Cops and Robbers on Dynamic Graphs: Offline and Online Case

We examine the classic game of Cops and Robbers played on models of dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a graph instance is generated as a subgraph of the underlying graph of the model. The cops and the robber take their turns on the current graph in...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Discrete mathematics and theoretical computer science Ročník 25:1; číslo Discrete Algorithms; s. 1 - 20
Hlavní autoři: Balev, Stefan, Jiménez Laredo, Juan, Lamprou, Ioannis, Pigné, Yoann, Sanlaville, Eric
Médium: Journal Article
Jazyk:angličtina
Vydáno: Nancy DMTCS 01.01.2023
Discrete Mathematics & Theoretical Computer Science
Témata:
[info.info-dm]computer science [cs]/discrete mathematics [cs.dm]
[info.info-ro]computer science [cs]/operations research [cs.ro]
Algorithms
Apexes
Computer Science
cops and robbers
Discrete Mathematics
dynamic graphs
Evolution
Games
Graph theory
Graphs
offline
online
Operations Research
Robbery
sparse
cops and robbers
dynamic graphs
offline
online
sparse
ISSN:1365-8050, 1462-7264, 1365-8050
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract We examine the classic game of Cops and Robbers played on models of dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a graph instance is generated as a subgraph of the underlying graph of the model. The cops and the robber take their turns on the current graph instance. The cops win if they can capture the robber at some point in time. Otherwise, the robber wins. In the offline case, the players are fully aware of the evolution sequence, up to some finite time horizon T. We provide a O(n 2k+1 T) algorithm to decide whether a given evolution sequence for an underlying graph with n vertices is k-cop-win via a reduction to a reachability game. In the online case, there is no knowledge of the evolution sequence, and the game might go on forever. Also, each generated instance is required to be connected. We provide a nearly tight characterization for sparse underlying graphs, i.e., with at most linear number of edges. We prove λ + 1 cops suffice to capture the robber in any underlying graph with n − 1 + λ edges. Further, we define a family of underlying graphs with n−1+λ edges where λ−1 cops are necessary (and sufficient) for capture.
AbstractList We examine the classic game of Cops and Robbers played on models of dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a graph instance is generated as a subgraph of the underlying graph of the model. The cops and the robber take their turns on the current graph instance. The cops win if they can capture the robber at some point in time. Otherwise, the robber wins. In the offline case, the players are fully aware of the evolution sequence, up to some finite time horizon T. We provide a O(n 2k+1 T) algorithm to decide whether a given evolution sequence for an underlying graph with n vertices is k-cop-win via a reduction to a reachability game. In the online case, there is no knowledge of the evolution sequence, and the game might go on forever. Also, each generated instance is required to be connected. We provide a nearly tight characterization for sparse underlying graphs, i.e., with at most linear number of edges. We prove λ + 1 cops suffice to capture the robber in any underlying graph with n − 1 + λ edges. Further, we define a family of underlying graphs with n−1+λ edges where λ−1 cops are necessary (and sufficient) for capture.
We examine the classic game of Cops and Robbers played on dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a graph instance is generated as a subgraph of the (static) underlying graph. The cops and the robber take their turns on the current graph instance. The cops win if they can capture the robber at some point in time. Otherwise, the robber wins. In the offline case, the players are fully aware of the evolution sequence, up to some finite time horizon T. We provide a O(n2k+1T) algorithm to decide whether a given evolution sequence for an underlying graph with n vertices is k-cop-win via a reduction to a reachability game. In the online case, there is no knowledge of the evolution sequence, and the game might go on forever. Also, each generated instance is required to be connected. We provide a nearly tight characterization for sparse underlying graphs with at most a linear number of edges. We prove A + 1 cops suffice to capture the robber in any underlying graph with n - 1 + A edges. Furthermore, we define a family of underlying graphs with n - 1 + A edges where A - 1 cops are necessary (and sufficient) for capture.
