Incremental Medians via Online Bidding

In the k -median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F . The goal is to find a set F of k facilities that minimizes the sum, over all c...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Algorithmica Ročník 50; číslo 4; s. 455 - 478
Hlavní autori:	Chrobak, Marek, Kenyon, Claire, Noga, John, Young, Neal E.
Médium:	Journal Article Konferenčný príspevok..
Jazyk:	English
Vydavateľské údaje:	New York Springer-Verlag 01.04.2008 Springer
Predmet:	Algorithm Analysis and Problem Complexity Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer Systems Organization and Communication Networks Data Structures and Information Theory Exact sciences and technology Logistics Mathematics of Computing Operational research and scientific management Operational research. Management science Theoretical computing Theory of Computation Competitive Ratio Incremental Algorithm Facility Location Problem Deterministic Algorithm Fractional Median On line Bidding Refinement method Competitiveness Median Graph theory Polynomial method Approximation algorithm Randomized algorithm Combinatorial optimization Competitive algorithms Polynomial time Optimum Upper bound Randomization Randomized design User service Theorem proving K median problem Minimal distance Metric Deterministic approach Deterministic algorithms
ISSN:	0178-4617, 1432-0541
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Abstract	In the k -median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F . The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following the work of Mettu and Plaxton, we study the incremental medians problem, where k is not known in advance. An incremental algorithm produces a nested sequence of facility sets F 1 ⊆ F 2 ⊆ ⋅⋅⋅ ⊆ F n , where \| F k \|= k for each k . Such an algorithm is called c -cost-competitive if the cost of each F k is at most c times the optimum k -median cost. We give improved incremental algorithms for the metric version of this problem: an 8-cost-competitive deterministic algorithm, a 2 e ≈5.44-cost-competitive randomized algorithm, a (24+ ε )-cost-competitive, polynomial-time deterministic algorithm, and a 6 e + ε ≈16.31-cost-competitive, polynomial-time randomized algorithm. We also consider the competitive ratio with respect to size . An algorithm is s -size-competitive if the cost of each F k is at most the minimum cost of any set of k facilities, while the size of F k is at most sk . We show that the optimal size-competitive ratios for this problem, in the deterministic and randomized cases, are 4 and e . For polynomial-time algorithms, we present the first polynomial-time O (log m )-size-approximation algorithm for the offline problem, as well as a polynomial-time O (log m )-size-competitive algorithm for the incremental problem. Our upper bound proofs reduce the incremental medians problem to the following online bidding problem: faced with some unknown threshold T ∈ℝ + , an algorithm must submit “bids” b ∈ℝ + until it submits a bid b ≥ T , paying the sum of all its bids. We present folklore algorithms for online bidding and prove that they are optimally competitive. We extend some of the above results for incremental medians to approximately metric distance functions and to incremental fractional medians. Finally, we consider a restricted version of the incremental medians problem where k is restricted to one of two given values, for which we give a deterministic algorithm with a nearly optimal cost-competitive ratio.
AbstractList	In the k -median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F . The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following the work of Mettu and Plaxton, we study the incremental medians problem, where k is not known in advance. An incremental algorithm produces a nested sequence of facility sets F 1 ⊆ F 2 ⊆ ⋅⋅⋅ ⊆ F n , where \| F k \|= k for each k . Such an algorithm is called c -cost-competitive if the cost of each F k is at most c times the optimum k -median cost. We give improved incremental algorithms for the metric version of this problem: an 8-cost-competitive deterministic algorithm, a 2 e ≈5.44-cost-competitive randomized algorithm, a (24+ ε )-cost-competitive, polynomial-time deterministic algorithm, and a 6 e + ε ≈16.31-cost-competitive, polynomial-time randomized algorithm. We also consider the competitive ratio with respect to size . An algorithm is s -size-competitive if the cost of each F k is at most the minimum cost of any set of k facilities, while the size of F k is at most sk . We show that the optimal size-competitive ratios for this problem, in the deterministic and randomized cases, are 4 and e . For polynomial-time algorithms, we present the first polynomial-time O (log m )-size-approximation algorithm for the offline problem, as well as a polynomial-time O (log m )-size-competitive algorithm for the incremental problem. Our upper bound proofs reduce the incremental medians problem to the following online bidding problem: faced with some unknown threshold T ∈ℝ + , an algorithm must submit “bids” b ∈ℝ + until it submits a bid b ≥ T , paying the sum of all its bids. We present folklore algorithms for online bidding and prove that they are optimally competitive. We extend some of the above results for incremental medians to approximately metric distance functions and to incremental fractional medians. Finally, we consider a restricted version of the incremental medians problem where k is restricted to one of two given values, for which we give a deterministic algorithm with a nearly optimal cost-competitive ratio.
