Distance-based vertex identification in graphs: The outer multiset dimension

The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u | S ) = { | d G ( u , w 1 ) , … , d G ( u , w t ) | } . A subset of vertices S such that m ( u | S ) = m ( v | S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Gil-Pons, Reynaldo [verfasserIn] Ramírez-Cruz, Yunior [verfasserIn] Trujillo-Rasua, Rolando [verfasserIn] Yero, Ismael G. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Resolvability Privacy Resolving set Multiset resolving set Metric dimension Outer multiset dimension

Übergeordnetes Werk:	Enthalten in: Applied mathematics and computation - New York, NY : Elsevier, 1975, 363
Übergeordnetes Werk:	volume:363

DOI / URN:	10.1016/j.amc.2019.124612

Katalog-ID:	ELV002805391

Internformat


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520			\|a The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u \| S ) = { \| d G ( u , w 1 ) , … , d G ( u , w t ) \| } . A subset of vertices S such that m ( u \| S ) = m ( v \| S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases.
650		4	\|a Resolvability
650		4	\|a Privacy
650		4	\|a Resolving set
650		4	\|a Multiset resolving set
650		4	\|a Metric dimension
650		4	\|a Outer multiset dimension
700	1		\|a Ramírez-Cruz, Yunior \|e verfasserin \|4 aut
700	1		\|a Trujillo-Rasua, Rolando \|e verfasserin \|0 (orcid)0000-0002-8714-4626 \|4 aut
700	1		\|a Yero, Ismael G. \|e verfasserin \|0 (orcid)0000-0002-1619-1572 \|4 aut
773	0	8	\|i Enthalten in \|t Applied mathematics and computation \|d New York, NY : Elsevier, 1975 \|g 363 \|h Online-Ressource \|w (DE-627)26555022X \|w (DE-600)1465428-3 \|w (DE-576)078314976 \|7 nnns
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912			\|a GBV_ILN_2015
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912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
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912			\|a GBV_ILN_2147
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912			\|a GBV_ILN_2507
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912			\|a GBV_ILN_4393
936	b	k	\|a 31.80 \|j Angewandte Mathematik
936	b	k	\|a 31.76 \|j Numerische Mathematik
951			\|a AR
952			\|d 363

