Lattice polyhedra and submodular flows

Lattice polyhedra, as introduced by Gröflin and Hoffman, form a common framework for various discrete optimization problems. They are specified by a lattice structure on the underlying matrix satisfying certain sub- and supermodularity constraints. Lattice polyhedra provide one of the most general f...

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Published in:	Japan journal of industrial and applied mathematics Vol. 29; no. 3; pp. 441 - 451
Main Authors:	Fujishige, Satoru, Peis, Britta
Format:	Journal Article
Language:	English
Published:	Japan Springer Japan 01.10.2012 Springer Nature B.V
Subjects:	Applications of Mathematics Computational Mathematics and Numerical Analysis Mathematics Mathematics and Statistics Original Paper Edmonds–Giles polyhedra Distributive lattices 06 (Order, Lattices, Ordered algebraic structures) Lattice polyhedra
ISSN:	0916-7005, 1868-937X
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Abstract	Lattice polyhedra, as introduced by Gröflin and Hoffman, form a common framework for various discrete optimization problems. They are specified by a lattice structure on the underlying matrix satisfying certain sub- and supermodularity constraints. Lattice polyhedra provide one of the most general frameworks of total dual integral systems. So far no combinatorial algorithm has been found for the corresponding linear optimization problem. We show that the important class of lattice polyhedra in which the underlying lattice is of modular characteristic can be reduced to the Edmonds–Giles polyhedra. Thus, submodular flow algorithms can be applied to this class of lattice polyhedra. In contrast to a previous result of Schrijver, we do not explicitly require that the lattice is distributive. Moreover, our reduction is very simple in that it only uses an arbitrary maximal chain in the lattice.
AbstractList	Issue Title: Special Issue on Discrete Structure and Optimization Lattice polyhedra, as introduced by Gröflin and Hoffman, form a common framework for various discrete optimization problems. They are specified by a lattice structure on the underlying matrix satisfying certain sub- and supermodularity constraints. Lattice polyhedra provide one of the most general frameworks of total dual integral systems. So far no combinatorial algorithm has been found for the corresponding linear optimization problem. We show that the important class of lattice polyhedra in which the underlying lattice is of modular characteristic can be reduced to the Edmonds-Giles polyhedra. Thus, submodular flow algorithms can be applied to this class of lattice polyhedra. In contrast to a previous result of Schrijver, we do not explicitly require that the lattice is distributive. Moreover, our reduction is very simple in that it only uses an arbitrary maximal chain in the lattice.[PUBLICATION ABSTRACT] Lattice polyhedra, as introduced by Gröflin and Hoffman, form a common framework for various discrete optimization problems. They are specified by a lattice structure on the underlying matrix satisfying certain sub- and supermodularity constraints. Lattice polyhedra provide one of the most general frameworks of total dual integral systems. So far no combinatorial algorithm has been found for the corresponding linear optimization problem. We show that the important class of lattice polyhedra in which the underlying lattice is of modular characteristic can be reduced to the Edmonds–Giles polyhedra. Thus, submodular flow algorithms can be applied to this class of lattice polyhedra. In contrast to a previous result of Schrijver, we do not explicitly require that the lattice is distributive. Moreover, our reduction is very simple in that it only uses an arbitrary maximal chain in the lattice.
Author	Peis, Britta Fujishige, Satoru
Author_xml	– sequence: 1 givenname: Satoru surname: Fujishige fullname: Fujishige, Satoru organization: Research Institute for Mathematical Sciences, Kyoto University – sequence: 2 givenname: Britta surname: Peis fullname: Peis, Britta email: peis@math.tu-berlin.de organization: TU Berlin
