected, connected network G = ( V , E ) with weights on the edges, the cut basis problem is asking for a maximal number of linear independent cuts such that the sum of the cut weights is minimized. Surprisingly, this problem has not attained as much attention as another graph theoretic...
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| Vydáno v: | Discrete Applied Mathematics Ročník 158; číslo 4; s. 277 - 290 |
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| Jazyk: | angličtina |
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Elsevier B.V
28.02.2010
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| ISSN: | 0166-218X, 1872-6771 |
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| Abstract | Given an undirected, connected network
G
=
(
V
,
E
)
with weights on the edges, the cut basis problem is asking for a maximal number of linear independent cuts such that the sum of the cut weights is minimized. Surprisingly, this problem has not attained as much attention as another graph theoretic problem closely related to it, namely, the cycle basis problem. We consider two versions of the problem: the unconstrained and the fundamental cut basis problem.
For the unconstrained case, where the cuts in the basis can be of an arbitrary kind, the problem can be written as a multiterminal network flow problem, and is thus solvable in strongly polynomial time. In contrast, the fundamental cut basis problem, where all cuts in the basis are obtained by deleting an edge, each from a spanning tree
T
, is shown to be NP-hard. In this proof, we also show that a tree which induces the minimum fundamental cycle basis is also an optimal solution for the minimum fundamental cut basis problem in unweighted graphs.
We present heuristics, integer programming formulations and summarize first experiences with numerical tests. |
|---|---|
| AbstractList | Given an undirected, connected network
G
=
(
V
,
E
)
with weights on the edges, the cut basis problem is asking for a maximal number of linear independent cuts such that the sum of the cut weights is minimized. Surprisingly, this problem has not attained as much attention as another graph theoretic problem closely related to it, namely, the cycle basis problem. We consider two versions of the problem: the unconstrained and the fundamental cut basis problem.
For the unconstrained case, where the cuts in the basis can be of an arbitrary kind, the problem can be written as a multiterminal network flow problem, and is thus solvable in strongly polynomial time. In contrast, the fundamental cut basis problem, where all cuts in the basis are obtained by deleting an edge, each from a spanning tree
T
, is shown to be NP-hard. In this proof, we also show that a tree which induces the minimum fundamental cycle basis is also an optimal solution for the minimum fundamental cut basis problem in unweighted graphs.
We present heuristics, integer programming formulations and summarize first experiences with numerical tests. |
| Author | Bunke, Florentine Schwahn, Anne M. Maffioli, Francesco Hamacher, Horst W. |
| Author_xml | – sequence: 1 givenname: Florentine surname: Bunke fullname: Bunke, Florentine email: flobunke@mathematik.uni-kl.de organization: Department of Mathematics, Technische Universität Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany – sequence: 2 givenname: Horst W. surname: Hamacher fullname: Hamacher, Horst W. email: hamacher@mathematik.uni-kl.de organization: Department of Mathematics, Technische Universität Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany – sequence: 3 givenname: Francesco surname: Maffioli fullname: Maffioli, Francesco email: maffioli@elet.polimi.it organization: Department of Electronics and Information, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan, Italy – sequence: 4 givenname: Anne M. surname: Schwahn fullname: Schwahn, Anne M. email: a.m.schwahn@googlemail.com organization: Department of Mathematics, Technische Universität Kaiserslautern, P.O. Box 3049, 67653 Kaiserslautern, Germany |
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| Keywords | Integer programming Graph and network algorithms Cut basis problem |