Indexfelder

author_variant	r g p rgp y r c yrc r t r rtr i g y ig igy
matchkey_str	gilponsreynaldoramrezcruzyuniortrujillor:2019----:itneaevreietfctoigahteue
hierarchy_sort_str	2019
bklnumber	31.80 31.76
publishDate	2019
allfields	10.1016/j.amc.2019.124612 doi (DE-627)ELV002805391 (ELSEVIER)S0096-3003(19)30604-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Gil-Pons, Reynaldo verfasserin aut Distance-based vertex identification in graphs: The outer multiset dimension 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u \| S ) = { \| d G ( u , w 1 ) , … , d G ( u , w t ) \| } . A subset of vertices S such that m ( u \| S ) = m ( v \| S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases. Resolvability Privacy Resolving set Multiset resolving set Metric dimension Outer multiset dimension Ramírez-Cruz, Yunior verfasserin aut Trujillo-Rasua, Rolando verfasserin (orcid)0000-0002-8714-4626 aut Yero, Ismael G. verfasserin (orcid)0000-0002-1619-1572 aut Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 363 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:363 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 363
spelling	10.1016/j.amc.2019.124612 doi (DE-627)ELV002805391 (ELSEVIER)S0096-3003(19)30604-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Gil-Pons, Reynaldo verfasserin aut Distance-based vertex identification in graphs: The outer multiset dimension 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u \| S ) = { \| d G ( u , w 1 ) , … , d G ( u , w t ) \| } . A subset of vertices S such that m ( u \| S ) = m ( v \| S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases. Resolvability Privacy Resolving set Multiset resolving set Metric dimension Outer multiset dimension Ramírez-Cruz, Yunior verfasserin aut Trujillo-Rasua, Rolando verfasserin (orcid)0000-0002-8714-4626 aut Yero, Ismael G. verfasserin (orcid)0000-0002-1619-1572 aut Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 363 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:363 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 363
allfields_unstemmed	10.1016/j.amc.2019.124612 doi (DE-627)ELV002805391 (ELSEVIER)S0096-3003(19)30604-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Gil-Pons, Reynaldo verfasserin aut Distance-based vertex identification in graphs: The outer multiset dimension 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u \| S ) = { \| d G ( u , w 1 ) , … , d G ( u , w t ) \| } . A subset of vertices S such that m ( u \| S ) = m ( v \| S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases. Resolvability Privacy Resolving set Multiset resolving set Metric dimension Outer multiset dimension Ramírez-Cruz, Yunior verfasserin aut Trujillo-Rasua, Rolando verfasserin (orcid)0000-0002-8714-4626 aut Yero, Ismael G. verfasserin (orcid)0000-0002-1619-1572 aut Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 363 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:363 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 363
allfieldsGer	10.1016/j.amc.2019.124612 doi (DE-627)ELV002805391 (ELSEVIER)S0096-3003(19)30604-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Gil-Pons, Reynaldo verfasserin aut Distance-based vertex identification in graphs: The outer multiset dimension 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u \| S ) = { \| d G ( u , w 1 ) , … , d G ( u , w t ) \| } . A subset of vertices S such that m ( u \| S ) = m ( v \| S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases. Resolvability Privacy Resolving set Multiset resolving set Metric dimension Outer multiset dimension Ramírez-Cruz, Yunior verfasserin aut Trujillo-Rasua, Rolando verfasserin (orcid)0000-0002-8714-4626 aut Yero, Ismael G. verfasserin (orcid)0000-0002-1619-1572 aut Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 363 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:363 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 363
allfieldsSound	10.1016/j.amc.2019.124612 doi (DE-627)ELV002805391 (ELSEVIER)S0096-3003(19)30604-6 DE-627 ger DE-627 rda eng 510 DE-600 31.80 bkl 31.76 bkl Gil-Pons, Reynaldo verfasserin aut Distance-based vertex identification in graphs: The outer multiset dimension 2019 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u \| S ) = { \| d G ( u , w 1 ) , … , d G ( u , w t ) \| } . A subset of vertices S such that m ( u \| S ) = m ( v \| S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases. Resolvability Privacy Resolving set Multiset resolving set Metric dimension Outer multiset dimension Ramírez-Cruz, Yunior verfasserin aut Trujillo-Rasua, Rolando verfasserin (orcid)0000-0002-8714-4626 aut Yero, Ismael G. verfasserin (orcid)0000-0002-1619-1572 aut Enthalten in Applied mathematics and computation New York, NY : Elsevier, 1975 363 Online-Ressource (DE-627)26555022X (DE-600)1465428-3 (DE-576)078314976 nnns volume:363 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4313 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4393 31.80 Angewandte Mathematik 31.76 Numerische Mathematik AR 363
language	English
source	Enthalten in Applied mathematics and computation 363 volume:363
sourceStr	Enthalten in Applied mathematics and computation 363 volume:363
format_phy_str_mv	Article
bklname	Angewandte Mathematik Numerische Mathematik
institution	findex.gbv.de
topic_facet	Resolvability Privacy Resolving set Multiset resolving set Metric dimension Outer multiset dimension
dewey-raw	510
isfreeaccess_bool	false
container_title	Applied mathematics and computation
authorswithroles_txt_mv	Gil-Pons, Reynaldo @@aut@@ Ramírez-Cruz, Yunior @@aut@@ Trujillo-Rasua, Rolando @@aut@@ Yero, Ismael G. @@aut@@
publishDateDaySort_date	2019-01-01T00:00:00Z
hierarchy_top_id	26555022X
dewey-sort	3510
id	ELV002805391
language_de	englisch
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author	Gil-Pons, Reynaldo
spellingShingle	Gil-Pons, Reynaldo ddc 510 bkl 31.80 bkl 31.76 misc Resolvability misc Privacy misc Resolving set misc Multiset resolving set misc Metric dimension misc Outer multiset dimension Distance-based vertex identification in graphs: The outer multiset dimension
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topic_title	510 DE-600 31.80 bkl 31.76 bkl Distance-based vertex identification in graphs: The outer multiset dimension Resolvability Privacy Resolving set Multiset resolving set Metric dimension Outer multiset dimension
topic	ddc 510 bkl 31.80 bkl 31.76 misc Resolvability misc Privacy misc Resolving set misc Multiset resolving set misc Metric dimension misc Outer multiset dimension
topic_unstemmed	ddc 510 bkl 31.80 bkl 31.76 misc Resolvability misc Privacy misc Resolving set misc Multiset resolving set misc Metric dimension misc Outer multiset dimension
topic_browse	ddc 510 bkl 31.80 bkl 31.76 misc Resolvability misc Privacy misc Resolving set misc Multiset resolving set misc Metric dimension misc Outer multiset dimension
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title	Distance-based vertex identification in graphs: The outer multiset dimension
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title_full	Distance-based vertex identification in graphs: The outer multiset dimension
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title_sort	distance-based vertex identification in graphs: the outer multiset dimension
title_auth	Distance-based vertex identification in graphs: The outer multiset dimension
abstract	The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u \| S ) = { \| d G ( u , w 1 ) , … , d G ( u , w t ) \| } . A subset of vertices S such that m ( u \| S ) = m ( v \| S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases.
abstractGer	The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u \| S ) = { \| d G ( u , w 1 ) , … , d G ( u , w t ) \| } . A subset of vertices S such that m ( u \| S ) = m ( v \| S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases.
abstract_unstemmed	The characterisation of vertices in a network, in relation to other peers, has been used as a primitive in many computational procedures, such as node localisation and (de-)anonymisation. This article focuses on a characterisation type known as the multiset metric representation. Formally, given a graph G and a subset of vertices S = { w 1 , … , w t } ⊆ V ( G ) , the multiset representationof a vertex u ∈ V(G) with respect to S is the multiset m ( u \| S ) = { \| d G ( u , w 1 ) , … , d G ( u , w t ) \| } . A subset of vertices S such that m ( u \| S ) = m ( v \| S ) ⇔ u = v for every u, v ∈ V(G)∖S is said to be a multiset resolving set, and the cardinality of the smallest such set is the outer multiset dimension. We study the general behaviour of the outer multiset dimension, and determine its exact value for several graph families. We also show that computing the outer multiset dimension of arbitrary graphs is NP-hard, and provide methods for efficiently handling particular cases.
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title_short	Distance-based vertex identification in graphs: The outer multiset dimension
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author2	Ramírez-Cruz, Yunior Trujillo-Rasua, Rolando Yero, Ismael G.
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up_date	2024-07-06T17:30:41.873Z
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Distance-based vertex identification in graphs: The outer multiset dimension

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