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References	DietrichB.L.HoffmanA.J.On greedy algorithms, partially ordered sets, and submodular functionsIBM J. Res. Dev.2003472530195735010.1147/rd.471.0025 Hoffman, A.J., Schwartz, D.E.: On lattice polyhedra. In: Hajnal. A., Sos, V.T. (eds.) Proceedings of Fifth Hungarian Combinatorial Coll, pp. 593–598. North-Holland, Amsterdam (1978) EdmondsJ.GilesR.A min-max relation for submodular functions on graphsAnn. Discrete Math.1977118520446016910.1016/S0167-5060(08)70734-9 KrügerU.Structural aspects of ordered polymatroidsDiscrete Appl. Math.20009912514817438281016.9007910.1016/S0166-218X(99)00129-8 QueyranneM.SpieksmaF.TardellaF.A general class of greedily solvable linear programsMath. Oper. Res.19982389290816624300977.9004510.1287/moor.23.4.892 McCormick, S.T., Peis, B.: A primal-dual algorithm for weighted abstract cut packing. In: Proceeding of the 15th Conference on Integer Programming and Combinatorial Optimization (IPCO 2011). Springer, Berlin (2011) Faigle, U., Peis, B.: Two-phase greedy algorithms for some classes of combinatorial linear programs. In: SODA2008, pp. 161–166 (2008) Iwata, S., McCormick, S.T., Shigeno, M.: A faster algorithm for minimum cost submodular flows. In: Proceedings of 9th ACM-SIAM Symposium on Discrete Algorithms, pp. 167–174 (1998) IwataS.McCormickS.T.ShigenoM.A fast cost scaling algorithm for submodular flowInf. Process. Lett.200074123128176155310.1016/S0020-0190(00)00052-1 McCormick, S.T.: Submodular Function Minimization. In: Aardal, K., Nemhauser, G., Weismantel, R. (eds.) Handbook on Discrete Optimization, Chapter 7, pp. 321–391. Elsevier, Amsterdam (2006) Birkhoff, G.: Lattice Theory, vol. 91. American Mathematical Society, Providence (1991) FaigleU.KernW.On the core of ordered submodular cost gamesMath. Program.20008748348917575600980.9010310.1007/s101070050008 Schrijver, A.: Total dual integrality from directed graphs, crossing families and sub and supermodular functions. In: Pulleyblank, W.R. (ed.) Progress in Combinatorial Optimization, pp. 315–362. Academic Press, Dublin (1984) FrankA.Increasing the rooted-connectivity of a digraph by oneMath. Program.19998456557616947550930.0507410.1007/s101070050040 FujishigeS.Structures of polyhedra determined by submodular functions on crossing familiesMath. Program.1984291251417454040545.9009710.1007/BF02592217 FleischerL.IwataS.McCormickS.T.A faster capacity scaling algorithm for minimum cost submodular flowMath. Program.20029211913918922991046.9007310.1007/s101070100253 Fujishige, S.: Submodular functions and optimization, 2nd Edn. In: Annals of Discrete Mathematics, vol. 58. Elsevier, Amsterdam (2005) McCormickS.T.FujishigeS.Strongly polynomial and fully combinatorial algorithms for bisubmodular function minimizationMath. Program.20101228712025337541190.6509910.1007/s10107-008-0242-9 FaigleU.KernW.Submodular linear programs on forestsMath. Program.19967219520613868340856.90071 GröflinH.HoffmanA.J.Lattice polyhedra II: generalization, constructions and examplesAnn. Discrete Math.1982151892030507.90062 Schrijver, A.: Combinatorial Optimization. Springer, Berlin (2003) FujishigeS.IwataS.Algorithms for submodular flows. Special issue on algorithm engineering: surveysIEICE Trans. Inf. Syst.2000E83-D322329 S. Fujishige (84_CR11) 2000; E83-D 84_CR22 84_CR10 84_CR21 84_CR14 84_CR1 84_CR13 U. Faigle (84_CR4) 1996; 72 U. Faigle (84_CR5) 2000; 87 84_CR19 B.L. Dietrich (84_CR2) 2003; 47 84_CR17 H. Gröflin (84_CR12) 1982; 15 S.T. McCormick (84_CR18) 2010; 122 A. Frank (84_CR8) 1999; 84 U. Krüger (84_CR16) 2000; 99 M. Queyranne (84_CR20) 1998; 23 L. Fleischer (84_CR7) 2002; 92 84_CR6 S. Iwata (84_CR15) 2000; 74 J. Edmonds (84_CR3) 1977; 1 S. Fujishige (84_CR9) 1984; 29
References_xml	– reference: Schrijver, A.: Total dual integrality from directed graphs, crossing families and sub and supermodular functions. In: Pulleyblank, W.R. (ed.) Progress in Combinatorial Optimization, pp. 315–362. Academic Press, Dublin (1984) – reference: EdmondsJ.GilesR.A min-max relation for submodular functions on graphsAnn. Discrete Math.1977118520446016910.1016/S0167-5060(08)70734-9 – reference: McCormickS.T.FujishigeS.Strongly polynomial and fully combinatorial algorithms for bisubmodular function minimizationMath. Program.20101228712025337541190.6509910.1007/s10107-008-0242-9 – reference: KrügerU.Structural aspects of ordered polymatroidsDiscrete Appl. Math.20009912514817438281016.9007910.1016/S0166-218X(99)00129-8 – reference: FrankA.Increasing the rooted-connectivity of a digraph by oneMath. Program.19998456557616947550930.0507410.1007/s101070050040 – reference: FleischerL.IwataS.McCormickS.T.A faster capacity scaling algorithm for minimum cost submodular flowMath. Program.20029211913918922991046.9007310.1007/s101070100253 – reference: DietrichB.L.HoffmanA.J.On greedy algorithms, partially ordered sets, and submodular functionsIBM