Author	Chrobak, Marek Kenyon, Claire Young, Neal E. Noga, John
Author_xml	– sequence: 1 givenname: Marek surname: Chrobak fullname: Chrobak, Marek organization: Department of Computer Science, University of California – sequence: 2 givenname: Claire surname: Kenyon fullname: Kenyon, Claire organization: Computer Science Department, Brown University – sequence: 3 givenname: John surname: Noga fullname: Noga, John organization: Department of Computer Science, California State University – sequence: 4 givenname: Neal E. surname: Young fullname: Young, Neal E. email: algorithmica@neal.young.name organization: Department of Computer Science, University of California
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20365167$$DView record in Pascal Francis
BookMark	eNp9kD1PwzAURS1UJNrCD2DLApvh2Y7jZISKj0pFXWC2HPulcpU6lR1Q-fekCiwMne4d7rnDmZFJ6AIScs3gjgGo-wSQS0GHSisASQ9nZMpywSnInE3IFJgqaV4wdUFmKW0BGFdVMSW3y2Aj7jD0ps3e0HkTUvblTbYOrQ-YPXrnfNhckvPGtAmvfnNOPp6f3hevdLV-WS4eVtQKVva0kFY20jbATIVcqarOEaUSliOCMyhZ2QjBHTrJlWtqIY1wJaiK2RoUt2JObsbfvUnWtE00wfqk99HvTPzWHEQhWaGGnRp3NnYpRWy09b3pfRf6aHyrGeijFj1q0cd61KIPA8n-kX_npxg-MmnYhg1Gve0-YxhEnIB-AOscdjQ
CitedBy_id	crossref_primary_10_1016_j_tcs_2009_09_029 crossref_primary_10_1016_j_ipl_2010_03_016 crossref_primary_10_1016_j_tcs_2015_09_021 crossref_primary_10_1155_2013_313868 crossref_primary_10_1016_j_tcs_2021_02_016 crossref_primary_10_1016_j_ic_2017_12_002 crossref_primary_10_1016_j_ipl_2009_07_006 crossref_primary_10_1007_s00453_019_00625_1 crossref_primary_10_1002_net_21595 crossref_primary_10_1137_110844210 crossref_primary_10_1007_s10878_015_9933_3 crossref_primary_10_1007_s11432_014_5065_0 crossref_primary_10_1016_j_disopt_2016_08_005 crossref_primary_10_1007_s10107_020_01576_0 crossref_primary_10_1137_070698257 crossref_primary_10_1590_0104_6632_20190361s20170379 crossref_primary_10_1016_j_ejor_2015_08_060
Cites_doi	10.1007/11682462_31 10.1007/978-3-540-39658-1_6 10.1007/3-540-61440-0_166 10.1016/j.ipl.2005.09.009 10.1016/0304-3975(94)90151-1 10.1109/FOCS.2006.39 10.1145/347476.347479 10.1006/jagm.2000.1100 10.1006/inco.1996.0092 10.1145/375827.375845 10.1016/0020-0190(92)90208-D 10.1145/950620.950621 10.1137/S0097539701383443 10.1137/S0097539701398594 10.1023/A:1008023416823 10.1137/S0097539702416402 10.1016/j.jcss.2004.10.006
ContentType	Journal Article Conference Proceeding
Copyright	Springer Science+Business Media, LLC 2007 2008 INIST-CNRS
Copyright_xml	– notice: Springer Science+Business Media, LLC 2007 – notice: 2008 INIST-CNRS
DBID	AAYXX CITATION IQODW
DOI	10.1007/s00453-007-9005-x
DatabaseName	CrossRef Pascal-Francis
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science Applied Sciences
EISSN	1432-0541
EndPage	478
ExternalDocumentID	20365167 10_1007_s00453_007_9005_x
GroupedDBID	-4Z -59 -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABFSI ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP E.L EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9O PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UQL UTJUX UZXMN VC2 VFIZW VH1 VXZ W23 W48 WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZY4 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION IQODW