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| References | Alon, Karp, Peleg, West (b1) 1995; 24 Gomory, Hu (b14) 1961; 9 F. Bunke, H.W. Hamacher, F. Maffioli, A.M. Schwahn, Minimum cut bases in undirected networks, Report in Wirtschaftsmathematik 108, University of Kaiserslautern, 2007. Hassin, Tamir (b20) 1995; 53 A.M. Schwahn, Minimum fundamental cut basis problem, Diploma Thesis, University of Kaiserslautern, 2005 Hartvigsen, Mardon (b19) 1991; 94 Sysło (b28) 1979; 9 Golynski, Horton (b13) 2002; vol. 2368 Kavitha (b22) 2008; vol. 5124 Gusfield (b17) 1990; 19 Deo, Kumar, Parson (b6) 1995; 107 F. Bunke, Circuit bases problems in binary matroids, Ph.D. Thesis, Department of Mathematics, University of Kaiserslautern, 2006 J.C. de Pina, Applications of shortest path methods, Ph.D. Thesis, University of Amsterdam, Netherlands,1995 Liebchen, Wünsch (b25) 2008; 156 Kavitha, Mehlhorn, Michail, Paluch (b23) 2004; vol. 3142 Goldberg, Rao (b12) 1998; 45 Seshu, Reed (b31) 1961 Amaldi, Liberti, Maffioli, Maculan (b2) 2009; 69 Deo, Prabhu, Krishnamoorty (b7) 1982; 8 C. Liebchen, R.H. Möhring, Information on MIPLIB’s instances, Tech. Rep. 49, TU Berlin, 2003 Gueret, Prins, Sevaux (b16) 2000 Horton (b21) 1987; 16 MIPLIB - Mixed integer problem library Grötschel (b15) 1977; vol. 36 Galbiati, Amaldi (b10) 2003; vol. 2909 Sysło (b29) 1981 Barahona, Grötschel (b3) 1986; 40 Liebchen, Wünsch, Köhler, Reich, Rizzi (b26) 2007; vol. 4525 Galbiati (b9) 2001; vol. 2223 G. Galbiati, R. Rizzi, E. Amaldi, On the approximability of the minimum strictly fundamental cycle bases problem, (Submitted for publication) Hamacher, Queyranne (b18) 1985; 4 Galbiati (10.1016/j.dam.2009.07.015_b10) 2003; vol. 2909 Amaldi (10.1016/j.dam.2009.07.015_b2) 2009; 69 Hartvigsen (10.1016/j.dam.2009.07.015_b19) 1991; 94 Sysło (10.1016/j.dam.2009.07.015_b28) 1979; 9 Hassin (10.1016/j.dam.2009.07.015_b20) 1995; 53 Deo (10.1016/j.dam.2009.07.015_b7) 1982; 8 Golynski (10.1016/j.dam.2009.07.015_b13) 2002; vol. 2368 Gusfield (10.1016/j.dam.2009.07.015_b17) 1990; 19 Barahona (10.1016/j.dam.2009.07.015_b3) 1986; 40 10.1016/j.dam.2009.07.015_b8 10.1016/j.dam.2009.07.015_b5 10.1016/j.dam.2009.07.015_b4 Sysło (10.1016/j.dam.2009.07.015_b29) 1981 10.1016/j.dam.2009.07.015_b24 10.1016/j.dam.2009.07.015_b27 Grötschel (10.1016/j.dam.2009.07.015_b15) 1977; vol. 36 Horton (10.1016/j.dam.2009.07.015_b21) 1987; 16 Kavitha (10.1016/j.dam.2009.07.015_b22) 2008; vol. 5124 Gomory (10.1016/j.dam.2009.07.015_b14) 1961; 9 Hamacher (10.1016/j.dam.2009.07.015_b18) 1985; 4 Gueret (10.1016/j.dam.2009.07.015_b16) 2000 Goldberg (10.1016/j.dam.2009.07.015_b12) 1998; 45 Galbiati (10.1016/j.dam.2009.07.015_b9) 2001; vol. 2223 Kavitha (10.1016/j.dam.2009.07.015_b23) 2004; vol. 3142 10.1016/j.dam.2009.07.015_b30 Liebchen (10.1016/j.dam.2009.07.015_b26) 2007; vol. 4525 Seshu (10.1016/j.dam.2009.07.015_b31) 1961 Liebchen (10.1016/j.dam.2009.07.015_b25) 2008; 156 Deo (10.1016/j.dam.2009.07.015_b6) 1995; 107 10.1016/j.dam.2009.07.015_b11 Alon (10.1016/j.dam.2009.07.015_b1) 1995; 24 |
| References_xml | – volume: 19 start-page: 143 year: 1990 end-page: 155 ident: b17 article-title: Very simple methods for all pairs network flow analysis publication-title: SIAM Journal on Computing – volume: 94 start-page: 81 year: 1991 end-page: 94 ident: b19 article-title: Cycle bases from orderings and coverings publication-title: Discrete Mathematics – reference: A.M. Schwahn, Minimum fundamental cut basis problem, Diploma Thesis, University of Kaiserslautern, 2005, – volume: vol. 2909 start-page: 151 year: 2003 end-page: 164 ident: b10 article-title: On the approximability of the minimum fundamental cycle basis problem publication-title: WAOA 2003: 1st International Workshop on Approximation and Online Algorithms – volume: vol. 2223 start-page: 116 year: 2001 end-page: 123 ident: b9 article-title: On min–max cycle bases publication-title: ISAAC 2001: 12th International Symposium on Algorithms and Computation – volume: vol. 4525 start-page: 365 year: 2007 end-page: 378 ident: b26 article-title: Benchmarks for strictly fundamental cycle bases publication-title: WEA 2007: International Workshop on Experimental Algorithms – volume: vol. 5124 start-page: 343 year: 2008 end-page: 354 ident: b22 article-title: On a special co-cycle basis of graphs publication-title: SWAT 2008: 11th Scandinavian Workshop on Algorithm Theory – reference: MIPLIB - Mixed integer problem library, – volume: 9 start-page: 551 year: 1961 end-page: 570 ident: b14 article-title: Multi-terminal network flows publication-title: Journal