J. Res. Dev.2003472530195735010.1147/rd.471.0025 – reference: Fujishige, S.: Submodular functions and optimization, 2nd Edn. In: Annals of Discrete Mathematics, vol. 58. Elsevier, Amsterdam (2005) – reference: FujishigeS.IwataS.Algorithms for submodular flows. Special issue on algorithm engineering: surveysIEICE Trans. Inf. Syst.2000E83-D322329 – reference: Hoffman, A.J., Schwartz, D.E.: On lattice polyhedra. In: Hajnal. A., Sos, V.T. (eds.) Proceedings of Fifth Hungarian Combinatorial Coll, pp. 593–598. North-Holland, Amsterdam (1978) – reference: Iwata, S., McCormick, S.T., Shigeno, M.: A faster algorithm for minimum cost submodular flows. In: Proceedings of 9th ACM-SIAM Symposium on Discrete Algorithms, pp. 167–174 (1998) – reference: McCormick, S.T.: Submodular Function Minimization. In: Aardal, K., Nemhauser, G., Weismantel, R. (eds.) Handbook on Discrete Optimization, Chapter 7, pp. 321–391. Elsevier, Amsterdam (2006) – reference: IwataS.McCormickS.T.ShigenoM.A fast cost scaling algorithm for submodular flowInf. Process. Lett.200074123128176155310.1016/S0020-0190(00)00052-1 – reference: QueyranneM.SpieksmaF.TardellaF.A general class of greedily solvable linear programsMath. Oper. Res.19982389290816624300977.9004510.1287/moor.23.4.892 – reference: FaigleU.KernW.Submodular linear programs on forestsMath. Program.19967219520613868340856.90071 – reference: Schrijver, A.: Combinatorial Optimization. Springer, Berlin (2003) – reference: McCormick, S.T., Peis, B.: A primal-dual algorithm for weighted abstract cut packing. In: Proceeding of the 15th Conference on Integer Programming and Combinatorial Optimization (IPCO 2011). Springer, Berlin (2011) – reference: Birkhoff, G.: Lattice Theory, vol. 91. American Mathematical Society, Providence (1991) – reference: FaigleU.KernW.On the core of ordered submodular cost gamesMath. Program.20008748348917575600980.9010310.1007/s101070050008 – reference: FujishigeS.Structures of polyhedra determined by submodular functions on crossing familiesMath. Program.1984291251417454040545.9009710.1007/BF02592217 – reference: Faigle, U., Peis, B.: Two-phase greedy algorithms for some classes of combinatorial linear programs. In: SODA2008, pp. 161–166 (2008) – reference: GröflinH.HoffmanA.J.Lattice polyhedra II: generalization, constructions and examplesAnn. Discrete Math.1982151892030507.90062 – ident: 84_CR10 – ident: 84_CR1 – volume: 15 start-page: 189 year: 1982 ident: 84_CR12 publication-title: Ann. Discrete Math. – ident: 84_CR13 – ident: 84_CR14 – ident: 84_CR6 – volume: 84 start-page: 565 year: 1999 ident: 84_CR8 publication-title: Math. Program. doi: 10.1007/s101070050040 – volume: 47 start-page: 25 year: 2003 ident: 84_CR2 publication-title: IBM J. Res. Dev. doi: 10.1147/rd.471.0025 – volume: 72 start-page: 195 year: 1996 ident: 84_CR4 publication-title: Math. Program. – volume: 99 start-page: 125 year: 2000 ident: 84_CR16 publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(99)00129-8 – volume: 87 start-page: 483 year: 2000 ident: 84_CR5 publication-title: Math. Program. doi: 10.1007/s101070050008 – volume: 23 start-page: 892 year: 1998 ident: 84_CR20 publication-title: Math. Oper. Res. doi: 10.1287/moor.23.4.892 – volume: 1 start-page: 185 year: 1977 ident: 84_CR3 publication-title: Ann. Discrete Math. doi: 10.1016/S0167-5060(08)70734-9 – volume: 92 start-page: 119 year: 2002 ident: 84_CR7 publication-title: Math. Program. doi: 10.1007/s101070100253 – ident: 84_CR19 doi: 10.1007/978-3-642-20807-2_26 – volume: 74 start-page: 123 year: 2000 ident: 84_CR15 publication-title: Inf. Process. Lett. doi: 10.1016/S0020-0190(00)00052-1 – ident: 84_CR21 – volume: 122 start-page: 87 year: 2010 ident: 84_CR18 publication-title: Math. Program. doi: 10.1007/s10107-008-0242-9 – volume: E83-D start-page: 322 year: 2000 ident: 84_CR11 publication-title: IEICE Trans. Inf. Syst. – volume: 29 start-page: 125 year: 1984 ident: 84_CR9 publication-title: Math. Program. doi: 10.1007/BF02592217 – ident: 84_CR22 doi: 10.1016/B978-0-12-566780-7.50025-8 – ident: 84_CR17 doi: 10.1016/S0927-0507(05)12007-6
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Snippet	Lattice polyhedra, as introduced by Gröflin and Hoffman, form a common framework for various discrete optimization problems. They are specified by a lattice... Issue Title: Special Issue on Discrete Structure and Optimization Lattice polyhedra, as introduced by Gröflin and Hoffman, form a common framework for various...
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