ID	FETCH-LOGICAL-c318t-65c5f5cf01a9e2779b4ee573c2ee0dae518f332ded527dfb35a3d80791cb072c3
IEDL.DBID	RSV
ISICitedReferencesCount	31
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000253895900004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0178-4617
IngestDate	Wed Apr 02 07:18:00 EDT 2025 Sat Nov 29 03:45:23 EST 2025 Tue Nov 18 22:33:02 EST 2025 Fri Feb 21 02:40:20 EST 2025
IsPeerReviewed	true
IsScholarly	true
Issue	4
Keywords	Competitive Ratio Incremental Algorithm Facility Location Problem Deterministic Algorithm Fractional Median On line Bidding Refinement method Competitiveness Median Graph theory Polynomial method Approximation algorithm Randomized algorithm Combinatorial optimization Competitive algorithms Polynomial time Optimum Upper bound Randomization Randomized design User service Theorem proving K median problem Minimal distance Metric Deterministic approach Deterministic algorithms
Language	English
License	http://www.springer.com/tdm CC BY 4.0
LinkModel	DirectLink
MeetingName	Latin American Theoretical Informatics Conference (LATIN)
MergedId	FETCHMERGED-LOGICAL-c318t-65c5f5cf01a9e2779b4ee573c2ee0dae518f332ded527dfb35a3d80791cb072c3
PageCount	24
ParticipantIDs	pascalfrancis_primary_20365167 crossref_citationtrail_10_1007_s00453_007_9005_x crossref_primary_10_1007_s00453_007_9005_x springer_journals_10_1007_s00453_007_9005_x
PublicationCentury	2000
PublicationDate	2008-04-01
PublicationDateYYYYMMDD	2008-04-01
PublicationDate_xml	– month: 04 year: 2008 text: 2008-04-01 day: 01
PublicationDecade	2000
PublicationPlace	New York
PublicationPlace_xml	– name: New York – name: New York, NY
PublicationTitle	Algorithmica
PublicationTitleAbbrev	Algorithmica
PublicationYear	2008
Publisher	Springer-Verlag Springer
Publisher_xml	– name: Springer-Verlag – name: Springer
References	ChrobakM.KenyonC.NogaJ.YoungN.Online medians via online biddingProc. 7th Latin American Theoretical Informatics Symp. (LATIN)2006BerlinSpringer311322 GoemansM.KleinbergJ.An improved approximation ratio for the minimum latency problemProc. 7th Symp. on Discrete Algorithms (SODA)1996New YorkACM/SIAM152158 JainK.MahdianM.MarkakisE.SaberiA.VaziraniV.V.Greedy facility location algorithms analyzed using dual fitting with factor-revealing lpJ. ACM20035079582410.1145/950620.9506212146253 CharikarM.ChekuriC.FederT.MotwaniR.Incremental clustering and dynamic information retrievalProc. 29th Symp. Theory of Computing (STOC)1997New YorkACM626635 DasguptaS.LongP.M.Performance guarantees for hierarchical clusteringJ. Comput. Syst. Sci.20057045555691101.6898010.1016/j.jcss.2004.10.0062136964 KoutsoupiasE.Weak adversaries for the k-server problemProc. 40th Symp. Foundations of Computer Science (FOCS)1999New YorkIEEE444449 YoungN.E.K-medians, facility location, and the Chernoff–Wald boundProc. 11th Symp. on Discrete Algorithms (SODA)2000New YorkACM/SIAM8695 LinG.NagarajanC.RajamaranR.WilliamsonD.P.A general approach for incremental approximation and hierarchical clusteringProc. 17th Symp. on Discrete Algorithms (SODA)2006New YorkACM/SIAM CharikarM.GuhaS.TardosE.ShmoysD.B.A constant-factor approximation algorithm for the k-median problemProc. 31st Symp. Theory of Computing (STOC)1999New YorkACM110 LinJ.