Matroid Secretary for Regular and Decomposable Matroids

In the matroid secretary problem we are given a stream of elements in random order and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from the assumption that decisions are irrevocab...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on computing Vol. 43; no. 5; pp. 1807 - 1830
Main Authors: Dinitz, Michael, Kortsarz, Guy
Format: Journal Article
Language:English
Published: 01.01.2014
Subjects:
Algorithms
Decisions
Decomposition
Graph theory
Graphs
Reproduction
Streams
Vector spaces
Italy, Marche, Pesaro, Fano
ISSN:0097-5397, 1095-7111
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract In the matroid secretary problem we are given a stream of elements in random order and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from the assumption that decisions are irrevocable : if we choose to accept an element when it is presented by the stream, then we can never get rid of it, and if we choose not to accept it, then we cannot later add it. Babaioff, Immorlica, and Kleinberg [Proceedings of SODA' 07] introduced this problem, gave O(1)-competitive algorithms for certain classes of matroids, and conjectured that every matroid admits an O(1)-competitive algorithm. However, most matroids that are known to admit an O(1)-competitive algorithm can be easily represented using graphs (e.g., graphic, cographic, and transversal matroids). In particular, there is very little known about $F$-representable matroids (the class of matroids that can be represented as elements of a vector space over a field $F$), which are one of the foundational types of matroids. Moreover, most of the known techniques are as dependent on graph theory as they are on matroid theory. We go beyond graphs by giving O(1)-competitive algorithms for regular matroids (the class of matroids that are representable over any field) and use techniques that are fundamentally matroid-theoretic rather than graph-theoretic. Our main technique is to leverage the seminal regular matroid decomposition theorem of Seymour, which gives a method for decomposing any regular matroid into matroids which are graphic, cographic, or isomorphic to a simple 10-element matroid. We show how to combine in a black-box manner any algorithms for these basic classes into an algorithm for a given regular matroid, i.e., how to respect the decomposition. In fact, this allows us to generalize beyond regular matroids to any class of matroids that admits such a decomposition into classes for which we already have good algorithms. In particular, we give an O(1)-competitive algorithm for the class ofmax-flow min-cut matroids, which Seymour showed can be decomposed into regular matroids and copies of the Fano matroid.
AbstractList In the matroid secretary problem we are given a stream of elements in random order and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from the assumption that decisions are irrevocable : if we choose to accept an element when it is presented by the stream, then we can never get rid of it, and if we choose not to accept it, then we cannot later add it. Babaioff, Immorlica, and Kleinberg [Proceedings of SODA' 07] introduced this problem, gave O(1)-competitive algorithms for certain classes of matroids, and conjectured that every matroid admits an O(1)-competitive algorithm. However, most matroids that are known to admit an O(1)-competitive algorithm can be easily represented using graphs (e.g., graphic, cographic, and transversal matroids). In particular, there is very little known about $F$-representable matroids (the class of matroids that can be represented as elements of a vector space over a field $F$), which are one of the foundational types of matroids. Moreover, most of the known techniques are as dependent on graph theory as they are on matroid theory. We go beyond graphs by giving O(1)-competitive algorithms for regular matroids (the class of matroids that are representable over any field) and use techniques that are fundamentally matroid-theoretic rather than graph-theoretic. Our main technique is to leverage the seminal regular matroid decomposition theorem of Seymour, which gives a method for decomposing any regular matroid into matroids which are graphic, cographic, or isomorphic to a simple 10-element matroid. We show how to combine in a black-box manner any algorithms for these basic classes into an algorithm for a given regular matroid, i.e., how to respect the decomposition. In fact, this allows us to generalize beyond regular matroids to any class of matroids that admits such a decomposition into classes for which we already have good algorithms. In particular, we give an O(1)-competitive algorithm for the class ofmax-flow min-cut matroids, which Seymour showed can be decomposed into regular matroids and copies of the Fano matroid.