Author Pigné, Yoann
Lamprou, Ioannis
Balev, Stefan
Jiménez Laredo, Juan
Sanlaville, Eric
Author_xml – sequence: 1
  givenname: Stefan
  surname: Balev
  fullname: Balev, Stefan
  organization: Equipe Réseaux d'interactions et Intelligence Collective
– sequence: 2
  givenname: Juan
  surname: Jiménez Laredo
  fullname: Jiménez Laredo, Juan
  organization: Equipe Réseaux d'interactions et Intelligence Collective
– sequence: 3
  givenname: Ioannis
  surname: Lamprou
  fullname: Lamprou, Ioannis
  organization: National and Kapodistrian University of Athens
– sequence: 4
  givenname: Yoann
  surname: Pigné
  fullname: Pigné, Yoann
– sequence: 5
  givenname: Eric
  orcidid: 0000-0001-9482-3945
  surname: Sanlaville
  fullname: Sanlaville, Eric
  organization: Equipe Réseaux d'interactions et Intelligence Collective
BackLink https://normandie-univ.hal.science/hal-02927320$$DView record in HAL
BookMark eNpVkVFLwzAUhYNMcJs--QcKPolsJrlp0urTmLoNBgPR55Clievokpp0wv69WyuiT_dw-Pjgcgao57wzCF0TPGac5tl9sWt0HGciY2eoT4CnowynuPcnX6BBjFuMCc2Z6KPHqa9jolyRvPr12oSYeJc8HZzalTqZBVVv4kOysrYqnWmxlWvjVEVzic6tqqK5-rlD9P7y_Dadj5ar2WI6WY40pLwZMW0t5VaprDBE40JDpgrAuiCcQG6s5SCM4ACUFhR0TgQhawKaQWrBCAVDtOi8hVdbWYdyp8JBelXKtvDhQ6rQlLoyUlFubMoJJmCZ0ZADE9hwkbO1PZrSo-u2c21U9U81nyzlqcM0pwIo_jqxNx1bB_-5N7GRW78P7viqBMwywjGj5EjddZQOPsZg7K-WYNmuIttV5GkV-AbFhn6T
ContentType Journal Article
Copyright Copyright DMTCS 2023
licence_http://creativecommons.org/publicdomain/zero
Copyright_xml – notice: Copyright DMTCS 2023
– notice: licence_http://creativecommons.org/publicdomain/zero
DBID AAYXX
CITATION
8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BFMQW
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
1XC
VOOES
DOA
DOI 10.46298/dmtcs.8784
DatabaseName CrossRef
ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
AUTh Library subscriptions: ProQuest Central
Continental Europe Database
Technology Collection
ProQuest One Community College
ProQuest Central
SciTech Premium Collection
ProQuest Engineering Collection
Engineering Database
ProQuest Central Premium
ProQuest One Academic (New)
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
Hyper Article en Ligne (HAL)
Hyper Article en Ligne (HAL) (Open Access)
Open Access: DOAJ - Directory of Open Access Journals
DatabaseTitle CrossRef
Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
Continental Europe Database
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
Engineering Collection
DatabaseTitleList
Publicly Available Content Database

CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 2
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
Computer Science
EISSN 1365-8050
EndPage 20
ExternalDocumentID oai_doaj_org_article_a26ef561013f4ec393470e6794bf7a35
oai:HAL:hal-02927320v5
10_46298_dmtcs_8784
Genre Feature
GroupedDBID -~9
.4S
.DC
29G
2WC
5GY
5VS
8FE
8FG
AAFWJ
AAYXX
ABDBF
ABJCF
ABUWG
ACGFO
ACIWK
ACUHS
ADBBV
ADQAK
AENEX
AFFHD
AFKRA
AFPKN
AIAGR
ALMA_UNASSIGNED_HOLDINGS
AMVHM
ARCSS
B0M
BAIFH
BBTPI
BCNDV
BENPR
BFMQW
BGLVJ
BPHCQ
CCPQU
CITATION
EAP
EBS
ECS
EDO
EJD
EMK
EPL
EST
ESX
GROUPED_DOAJ
HCIFZ
I-F
IAO
IBB
ICD
ITC
J9A
KQ8
KWQ
L6V
M7S
MK~
ML~
OK1
OVT
P2P
PHGZM
PHGZT
PIMPY
PQGLB
PQQKQ
PROAC
PTHSS
PV9
REM
RNS
RSU
RZL
TR2
TUS
XSB
~8M
ADOJU
AZQEC
DWQXO
PKEHL
PQEST
PQUKI
PRINS
1XC
ADCSY
AGGLG
VOOES
ID FETCH-LOGICAL-c356t-4cff26faa8de1c0dc38ad30cd16139eff637e763322d23c91711b13c435f3e7a3
IEDL.DBID DOA
ISICitedReferencesCount 2