-H.VitterJ.S.ε-approximations with minimum packing constraint violation (extended abstract)Proc. 24th Symp. Theory of Computing (STOC)1992New YorkACM771782 LinJ.-H.VitterJ.S.Approximation algorithms for geometric median problemsInf. Process. Lett.1992442452490764.6807910.1016/0020-0190(92)90208-D1202349 CharikarM.GuhaS.Improved combinatorial algorithms for facility location problemsSIAM J. Comput.20053448038241075.6810010.1137/S00975397013985942148859 ChrobakM.KenyonC.YoungN.E.The reverse greedy algorithm for the k-median problemInf. Process. Lett.200697687210.1016/j.ipl.2005.09.0092187051 CharikarM.GuhaS.Improved combinatorial algorithms for the facility location and k-median problemsProc. 40th Symp. Foundations of Computer Science (FOCS)1999New YorkIEEE378388 GoemansM.KleinbergJ.An improved approximation ratio for the minimum latency problemMath. Program.199882111112410.1007/BF015858671627628 ChekuriC.GoelA.KhannaS.KumarA.Multi-processor scheduling to minimize flow time with ε-resource augmentationProc. 36th Symp. Theory of Computing (STOC)2004New YorkACM363372 FaginR.StockmeyerL.Relaxing the triangle inequality in pattern matchingInt. J. Comput. Vis.19983021923110.1023/A:1008023416823 KalyanasundaramB.PruhsK.Speed is as powerful as clairvoyanceJ. ACM20004721422110.1145/347476.3474791866172 AryaV.GargN.KhandekarR.MeyersonA.MunagalaK.PanditV.Local search heuristic for k-median and facility location problemsProc. 33rd Symp. Theory of Computing (STOC)2001New YorkACM2129 MettuR.R.Greg PlaxtonC.The online median problemSIAM J. Comput.2003328168321128.9055010.1137/S00975397013834432001756 AryaV.GargN.KhandekarR.MeyersonA.MunagalaK.PanditV.Local search heuristics for k-median and facility location problemsSIAM J. Comput.20043335445621105.6811810.1137/S00975397024164022066641 KorupoluM.R.Greg PlaxtonC.RajaramanR.Analysis of a local search heuristic for facility location problemsJ. Algorithms2000371461880962.6804410.1006/jagm.2000.11001783252 MettuR.R.Greg PlaxtonC.The online median problemProc. 41st Symp. Foundations of Computer Science (FOCS)2000New YorkIEEE33934810.1109/SFCS.2000.892122 Buchbinder, N., Naor, J.: Improved bounds for online routing and packing via a primal-dual approach. In: Proc. 46th Symp. Foundations of Computer Science (FOCS), pp. 293–304 (2006) Chakrabarti, S., Phillips, C.A., Schulz, A.S., Shmoys, D.B., Stein, C., Wein, J.: Improved scheduling algorithms for minsum criteria. In: Automata, Languages and Programming, pp. 646–657 (1996) MotwaniR.PhillipsS.TorngE.Nonclairvoyant schedulingTheor. Comput. Sci.1994130117470820.9005610.1016/0304-3975(94)90151-11287130 JainK.VaziraniV.V.Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxationJ. ACM20014827429610.1145/375827.3758451868717 Archer, A., Rajagopalan, R., Shmoys, D.B.: Lagrangian relaxation for the k-median problem: new insights and continuity properties. In: Proc. 11th European Symp. on Algorithms (ESA), pp. 31–42 (2003) KaoM.-Y.ReifJ.H.TateS.R.Searching in an unknown environment: An optimal randomized algorithm for the cow-path problemInf. Comput.1996131163800876.6803010.1006/inco.1996.00921425815Preliminary version appeared in the Proceedings of the Symp. on Discrete Algorithms, Austin, TX, January 1993 JainK.MahdianM.SaberiA.A new greedy approach for facility location problemsProc. 