Author Kortsarz, Guy
Dinitz, Michael
Author_xml – sequence: 1
  givenname: Michael
  surname: Dinitz
  fullname: Dinitz, Michael
– sequence: 2
  givenname: Guy
  surname: Kortsarz
  fullname: Kortsarz, Guy
BookMark eNqF0E1LxDAQBuAgK7i7evAf9KiHuplMPtqjrJ-wIvgB3kqaJlLpNjXJHvz3dtnFgwiehoFnBt53Ria97y0hp0AvAFAtAGnJKdK3AzIFWopcAcCETCktVS6wVEdkFuMHpcA54JSoB52Cb5vs2Zpgkw5fmfMhe7Lvm06HTPdNdmWNXw8-6rqz2Z7HY3LodBftyX7OyevN9cvyLl893t4vL1e5YaVIOSpnBGOoGbeK2gaYQw1oauQNSjTMSKEKKSwwUYPCwtTAXbldZMOowzk52_0dgv_c2JiqdRuN7TrdW7-JFagxWMGphP-pZCUKibIY6fmOmuBjDNZVQ2jXY_gKaLXtsfrpcbSLX9a0SafW9ynotvvj4hs1lXOX
CitedBy_id crossref_primary_10_1137_16M1105220
crossref_primary_10_1137_17M1151250
crossref_primary_10_1287_moor_2023_1381
crossref_primary_10_1137_16M1107899
crossref_primary_10_1007_s10107_025_02253_w
crossref_primary_10_1287_moor_2017_0876
crossref_primary_10_1007_s00224_015_9642_4
crossref_primary_10_1287_moor_2021_1137
crossref_primary_10_1007_s10107_024_02177_x
crossref_primary_10_1145_3355629
crossref_primary_10_1007_s10107_024_02148_2
crossref_primary_10_1016_j_geb_2018_05_006
crossref_primary_10_1007_s40305_015_0116_9
crossref_primary_10_1145_3212512
crossref_primary_10_1007_s00446_018_0327_5
crossref_primary_10_1287_moor_2020_1083
Cites_doi 10.1145/1399589.1399596
10.1016/0095-8956(90)90030-4
10.1016/S0095-8956(81)80029-9
10.1016/0095-8956(77)90031-4
10.1145/2500121
10.1145/2491533.2491557
10.1016/0095-8956(80)90075-1
10.1007/s00453-010-9457-2
ContentType Journal Article
DBID AAYXX
CITATION
7QH
7UA
C1K
F1W
H96
L.G
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1137/13094030X
DatabaseName CrossRef
Aqualine
Water Resources Abstracts
Environmental Sciences and Pollution Management
ASFA: Aquatic Sciences and Fisheries Abstracts
Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources
Aquatic Science & Fisheries Abstracts (ASFA) Professional
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Aquatic Science & Fisheries Abstracts (ASFA) Professional
Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources
Aqualine
ASFA: Aquatic Sciences and Fisheries Abstracts
Water Resources Abstracts
Environmental Sciences and Pollution Management
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList Aquatic Science & Fisheries Abstracts (ASFA) Professional
Computer and Information Systems Abstracts
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
Computer Science
EISSN 1095-7111
EndPage 1830
ExternalDocumentID 10_1137_13094030X
GeographicLocations Italy, Marche, Pesaro, Fano
GeographicLocations_xml – name: Italy, Marche, Pesaro, Fano
GroupedDBID --Z
-DZ
-~X
.4S
.DC
123
4.4
7RQ
7WY
7X2
7XC
88I
8CJ
8FE
8FG
8FH
8FL
8G5
8V8
AALVN
AASXH
AAYXX
ABDBF
ABDPE
ABJCF
ABKAD
ABMZU
ABPPZ
ABUFD
ABUWG
ACBEA
ACGFO
ACGOD
ACIWK
ACNCT
ACPRK
ACUHS
ADBBV
ADMHC
ADXHL
AEMOZ
AENEX
AFFHD
AFKRA
AFRAH
AHQJS
AKVCP
ALMA_UNASSIGNED_HOLDINGS
ANXRF
ARAPS
ARCSS
ATCPS
AZQEC
BBNVY
BENPR
BEZIV
BGLVJ
BHPHI
BPHCQ
CCPQU
CITATION
CS3
CZ9
D1I
D1J
D1K
DQ2
DU5
DWQXO
EAP
EAS
EBR
EBS
EBU
ECS
EDO
EJD
EMK
EST
ESX
FRNLG
GNUQQ
GUQSH
H13
HCIFZ
H~9
I-F
K1G
K6-
K60
K6V
K6~
K7-
KB.