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000957275300001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1365-8050
1462-7264
IngestDate Fri Oct 03 12:51:02 EDT 2025
Wed Dec 10 14:57:35 EST 2025
Fri Jul 25 12:14:18 EDT 2025
Sat Nov 29 02:48:26 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue Discrete Algorithms
Keywords cops and robbers
dynamic graphs
offline
online
sparse
Language English
License licence_http://creativecommons.org/publicdomain/zero/: http://creativecommons.org/publicdomain/zero
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c356t-4cff26faa8de1c0dc38ad30cd16139eff637e763322d23c91711b13c435f3e7a3
Notes SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ORCID 0000-0001-9482-3945
0000-0002-3570-7490
0009-0001-8966-2021
OpenAccessLink https://doaj.org/article/a26ef561013f4ec393470e6794bf7a35
PQID 3048160421
PQPubID 946337
PageCount 20
ParticipantIDs doaj_primary_oai_doaj_org_article_a26ef561013f4ec393470e6794bf7a35
hal_primary_oai_HAL_hal_02927320v5
proquest_journals_3048160421
crossref_primary_10_46298_dmtcs_8784
PublicationCentury 2000
PublicationDate 2023-01-01
PublicationDateYYYYMMDD 2023-01-01
PublicationDate_xml – month: 01
  year: 2023
  text: 2023-01-01
  day: 01
PublicationDecade 2020
PublicationPlace Nancy
PublicationPlace_xml – name: Nancy
PublicationTitle Discrete mathematics and theoretical computer science
PublicationYear 2023
Publisher DMTCS
Discrete Mathematics & Theoretical Computer Science
Publisher_xml – name: DMTCS
– name: Discrete Mathematics & Theoretical Computer Science
SSID ssj0012947
ssib044734695
Score 2.2742236
Snippet We examine the classic game of Cops and Robbers played on models of dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a...
We examine the classic game of Cops and Robbers played on dynamic graphs, that is, graphs evolving over discrete time steps. At each time step, a graph...
SourceID doaj
hal
proquest
crossref
SourceType Open Website
Open Access Repository
Aggregation Database
Index Database
StartPage 1
SubjectTerms [info.info-dm]computer science [cs]/discrete mathematics [cs.dm]
[info.info-ro]computer science [cs]/operations research [cs.ro]
Algorithms
Apexes
Computer Science
cops and robbers
Discrete Mathematics
dynamic graphs
Evolution
Games
Graph theory
Graphs
offline
online
Operations Research
Robbery
sparse
SummonAdditionalLinks – databaseName: Engineering Database
  dbid: M7S
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NT9wwELUocGgPpUBRt9DKQlwDie3YCRwQLFAO5UN8SNys2B63HEiWzcLvZ-xkF9FDL-ToWImV8cw825P3CNkCBVZJo5JcmTwRzJukctYkOVeFkcpaYUQUm1Dn58XdXXnZb7i1fVnlNCbGQO0aG_bId3ggNpE4xbL90WMSVKPC6WovofGBLASWhCyW7l3PThFYKVT3T56QrCx2js5uhtfbhSrEmywUyfoxt_wNpZD_ROSYZk6W3jvAL-RzDzDpQTcjlskc1CtkaSreQHtfXiGfzmaEre0q2Rs2o5ZWtaNXjTEICWlT06NOrZ7-CqTW7S698D6A0titoyilQ0yCX8ntyfHN8DTpdRUSy3M5SYT1nklfVYWDzKbO8qJyPLUO0R8vwXvJFWDcQV93jFtc0GWZybhFZOU5qIqvkfm6qeEboakHZoBDIXHZZV1pPKigHIFXBazMB2Rr-p31qKPP0LjsiObQ7mFiWx3MMSCHwQazLoHzOjY04z-6dyFdMQk-wL2MewGWl1yoFCQGFONxUPiuTbTgm2ecHvzWoS1lJcI0lj5jp42p9XTvra1-Nd33_99eJx-D3Hy3BbNB5ifjJ_hBFu3z5L4d_4yT7wWF0OH1
  priority: 102
  providerName: ProQuest
Title Cops and Robbers on Dynamic Graphs: Offline and Online Case
URI https://www.proquest.com/docview/3048160421
https://normandie-univ.hal.science/hal-02927320
https://doaj.org/article/a26ef561013f4ec393470e6794bf7a35
Volume 25:1