34th Symp. Theory of Computing (STOC)2002New YorkACM731740 K. Jain (9005_CR17) 2003; 50 K. Jain (9005_CR19) 2001; 48 M. Chrobak (9005_CR12) 2006; 97 K. Jain (9005_CR18) 2002 B. Kalyanasundaram (9005_CR20) 2000; 47 G. Lin (9005_CR24) 2006 M. Goemans (9005_CR16) 1998; 82 9005_CR5 9005_CR4 M.-Y. Kao (9005_CR21) 1996; 131 R. Fagin (9005_CR14) 1998; 30 M. Charikar (9005_CR8) 2005; 34 R.R. Mettu (9005_CR27) 2000 M.R. Korupolu (9005_CR22) 2000; 37 N.E. Young (9005_CR30) 2000 M. Charikar (9005_CR9) 1999 S. Dasgupta (9005_CR13) 2005; 70 M. Chrobak (9005_CR11) 2006 E. Koutsoupias (9005_CR23) 1999 J.-H. Lin (9005_CR26) 1992 M. Charikar (9005_CR6) 1997 M. Charikar (9005_CR7) 1999 M. Goemans (9005_CR15) 1996 9005_CR1 V. Arya (9005_CR2) 2001 C. Chekuri (9005_CR10) 2004 J.-H. Lin (9005_CR25) 1992; 44 V. Arya (9005_CR3) 2004; 33 R.R. Mettu (9005_CR28) 2003; 32 R. Motwani (9005_CR29) 1994; 130
References_xml	– reference: JainK.MahdianM.SaberiA.A new greedy approach for facility location problemsProc. 34th Symp. Theory of Computing (STOC)2002New YorkACM731740 – reference: YoungN.E.K-medians, facility location, and the Chernoff–Wald boundProc. 11th Symp. on Discrete Algorithms (SODA)2000New YorkACM/SIAM8695 – reference: LinJ.-H.VitterJ.S.Approximation algorithms for geometric median problemsInf. Process. Lett.1992442452490764.6807910.1016/0020-0190(92)90208-D1202349 – reference: ChekuriC.GoelA.KhannaS.KumarA.Multi-processor scheduling to minimize flow time with ε-resource augmentationProc. 36th Symp. Theory of Computing (STOC)2004New YorkACM363372 – reference: FaginR.StockmeyerL.Relaxing the triangle inequality in pattern matchingInt. J. Comput. Vis.19983021923110.1023/A:1008023416823 – reference: CharikarM.GuhaS.TardosE.ShmoysD.B.A constant-factor approximation algorithm for the k-median problemProc. 31st Symp. Theory of Computing (STOC)1999New YorkACM110 – reference: LinJ.-H.VitterJ.S.ε-approximations with minimum packing constraint violation (extended abstract)Proc. 24th Symp. Theory of Computing (STOC)1992New YorkACM771782 – reference: Buchbinder, N., Naor, J.: Improved bounds for online routing and packing via a primal-dual approach. In: Proc. 46th Symp. Foundations of Computer Science (FOCS), pp. 293–304 (2006) – reference: KorupoluM.R.Greg PlaxtonC.RajaramanR.Analysis of a local search heuristic for facility location problemsJ. Algorithms2000371461880962.6804410.1006/jagm.2000.11001783252 – reference: GoemansM.KleinbergJ.An improved approximation ratio for the minimum latency problemProc. 7th Symp. on Discrete Algorithms (SODA)1996New YorkACM/SIAM152158 – reference: KalyanasundaramB.PruhsK.Speed is as powerful as clairvoyanceJ. ACM20004721422110.1145/347476.3474791866172 – reference: DasguptaS.LongP.M.Performance guarantees for hierarchical clusteringJ. Comput. Syst. Sci.20057045555691101.6898010.1016/j.jcss.2004.10.0062136964 – reference: Chakrabarti, S., Phillips, C.A., Schulz, A.S., Shmoys, D.B., Stein, C., Wein, J.: Improved scheduling algorithms for minsum criteria. In: Automata, Languages and Programming, pp. 646–657 (1996) – reference: JainK.VaziraniV.V.Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxationJ. ACM20014827429610.1145/375827.3758451868717 – reference: CharikarM.GuhaS.Improved combinatorial algorithms for the facility location and k-median problemsProc. 40th Symp. Foundations of Computer Science (FOCS)1999New YorkIEEE378388 – reference: AryaV.GargN.KhandekarR.MeyersonA.MunagalaK.PanditV.Local search heuristic for k-median and facility location problemsProc. 33rd Symp. Theory of Computing (STOC)2001New YorkACM2129 – reference: MettuR.R.Greg PlaxtonC.The online median problemProc. 41st Symp. Foundations of Computer Science (FOCS)2000New YorkIEEE33934810.1109/SFCS.2000.892122 – reference: CharikarM.GuhaS.Improved combinatorial algorithms for facility location problemsSIAM J. Comput.20053448038241075.6810010.1137/S00975397013985942148859 – reference: CharikarM.ChekuriC.FederT.MotwaniR.Incremental clustering and dynamic information retrievalProc. 29th Symp. Theory of Computing (STOC)1997New YorkACM626635 – reference: AryaV.GargN.KhandekarR.MeyersonA.MunagalaK.PanditV.Local search heuristics for k-median and facility location problemsSIAM J. Comput.20043335445621105.6811810.1137/S00975397024164022066641 – reference: ChrobakM.KenyonC.NogaJ.YoungN.Online medians via online biddingProc. 7th Latin American Theoretical Informatics Symp. (LATIN)2006BerlinSpringer311322 – reference: MettuR.R.Greg PlaxtonC.The online median problemSIAM J. Comput.2003328168321128.9055010.1137/S00975397013834432001756 – reference: Archer, A., Rajagopalan, R., Shmoys, D.B.: Lagrangian relaxation for the k-median problem: new insights and continuity properties. In: Proc. 11th European Symp. on Algorithms (ESA), pp. 31–42 (2003) – reference: MotwaniR.PhillipsS.TorngE.Nonclairvoyant schedulingTheor. Comput. Sci.1994130117470820.9005610.1016/0304-3975(94)90151-11287130 – reference: KoutsoupiasE.Weak adversaries for the k-server problemProc. 40th Symp. Foundations of Computer Science (FOCS)1999New YorkIEEE444449 – reference: JainK.MahdianM.MarkakisE.SaberiA.VaziraniV.V.Greedy facility location algorithms analyzed using dual fitting with factor-revealing lpJ. ACM20035079582410.1145/950620.9506212146253 – reference: ChrobakM.KenyonC.YoungN.E.The reverse greedy algorithm for the k-median problemInf. Process. Lett.200697687210.1016/j.ipl.2005.09.0092187051 – reference: GoemansM.KleinbergJ.An improved approximation ratio for the minimum latency problemMath. Program.199882111112410.1007/BF015858671627628 – reference: LinG.NagarajanC.RajamaranR.WilliamsonD.P.A general approach for incremental approximation and hierarchical clusteringProc. 17th Symp. on Discrete Algorithms (SODA)2006New YorkACM/SIAM – reference: KaoM.