Minimizing submodular functions over families of sets

Abstract We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizi...
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Gespeichert in:

Autor*in:	Goemans, M. X. [verfasserIn] Ramakrishnan, V. S.

Format:	Artikel
Sprache:	Englisch

Erschienen:	1995

Anmerkung:	© Akadémiai Kiadó 1995

Übergeordnetes Werk:	Enthalten in: Combinatorica - Springer-Verlag, 1981, 15(1995), 4 vom: Dez., Seite 499-513
Übergeordnetes Werk:	volume:15 ; year:1995 ; number:4 ; month:12 ; pages:499-513

Links:	Volltext

DOI / URN:	10.1007/BF01192523

Katalog-ID:	OLC2073864619

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allfields	10.1007/BF01192523 doi (DE-627)OLC2073864619 (DE-He213)BF01192523-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Goemans, M. X. verfasserin aut Minimizing submodular functions over families of sets 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Akadémiai Kiadó 1995 Abstract We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizing the submodular function over the sets containinga but notb. This leads to a polynomial-time algorithm for minimizing a submodular function over these families of sets. Our results apply, for example, to the families of odd cardinality subsets or even cardinality subsets separating two given vertices, or to the complement of a lattice family of subsets. We also derive that the second smallest value of a submodular function over a lattice family can be computed in polynomial-time. These results generalize and unify several known results. Ramakrishnan, V. S. aut Enthalten in Combinatorica Springer-Verlag, 1981 15(1995), 4 vom: Dez., Seite 499-513 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:15 year:1995 number:4 month:12 pages:499-513 https://doi.org/10.1007/BF01192523 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4323 AR 15 1995 4 12 499-513
spelling	10.1007/BF01192523 doi (DE-627)OLC2073864619 (DE-He213)BF01192523-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Goemans, M. X. verfasserin aut Minimizing submodular functions over families of sets 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Akadémiai Kiadó 1995 Abstract We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizing the submodular function over the sets containinga but notb. This leads to a polynomial-time algorithm for minimizing a submodular function over these families of sets. Our results apply, for example, to the families of odd cardinality subsets or even cardinality subsets separating two given vertices, or to the complement of a lattice family of subsets. We also derive that the second smallest value of a submodular function over a lattice family can be computed in polynomial-time. These results generalize and unify several known results. Ramakrishnan, V. S. aut Enthalten in Combinatorica Springer-Verlag, 1981 15(1995), 4 vom: Dez., Seite 499-513 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:15 year:1995 number:4 month:12 pages:499-513 https://doi.org/10.1007/BF01192523 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4323 AR 15 1995 4 12 499-513
allfields_unstemmed	10.1007/BF01192523 doi (DE-627)OLC2073864619 (DE-He213)BF01192523-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Goemans, M. X. verfasserin aut Minimizing submodular functions over families of sets 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Akadémiai Kiadó 1995 Abstract We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizing the submodular function over the sets containinga but notb. This leads to a polynomial-time algorithm for minimizing a submodular function over these families of sets. Our results apply, for example, to the families of odd cardinality subsets or even cardinality subsets separating two given vertices, or to the complement of a lattice family of subsets. We also derive that the second smallest value of a submodular function over a lattice family can be computed in polynomial-time. These results generalize and unify several known results. Ramakrishnan, V. S. aut Enthalten in Combinatorica Springer-Verlag, 1981 15(1995), 4 vom: Dez., Seite 499-513 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:15 year:1995 number:4 month:12 pages:499-513 https://doi.org/10.1007/BF01192523 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4323 AR 15 1995 4 12 499-513
allfieldsGer	10.1007/BF01192523 doi (DE-627)OLC2073864619 (DE-He213)BF01192523-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Goemans, M. X. verfasserin aut Minimizing submodular functions over families of sets 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Akadémiai Kiadó 1995 Abstract We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizing the submodular function over the sets containinga but notb. This leads to a polynomial-time algorithm for minimizing a submodular function over these families of sets. Our results apply, for example, to the families of odd cardinality subsets or even cardinality subsets separating two given vertices, or to the complement of a lattice family of subsets. We also derive that the second smallest value of a submodular function over a lattice family can be computed in polynomial-time. These results generalize and unify several known results. Ramakrishnan, V. S. aut Enthalten in Combinatorica Springer-Verlag, 1981 15(1995), 4 vom: Dez., Seite 499-513 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:15 year:1995 number:4 month:12 pages:499-513 https://doi.org/10.1007/BF01192523 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4323 AR 15 1995 4 12 499-513