of SIAM – volume: 24 start-page: 78 year: 1995 end-page: 100 ident: b1 article-title: A graph-theoretic game and its applications to the publication-title: SIAM Journal on Computing – year: 2000 ident: b16 article-title: Applications of Optimization with Xpress-MP – volume: 53 start-page: 109 year: 1995 end-page: 111 ident: b20 article-title: On the minimum diameter spanning tree problem publication-title: Information Processing Letters – year: 1961 ident: b31 article-title: Linear Graphs and Electrical Networks – volume: 69 start-page: 205 year: 2009 end-page: 233 ident: b2 article-title: Edge-swapping algorithms for the minimum fundamental cycle basis problem publication-title: Mathematical Methods of Operations Research – volume: 45 start-page: 783 year: 1998 end-page: 797 ident: b12 article-title: Beyond the flow decomposition barrier publication-title: Journal of the ACM – reference: -instances, Tech. Rep. 49, TU Berlin, 2003 – volume: 156 start-page: 569 year: 2008 end-page: 587 ident: b25 article-title: The zoo of tree spanner problems publication-title: Discrete Applied Mathematics – volume: 8 start-page: 26 year: 1982 end-page: 42 ident: b7 article-title: Algorithms for generating fundamental cycles in a graph publication-title: ACM Transactions on Mathematical Software – start-page: 577 year: 1981 end-page: 588 ident: b29 article-title: On some problems related to fundamental cycle sets of a graph publication-title: Proceedings of the 4th International Conference on the Theory of Applications of Graphs – volume: 107 start-page: 141 year: 1995 end-page: 154 ident: b6 article-title: Minimum-length fundamental-cycle set problem: New heuristics and an empirical investigation publication-title: Congressus Numerantium – volume: 16 start-page: 358 year: 1987 end-page: 366 ident: b21 article-title: A polynomial-time algorithm to find the shortest cycle basis of a graph publication-title: SIAM Journal on Computing – volume: vol. 36 year: 1977 ident: b15 article-title: Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme publication-title: Mathematical Systems in Economics – volume: vol. 3142 start-page: 846 year: 2004 end-page: 857 ident: b23 article-title: A faster algorithm for minimum cycle basis of graphs publication-title: ICALP 2004: 31st International Colloquium on Automata, Languages and Programming – volume: 40 start-page: 40 year: 1986 end-page: 62 ident: b3 article-title: On the cycle polytope of a binary matroid publication-title: Journal of Combinatorial Theory B – reference: F. Bunke, H.W. Hamacher, F. Maffioli, A.M. Schwahn, Minimum cut bases in undirected networks, Report in Wirtschaftsmathematik 108, University of Kaiserslautern, 2007. – volume: vol. 2368 start-page: 200 year: 2002 end-page: 209 ident: b13 article-title: A polynomial time algorithm to find the minimum cycle basis of a regular matroid publication-title: SWAT 2002: 8th Scandinavian Workshop on Algorithm Theory – reference: C. Liebchen, R.H. Möhring, Information on MIPLIB’s – volume: 9 start-page: 123 year: 1979 end-page: 132 ident: b28 article-title: On cycle bases of a graph publication-title: Networks – reference: F. Bunke, Circuit bases problems in binary matroids, Ph.D. Thesis, Department of Mathematics, University of Kaiserslautern, 2006 – reference: J.C. de Pina, Applications of shortest path methods, Ph.D. Thesis, University of Amsterdam, Netherlands,1995 – reference: G. Galbiati, R. Rizzi, E. Amaldi, On the approximability of the minimum strictly fundamental cycle bases problem, (Submitted for publication) – volume: 4 start-page: 123 year: 1985 end-page: 143 ident: b18 publication-title: Annals of Operations Research – volume: vol. 3142 start-page: 846 year: 2004 ident: 10.1016/j.dam.2009.07.015_b23 article-title: A faster algorithm for minimum cycle basis of graphs – ident: 10.1016/j.dam.2009.07.015_b24 – volume: 156 start-page: 569 issue: 5 year: 2008 ident: 10.1016/j.dam.2009.07.015_b25 article-title: The zoo of tree spanner problems publication-title: Discrete Applied Mathematics doi: 10.1016/j.dam.2007.07.001 – volume: 24 start-page: 78 issue: 1 year: 1995 ident: 10.1016/j.dam.2009.07.015_b1 article-title: A graph-theoretic game and its applications to the k-server problem publication-title: SIAM Journal on Computing doi: 10.1137/S0097539792224474 – year: 1961 ident: 10.1016/j.dam.2009.07.015_b31 – volume: 9 