-Y.ReifJ.H.TateS.R.Searching in an unknown environment: An optimal randomized algorithm for the cow-path problemInf. Comput.1996131163800876.6803010.1006/inco.1996.00921425815Preliminary version appeared in the Proceedings of the Symp. on Discrete Algorithms, Austin, TX, January 1993 – start-page: 444 volume-title: Proc. 40th Symp. Foundations of Computer Science (FOCS) year: 1999 ident: 9005_CR23 – start-page: 311 volume-title: Proc. 7th Latin American Theoretical Informatics Symp. (LATIN) year: 2006 ident: 9005_CR11 doi: 10.1007/11682462_31 – ident: 9005_CR1 doi: 10.1007/978-3-540-39658-1_6 – ident: 9005_CR5 doi: 10.1007/3-540-61440-0_166 – start-page: 1 volume-title: Proc. 31st Symp. Theory of Computing (STOC) year: 1999 ident: 9005_CR9 – start-page: 626 volume-title: Proc. 29th Symp. Theory of Computing (STOC) year: 1997 ident: 9005_CR6 – volume: 97 start-page: 68 year: 2006 ident: 9005_CR12 publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2005.09.009 – volume: 130 start-page: 17 issue: 1 year: 1994 ident: 9005_CR29 publication-title: Theor. Comput. Sci. doi: 10.1016/0304-3975(94)90151-1 – start-page: 21 volume-title: Proc. 33rd Symp. Theory of Computing (STOC) year: 2001 ident: 9005_CR2 – ident: 9005_CR4 doi: 10.1109/FOCS.2006.39 – volume: 47 start-page: 214 year: 2000 ident: 9005_CR20 publication-title: J. ACM doi: 10.1145/347476.347479 – start-page: 339 volume-title: Proc. 41st Symp. Foundations of Computer Science (FOCS) year: 2000 ident: 9005_CR27 – start-page: 363 volume-title: Proc. 36th Symp. Theory of Computing (STOC) year: 2004 ident: 9005_CR10 – volume: 37 start-page: 146 year: 2000 ident: 9005_CR22 publication-title: J. Algorithms doi: 10.1006/jagm.2000.1100 – volume: 131 start-page: 63 issue: 1 year: 1996 ident: 9005_CR21 publication-title: Inf. Comput. doi: 10.1006/inco.1996.0092 – volume: 48 start-page: 274 year: 2001 ident: 9005_CR19 publication-title: J. ACM doi: 10.1145/375827.375845 – volume: 44 start-page: 245 year: 1992 ident: 9005_CR25 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(92)90208-D – start-page: 152 volume-title: Proc. 7th Symp. on Discrete Algorithms (SODA) year: 1996 ident: 9005_CR15 – start-page: 86 volume-title: Proc. 11th Symp. on Discrete Algorithms (SODA) year: 2000 ident: 9005_CR30 – volume: 50 start-page: 795 year: 2003 ident: 9005_CR17 publication-title: J. ACM doi: 10.1145/950620.950621 – volume: 32 start-page: 816 year: 2003 ident: 9005_CR28 publication-title: SIAM J. Comput. doi: 10.1137/S0097539701383443 – volume-title: Proc. 17th Symp. on Discrete Algorithms (SODA) year: 2006 ident: 9005_CR24 – volume: 34 start-page: 803 issue: 4 year: 2005 ident: 9005_CR8 publication-title: SIAM J. Comput. doi: 10.1137/S0097539701398594 – volume: 82 start-page: 111 issue: 1 year: 1998 ident: 9005_CR16 publication-title: Math. Program. – start-page: 378 volume-title: Proc. 40th Symp. Foundations of Computer Science (FOCS) year: 1999 ident: 9005_CR7 – start-page: 771 volume-title: Proc. 24th Symp. Theory of Computing (STOC) year: 1992 ident: 9005_CR26 – start-page: 731 volume-title: Proc. 34th Symp. Theory of Computing (STOC) year: 2002 ident: 9005_CR18 – volume: 30 start-page: 219 year: 1998 ident: 9005_CR14 publication-title: Int. J. Comput. Vis. doi: 10.1023/A:1008023416823 – volume: 33 start-page: 544 issue: 3 year: 2004 ident: 9005_CR3 publication-title: SIAM J. Comput. doi: 10.1137/S0097539702416402 – volume: 70 start-page: 555 issue: 4 year: 2005 ident: 9005_CR13 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2004.10.006
SSID	ssj0012796
Score	2.0002713
Snippet	In the k -median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a...