allfieldsSound	10.1007/BF01192523 doi (DE-627)OLC2073864619 (DE-He213)BF01192523-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Goemans, M. X. verfasserin aut Minimizing submodular functions over families of sets 1995 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Akadémiai Kiadó 1995 Abstract We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizing the submodular function over the sets containinga but notb. This leads to a polynomial-time algorithm for minimizing a submodular function over these families of sets. Our results apply, for example, to the families of odd cardinality subsets or even cardinality subsets separating two given vertices, or to the complement of a lattice family of subsets. We also derive that the second smallest value of a submodular function over a lattice family can be computed in polynomial-time. These results generalize and unify several known results. Ramakrishnan, V. S. aut Enthalten in Combinatorica Springer-Verlag, 1981 15(1995), 4 vom: Dez., Seite 499-513 (DE-627)129957143 (DE-600)405133-6 (DE-576)015527492 0209-9683 nnns volume:15 year:1995 number:4 month:12 pages:499-513 https://doi.org/10.1007/BF01192523 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_62 GBV_ILN_70 GBV_ILN_105 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2027 GBV_ILN_2088 GBV_ILN_2244 GBV_ILN_4012 GBV_ILN_4046 GBV_ILN_4103 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4323 AR 15 1995 4 12 499-513
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topic_title	510 VZ 17,1 ssgn Minimizing submodular functions over families of sets
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title	Minimizing submodular functions over families of sets
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title_full	Minimizing submodular functions over families of sets
author_sort	Goemans, M. X.
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author_browse	Goemans, M. X. Ramakrishnan, V. S.
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title_sort	minimizing submodular functions over families of sets
title_auth	Minimizing submodular functions over families of sets
abstract	Abstract We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizing the submodular function over the sets containinga but notb. This leads to a polynomial-time algorithm for minimizing a submodular function over these families of sets. Our results apply, for example, to the families of odd cardinality subsets or even cardinality subsets separating two given vertices, or to the complement of a lattice family of subsets. We also derive that the second smallest value of a submodular function over a lattice family can be computed in polynomial-time. These results generalize and unify several known results. © Akadémiai Kiadó 1995
abstractGer	Abstract We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizing the submodular function over the sets containinga but notb. This leads to a polynomial-time algorithm for minimizing a submodular function over these families of sets. Our results apply, for example, to the families of odd cardinality subsets or even cardinality subsets separating two given vertices, or to the complement of a lattice family of subsets. We also derive that the second smallest value of a submodular function over a lattice family can be computed in polynomial-time. These results generalize and unify several known results. © Akadémiai Kiadó 1995
abstract_unstemmed	Abstract We consider the problem of characterizing the minimum of a submodular function when the minimization is restricted to a family of subsets. We show that, for many interesting cases, there exist two elementsa andb of the groundset such that the problem is equivalent to the problem of minimizing the submodular function over the sets containinga but notb. This leads to a polynomial-time algorithm for minimizing a submodular function over these families of sets. Our results apply, for example, to the families of odd cardinality subsets or even cardinality subsets separating two given vertices, or to the complement of a lattice family of subsets. We also derive that the second smallest value of a submodular function over a lattice family can be computed in polynomial-time. These results generalize and unify several known results. © Akadémiai Kiadó 1995
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title_short	Minimizing submodular functions over families of sets
url	https://doi.org/10.1007/BF01192523
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