start-page: 123 year: 1979 ident: 10.1016/j.dam.2009.07.015_b28 article-title: On cycle bases of a graph publication-title: Networks doi: 10.1002/net.3230090203 – volume: 4 start-page: 123 year: 1985 ident: 10.1016/j.dam.2009.07.015_b18 article-title: k best solutions to combinatorial optimization problems publication-title: Annals of Operations Research doi: 10.1007/BF02022039 – volume: 8 start-page: 26 issue: 1 year: 1982 ident: 10.1016/j.dam.2009.07.015_b7 article-title: Algorithms for generating fundamental cycles in a graph publication-title: ACM Transactions on Mathematical Software doi: 10.1145/355984.355988 – volume: vol. 4525 start-page: 365 year: 2007 ident: 10.1016/j.dam.2009.07.015_b26 article-title: Benchmarks for strictly fundamental cycle bases – volume: 40 start-page: 40 year: 1986 ident: 10.1016/j.dam.2009.07.015_b3 article-title: On the cycle polytope of a binary matroid publication-title: Journal of Combinatorial Theory B doi: 10.1016/0095-8956(86)90063-8 – volume: 45 start-page: 783 issue: 5 year: 1998 ident: 10.1016/j.dam.2009.07.015_b12 article-title: Beyond the flow decomposition barrier publication-title: Journal of the ACM doi: 10.1145/290179.290181 – volume: vol. 2368 start-page: 200 year: 2002 ident: 10.1016/j.dam.2009.07.015_b13 article-title: A polynomial time algorithm to find the minimum cycle basis of a regular matroid – volume: 53 start-page: 109 issue: 2 year: 1995 ident: 10.1016/j.dam.2009.07.015_b20 article-title: On the minimum diameter spanning tree problem publication-title: Information Processing Letters doi: 10.1016/0020-0190(94)00183-Y – year: 2000 ident: 10.1016/j.dam.2009.07.015_b16 – ident: 10.1016/j.dam.2009.07.015_b4 – ident: 10.1016/j.dam.2009.07.015_b8 – volume: vol. 2223 start-page: 116 year: 2001 ident: 10.1016/j.dam.2009.07.015_b9 article-title: On min–max cycle bases – volume: vol. 36 year: 1977 ident: 10.1016/j.dam.2009.07.015_b15 article-title: Polyedrische Charakterisierungen kombinatorischer Optimierungsprobleme – volume: 94 start-page: 81 year: 1991 ident: 10.1016/j.dam.2009.07.015_b19 article-title: Cycle bases from orderings and coverings publication-title: Discrete Mathematics doi: 10.1016/0012-365X(91)90317-U – volume: 107 start-page: 141 year: 1995 ident: 10.1016/j.dam.2009.07.015_b6 article-title: Minimum-length fundamental-cycle set problem: New heuristics and an empirical investigation publication-title: Congressus Numerantium – volume: 9 start-page: 551 issue: 4 year: 1961 ident: 10.1016/j.dam.2009.07.015_b14 article-title: Multi-terminal network flows publication-title: Journal of SIAM – ident: 10.1016/j.dam.2009.07.015_b27 – volume: vol. 2909 start-page: 151 year: 2003 ident: 10.1016/j.dam.2009.07.015_b10 article-title: On the approximability of the minimum fundamental cycle basis problem – volume: 69 start-page: 205 year: 2009 ident: 10.1016/j.dam.2009.07.015_b2 article-title: Edge-swapping algorithms for the minimum fundamental cycle basis problem publication-title: Mathematical Methods of Operations Research doi: 10.1007/s00186-008-0255-4 – volume: 19 start-page: 143 year: 1990 ident: 10.1016/j.dam.2009.07.015_b17 article-title: Very simple methods for all pairs network flow analysis publication-title: SIAM Journal on Computing doi: 10.1137/0219009 – ident: 10.1016/j.dam.2009.07.015_b11 – volume: 16 start-page: 358 issue: 2 year: 1987 ident: 10.1016/j.dam.2009.07.015_b21 article-title: A polynomial-time algorithm to find the shortest cycle basis of a graph publication-title: SIAM Journal on Computing doi: 10.1137/0216026 – start-page: 577 year: 1981 ident: 10.1016/j.dam.2009.07.015_b29 article-title: On some problems related to fundamental cycle sets of a graph – volume: vol. 5124 start-page: 343 year: 2008 ident: 10.1016/j.dam.2009.07.015_b22 article-title: On a special co-cycle basis of graphs – ident: 10.1016/j.dam.2009.07.015_b30 – ident: 10.1016/j.dam.2009.07.015_b5 |
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| Snippet | Given an undirected, connected network
G
=
(
V
,
E
)
with weights on the edges, the cut basis problem is asking for a maximal number of linear independent cuts... |
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| SubjectTerms | Cut basis problem Graph and network algorithms Integer programming |
| Title | Minimum cut bases in undirected networks |
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