SourceID	pascalfrancis crossref springer
SourceType	Index Database Enrichment Source Publisher
StartPage	455
SubjectTerms	Algorithm Analysis and Problem Complexity Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer Systems Organization and Communication Networks Data Structures and Information Theory Exact sciences and technology Logistics Mathematics of Computing Operational research and scientific management Operational research. Management science Theoretical computing Theory of Computation
Title	Incremental Medians via Online Bidding
URI	https://link.springer.com/article/10.1007/s00453-007-9005-x
Volume	50
WOSCitedRecordID	wos000253895900004&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: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1432-0541 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0012796 issn: 0178-4617 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1JSwMxFH5I9SCIdcW6lDmIByWQmTSTmaOKxYMUcSm9DVmhIG3p1OLPN282KC6gtzkkYXiTt0y-l-8DOPfR0PYU5UT46pj4KGmIZNwRzmOlJXfUFjpkwwcxGCSjUfpY3ePO6273GpIsInVz2Q2rD0bwaC1F-kxfOK77bJegXsPT87CBDiJRiHKh7Dzp-fxcQ5nfLbGSjLZmMvd2caWgxRdktEg4_fa_XnUHtqv6MrguN8QurNnJHrRr7YagcuV9uPCBoTwa9KMRrfEpK1iOZVByjwY3Y4NZ7QBe-3cvt_ek0kwg2nvngsRcc8e1o6FMbSREqnrWcsF0ZC010vIwcYxFxhoeCeMU45KZhIo01IqKSLNDaE2mE3sEQeQodTHS8SiFcGFinMX_QR8EqFaad4DWxst0RSiOuhZvWUOFXNghw0e0Q_bRgctmyqxk0_htcHflizQzEDvlYSw6cFWbP6s8L_95ueM_jT6BzbIzBHt0TqG1mL_bM9jQy8U4n3eLHfcJHaPOwA
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bS8MwFD6ICgrivOK8zD6ID0ogTZqmfVRxTJxDdI69leYGA5ljncOfb9IbDC-gb31IQjnNuTTfyfcBnNloqAOBGeK2OkY2SiqUUmYQY6GQKTNY5zpkgy7v9aLhMH4s73FnVbd7BUnmkbq-7OaqD4rc0Vrs6DNt4bgS2ITlCPOfngc1dEB4LsrlZOdRYPNzBWV-t8RCMtqYpJm1iykELb4go3nCaTf-9apbsFnWl95VsSG2YUmPd6BRaTd4pSvvwrkNDMXRoB3t0Bqbsrz5KPUK7lHveqRcVtuDl_Zt_6aDSs0EJK13zlDIJDNMGuynsSacxyLQmnEqidZYpZr5kaGUKK0Y4coIylKqIsxjXwrMiaT7sDx-G-sD8IjB2ISOjkcIBxdGymj3P2iDAJZCsibgyniJLAnFna7Fa1JTIed2SNyjs0Py0YSLesqkYNP4bXBr4YvUMxx2yvyQN-GyMn9Sel7283KHfxp9Cmud_kM36d717o9gvegScf06x7A8m77rE1iV89kom7by3fcJ2D_RpA
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFA6iIoI4rzgvsw_igxKWNk3TPnobimMM1LG30txgIHWsdfjzzekNhhcQ3_qQhHKSnHOS7-T7EDqz3lD7gjDMbXaMrZdUOKHMYMYCIRNmiC50yEZ9PhiE43E0rHROs7ravYYkyzcNwNKU5t2pMt3m4RtkIhTDNVsEVJo2iVzxoY4ejutPowZG8Hgh0AUS9Ni3sbqGNb8bYiEwbUyTzNrIlOIWX1DSIvj0Wv_-7S20WeWdzlW5ULbRkk53UKvWdHCqLb6Lzq3DKK8MbWtAcWwoc-aTxCk5SZ3riYJot4deenfPN_e40lLA0u7aHAdMMsOkIW4SaY_zSPhaM06lpzVRiWZuaCj1lFbM48oIyhKqQsIjVwrCPUn30XL6luoD5HiGEBMATY8QACOGymg4J1rnQKSQrI1IbchYVkTjoHfxGjcUyYUdYvgEO8QfbXTRdJmWLBu_Ne4szE7TAzBV5ga8jS7rqYirHZn9PNzhn1qforXhbS_uPwwej9B6WTwCZTzHaDmfvesTtCrn-SSbdYqF-AnLx9qI
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=proceeding&rft.title=Algorithmica&rft.atitle=Incremental+Medians+via+Online+Bidding&rft.au=CHROBAK%2C+Marek&rft.au=KENYON%2C+Claire&rft.au=NOGA%2C+John&rft.au=YOUNG%2C+Neal+E&rft.date=2008-04-01&rft.pub=Springer&rft.issn=0178-4617&rft.volume=50&rft.issue=4&rft.spage=455&rft.epage=478&rft_id=info:doi/10.1007%2Fs00453-007-9005-x&rft.externalDBID=n%2Fa&rft.externalDocID=20365167
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0178-4617&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0178-4617&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0178-4617&client=summon