WOSCitedRecordID wos000957275300001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 1365-8050
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0012947
  issn: 1365-8050
  databaseCode: DOA
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 1365-8050
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssib044734695
  issn: 1365-8050
  databaseCode: M~E
  dateStart: 19980101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
– providerCode: PRVPQU
  databaseName: Continental Europe Database
  customDbUrl:
  eissn: 1365-8050
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0012947
  issn: 1365-8050
  databaseCode: BFMQW
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/conteurope
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 1365-8050
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0012947
  issn: 1365-8050
  databaseCode: M7S
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 1365-8050
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0012947
  issn: 1365-8050
  databaseCode: BENPR
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Publicly Available Content Database
  customDbUrl:
  eissn: 1365-8050
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0012947
  issn: 1365-8050
  databaseCode: PIMPY
  dateStart: 19970101
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1Nb9QwEB2hwgEOfBRQF8rKQr2GJrZjx-XULluKRJdVAamcrNgeCw5kq2bpsb-dsZOtKBcu5JCDY0XWG9sz40zeA9hDjV4rp4tau7qQPLqiDd4VtdCNU9p76WQWm9CLRXN-bpZ_SH2lmrCBHngAbr_lCmNy8pWIEr0wQuoSFU0jF3UrMntpqc0mmRq_H3Aj9fA3nlTcNPvh59r3bxrdyFv-J9P0k1f5noog_9qLs4M5fgwPx8iQHQ4jegJ3sNuGRxvVBTYuwm14cHrDtNo_hbez1UXP2i6ws5VzFMuxVcfeDTLz7H1io-4P2KcYUzSZuw3comxG3usZfD2ef5mdFKMgQuFFrdaF9DFyFdu2CVj5MnjRtEGUPlDYJgzGqIRG2jBokQYuPGViVeUq4SkkigIJreew1a063AFWRuQOBTaK8iUfjIuok-QDXS1yU09gbwOTvRh4LyzlCxlNm9G0Cc0JHCUIb7oksurcQCa0owntv0w4gddkgFvvODn8aFNbyQ3FV7y8ok67G_vYcZn1ViS2G0X7TvXifwzkJdxPavLDCcsubK0vf-EruOev1j_6yyncPZovlmfTPNOmqUj0c7pfz-nJ8sPp8ttv0N_Zfg
linkProvider Directory of Open Access Journals
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwEB6VggQcKBQQhQIWKsfQxE7sGIRQ2aVs1d0F0UXqzcQv6KHJslmK-qf4jYzzWFQO3HogR8fKa77MfOPHfAA7TjgjuBZRJnQWpdTrqLBGRxkTuebCmFSnjdiEmE7z42P5cQ1-9XthwrLK3ic2jtpWJoyR77JQ2IQjxJI38-9RUI0Ks6u9hEYLi0N3_hNTtvr1wRDt-5zS_XezwSjqVAUiwzK-jFLjPeW-KHLrEhNbw_LCsthY5D5MOu85Ew7_OkS6pcxgOpMkOmEGeYVnThQMr3sFriKNoLJZKni0mrWgMhXtHsCUU5nvDiezwdGLXOTphajXiANgLPsWll7-FQGasLa_8b99kNtwqyPQZK9F_B1Yc-UmbPTiFKTzVZtwc7IqSFvfhVeDal6TorTkU6U1Ul5SlWR4XhanJ4a8D0W765fkg_eBdDfd2hKsZIBB_h58vpQXug_rZVW6B0Bi76h2zOUc00pjpfZOBGUMPApHZbYFO71d1bwtD6IwrWrMr-zp0tQqmH8L3gabr7qEmt5NQ7X4qjoXoQrKnQ90NmE-dYZJlorYcXSY2uND4b2eIWIuXGO0N1ahLaYSaSiNz7DTdo8W1XmjWv2BysN_n34K10ezyViND6aHj-AGRULXDjdtw_py8cM9hmvmbHlSL540wCfw5bKB9Rv6Wz-a
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Cops+and+Robbers+on+Dynamic+Graphs%3A+Offline+and+Online+Case&rft.jtitle=Discrete+mathematics+and+theoretical+computer+science&rft.au=Balev%2C+Stefan&rft.au=Jim%C3%A9nez+Laredo%2C+Juan+Luis&rft.au=Lamprou%2C+Ioannis&rft.au=Pign%C3%A9%2C+Yoann&rft.date=2023-01-01&rft.pub=DMTCS&rft.issn=1462-7264&rft.eissn=1365-8050&rft.volume=25%3A1&rft.issue=1&rft_id=info:doi/10.46298%2Fdmtcs.8784&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=oai%3AHAL%3Ahal-02927320v5
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1365-8050&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1365-8050&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1365-8050&client=summon