KC.
L6V
LK5
LK8
M0C
M0K
M1Q
M2O
M2P
M7P
M7R
M7S
MK~
NHB
OHT
P1Q
P2P
P62
PATMY
PDBOC
PHGZM
PHGZT
PQBIZ
PQBZA
PQGLB
PQQKQ
PROAC
PTHSS
PYCSY
RJG
RNS
RSI
S0W
TAE
TH9
TN5
TUS
TWZ
UHB
UQL
VOH
WH7
WHG
XJE
YNT
YYP
YZZ
ZCG
ZY4
7QH
7UA
C1K
F1W
H96
L.G
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c295t-37fc5223a24e70ed12f3a13cb34d363c2c657865e125b1738cb14f925b16d20f3
ISICitedReferencesCount 29
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000344753500011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0097-5397
IngestDate Sun Nov 09 10:50:44 EST 2025
Tue Oct 07 09:52:37 EDT 2025
Sat Nov 29 03:54:36 EST 2025
Tue Nov 18 21:33:55 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 5
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c295t-37fc5223a24e70ed12f3a13cb34d363c2c657865e125b1738cb14f925b16d20f3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
PQID 1629356368
PQPubID 23462
PageCount 24
ParticipantIDs proquest_miscellaneous_1709784061
proquest_miscellaneous_1629356368
crossref_primary_10_1137_13094030X
crossref_citationtrail_10_1137_13094030X
PublicationCentury 2000
PublicationDate 2014-01-00
20140101
PublicationDateYYYYMMDD 2014-01-01
PublicationDate_xml – month: 01
  year: 2014
  text: 2014-01-00
PublicationDecade 2010
PublicationTitle SIAM journal on computing
PublicationYear 2014
References Jaillet P. (atypb15) 2013
Dynkin E. B. (atypb8) 1963
Lovász L. (atypb19) 2006; 43
Korula N. (atypb17) 2009
atypb26
atypb11
atypb22
Feldman M. (atypb9) 2011
atypb23
Gupta A. (atypb13) 2010
Tutte W. T. (atypb28) 1958; 88
atypb2
Gharan S. O. (atypb12) 2011
atypb4
atypb7
atypb6
References_xml – start-page: 335
  year: 2011
  ident: atypb12
  publication-title: Berlin
– ident: atypb2
  doi: 10.1145/1399589.1399596
– volume: 88
  start-page: 144
  year: 1958
  ident: atypb28
  publication-title: Trans. Amer. Math. Soc.
– start-page: 218
  year: 2011
  ident: atypb9
  publication-title: Berlin
– start-page: 246
  year: 2010
  ident: atypb13
  publication-title: Berlin
– ident: atypb26
  doi: 10.1016/0095-8956(90)90030-4
– start-page: 254
  year: 2013
  ident: atypb15
  publication-title: Berlin
– ident: atypb11
  doi: 10.1016/S0095-8956(81)80029-9
– ident: atypb22
  doi: 10.1016/0095-8956(77)90031-4
– ident: atypb4
  doi: 10.1145/2500121
– volume: 43
  start-page: 75
  year: 2006
  ident: atypb19
  publication-title: S.)
– ident: atypb7
  doi: 10.1145/2491533.2491557
– ident: atypb23
  doi: 10.1016/0095-8956(80)90075-1
– ident: atypb6
  doi: 10.1007/s00453-010-9457-2
– start-page: 508
  year: 2009
  ident: atypb17
  publication-title: Berlin
– start-page: 4
  year: 1963
  ident: atypb8
  publication-title: Soviet Math. Dokl.
SSID ssj0014413
Score 2.275971
Snippet In the matroid secretary problem we are given a stream of elements in random order and asked to choose a set of elements that maximizes the total value of the...
SourceID proquest
crossref
SourceType Aggregation Database
Enrichment Source
Index Database
StartPage 1807
SubjectTerms Algorithms
Decisions
Decomposition
Graph theory
Graphs
Reproduction
Streams
Vector spaces
Title Matroid Secretary for Regular and Decomposable Matroids
URI https://www.proquest.com/docview/1629356368
https://www.proquest.com/docview/1709784061
Volume 43
WOSCitedRecordID wos000344753500011&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: PRVPQU
  databaseName: AAdvanced Technologies & Aerospace Database (subscription)
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: P5Z
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/hightechjournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ABI/INFORM Collection
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: 7WY
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/abicomplete
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ABI/INFORM Global
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: M0C
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/abiglobal
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Agricultural Science Database
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: M0K
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/agriculturejournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Biological Science Database
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: M7P
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/biologicalscijournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Career & Technical Education Database [Proquest]
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: 7RQ
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/career
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Computer Science Database
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: K7-
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/compscijour
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Engineering Database (subscription)
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: M7S
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Environmental Science Database
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: PATMY
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/environmentalscience
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Materials Science Database
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: KB.
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/materialsscijournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Military Database
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: M1Q
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/military
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central (subscription)
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: BENPR
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Research Library
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: M2O
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/pqrl
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Science Database
  customDbUrl:
  eissn: 1095-7111
  dateEnd: 20140531
  omitProxy: false
  ssIdentifier: ssj0014413
  issn: 0097-5397
  databaseCode: M2P
  dateStart: 19720301
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/sciencejournals
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Nb9MwFLfYxgEOfAwQG1AFxIFLRhw7dnJk0wCpaindEIVLlDiOVAmlU5JOg7-e92wnzcaExoHLUz7sVvHPeu9n-30Q8lqVaPd56YdZiCE5svBzxuBKFZzzhCWlUKbYhJxO48UimbkS940pJyCrKr64SM7-K9TwDMDG0Nl_gLv_UXgA1wA6SIAd5I2An-Du9rLAnXT0JaytR-bc1JyvnecxOpKvGhM15Zo3Q5Z6Auv7TU4J66i-bjsjh7R3CZrg11W3exNBU7dNVptXH9Y_h3sKlA_2FJyeTKQfMes5e6CtagQy5stONTrdaVMsuTkSDRQhjQM5MKqgOILrFbYN-WeYxo8Fi41V6k7irxir3oXQLF6YTPuuW2QnlFGCbn3jw4P-JAnonstEar_IZZeCrm_7rpc5yWWTbHjG6QNyzy0QvHcW2Ifklq52yf2u-IbndPEuuTvpE-42j4h0MHo96h6g7jnUPUDdG6Ludag_Jl_eH58effRdTQxfhUnUgj0oFVBmloVcy0AXNCxZRpnKGS-YYCpUAnSwiDQQ15xKFquc8jLBG1GEQcmekO1qVemnxBM6BvYbAIGnGac5zwIVxyKPRcGYolTtkTfdqKTKJYzHuiU_0j_Gfo-86pue2Swp1zV62Q1tCjoMD6aySq_WTUoFkM5IMBH_pY3EiCOkn_s3-bNn5M5mYj8n22291i_IbXXeLpt6RLbk_DPKr99GZOfweDqbw91Y-iMzeUBOgiMjxygptp2En4ycoZRWnoCcRd9_A4OueZo
linkProvider ProQuest
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=Matroid+Secretary+for+Regular+and+Decomposable+Matroids&rft.jtitle=SIAM+journal+on+computing&rft.au=Dinitz%2C+Michael&rft.au=Kortsarz%2C+Guy&rft.date=2014-01-01&rft.issn=0097-5397&rft.eissn=1095-7111&rft.volume=43&rft.issue=5&rft.spage=1807&rft.epage=1830&rft_id=info:doi/10.1137%2F13094030X&rft.externalDBID=n%2Fa&rft.externalDocID=10_1137_13094030X
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0097-5397&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0097-5397&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0097-5397&client=summon