On the distribution of binary search trees under the random permutation model
We study the distribution Q on the set Bn of binary search trees over a linearly ordered set of n records under the standard random permutation model. This distribution also arises as the stationary distribution for the move‐to‐root (MTR) Markov chain taking values in Bn when successive requests are...
Saved in:
| Published in: | Random structures & algorithms Vol. 8; no. 1; pp. 1 - 25 |
|---|---|
| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Wiley Subscription Services, Inc., A Wiley Company
01-01-1996
|
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We study the distribution Q on the set Bn of binary search trees over a linearly ordered set of n records under the standard random permutation model. This distribution also arises as the stationary distribution for the move‐to‐root (MTR) Markov chain taking values in Bn when successive requests are independent and identically distributed with each record equally likely. We identify the minimum and maximum values of the functional Q and the trees achieving those values and argue that Q is a crude measure of the “shape” of the tree. We study the distribution of Q(T) for two choices of distribution for random trees T; uniform over Bn and Q. In the latter case, we obtain a limiting normal distribution for −ln Q(T). © 1996 John Wiley & Sons, Inc. |
|---|---|
| AbstractList | We study the distribution Q on the set Bn of binary search trees over a linearly ordered set of n records under the standard random permutation model. This distribution also arises as the stationary distribution for the move‐to‐root (MTR) Markov chain taking values in Bn when successive requests are independent and identically distributed with each record equally likely. We identify the minimum and maximum values of the functional Q and the trees achieving those values and argue that Q is a crude measure of the “shape” of the tree. We study the distribution of Q(T) for two choices of distribution for random trees T; uniform over Bn and Q. In the latter case, we obtain a limiting normal distribution for −ln Q(T). © 1996 John Wiley & Sons, Inc. |
| Author | Fill, James Allen |
| Author_xml | – sequence: 1 givenname: James Allen surname: Fill fullname: Fill, James Allen organization: Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218-2692 |
| BookMark | eNp9kMFOwkAQhjcGEwF9hx7hUNzZbbtdNCakCpKgiGj0Num221CFlmxLlLe3BYMHjZnDzCT_fJl8LdLI8kwTIoH2gFJ23pmPg3EXqPRt5oDfASk9Cl2_D5fQ7w_G1_bjfABXvEd7wfSC2XBEmod0o54dZkufsxPSKoo3SqngjDfJ3TSzyoW24rQoTao2ZZpnVp5YKs1Cs7UKHZpoYZVG68LaZLE2u7QJszhfWWttVpsy3N2s8lgvT8lxEi4Lffbd2-R5ePMU3NqT6WgcDCZ2xLkEmyutJEgFXDkelY4rwNdKiIh5seBKKOoxyaKECgip60svqjKOG8UAOvJcwdtktudGJi8KoxNcm3RVPYxAsfaFWPvC2gDWBnDvC6uhKqx8Ye0LOVIMpsgQfpgf6VJvfwH_4_2B2-0V094zK7v688AMzTt6ggsXX-5HOPTgVcwe7nHEvwCsrYxt |
| ContentType | Journal Article |
| Copyright | Copyright © 1996 John Wiley & Sons, Inc. |
| Copyright_xml | – notice: Copyright © 1996 John Wiley & Sons, Inc. |
| DBID | BSCLL AAYXX CITATION |
| DOI | 10.1002/(SICI)1098-2418(199601)8:1<1::AID-RSA1>3.0.CO;2-1 |
| DatabaseName | Istex CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1098-2418 |
| EndPage | 25 |
| ExternalDocumentID | 10_1002__SICI_1098_2418_199601_8_1_1__AID_RSA1_3_0_CO_2_1 RSA1 ark_67375_WNG_F61X7QPN_G |
| Genre | article |
| GroupedDBID | -~X .3N .4S .DC .GA .Y3 05W 0R~ 10A 123 1L6 1OB 1OC 1ZS 31~ 33P 3SF 3WU 4.4 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHHS AANLZ AAONW AASGY AAXRX AAZKR ABCQN ABCUV ABEML ABIJN ABJNI ABPVW ACAHQ ACBWZ ACCFJ ACCZN ACGFO ACGFS ACIWK ACPOU ACSCC ACXBN ACXQS ADBBV ADEOM ADIZJ ADKYN ADMGS ADOZA ADXAS ADZMN AEEZP AEIGN AEIMD AENEX AEQDE AEUQT AEUYR AFBPY AFFPM AFGKR AFPWT AFZJQ AHBTC AIAGR AITYG AIURR AIWBW AJBDE AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN AMBMR AMYDB ARCSS ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BSCLL BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 FEDTE FSPIC G-S G.N GNP GODZA H.T H.X HBH HF~ HGLYW HHY HVGLF HZ~ H~9 IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M6L MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 N9A NF~ NNB O66 O9- OIG P2P P2W P2X P4D PALCI PQQKQ Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RWI RX1 SAMSI SUPJJ TN5 TUS UB1 V2E V8K W8V W99 WBKPD WH7 WIB WIH WIK WOHZO WQJ WRC WWM WXSBR WYISQ XBAML XG1 XPP XSW XV2 ZZTAW ~IA ~WT AAMNL AAYXX CITATION |
| ID | FETCH-LOGICAL-c3391-3beb919b13b460945718eb77c26d73b7b06292cf071a05896c94545cd11ec6573 |
| IEDL.DBID | 33P |
| ISSN | 1042-9832 |
| IngestDate | Fri Nov 22 00:43:28 EST 2024 Sat Aug 24 01:05:24 EDT 2024 Wed Oct 30 09:52:48 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c3391-3beb919b13b460945718eb77c26d73b7b06292cf071a05896c94545cd11ec6573 |
| Notes | istex:0E4BAFC8628E808EB87B0FAC000DC5C8ED9070AD ArticleID:RSA1 ark:/67375/WNG-F61X7QPN-G |
| PageCount | 25 |
| ParticipantIDs | crossref_primary_10_1002__SICI_1098_2418_199601_8_1_1__AID_RSA1_3_0_CO_2_1 wiley_primary_10_1002_SICI_1098_2418_199601_8_1_1_AID_RSA1_3_0_CO_2_1_RSA1 istex_primary_ark_67375_WNG_F61X7QPN_G |
| PublicationCentury | 1900 |
| PublicationDate | 1996-01 January 1996 1996-1-00 |
| PublicationDateYYYYMMDD | 1996-01-01 |
| PublicationDate_xml | – month: 01 year: 1996 text: 1996-01 |
| PublicationDecade | 1990 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Random structures & algorithms |
| PublicationTitleAlternate | Random Struct. Alg |
| PublicationYear | 1996 |
| Publisher | Wiley Subscription Services, Inc., A Wiley Company |
| Publisher_xml | – name: Wiley Subscription Services, Inc., A Wiley Company |
| References | R. P. Dobrow and J. A. Fill, On the Markov chain for the move-to-root rule for binary search trees, Ann. Appl. Probab. 5, 1-19 (1995). R. P. Dobrow and J. A. Fill, Rates of convergence for the move-to-root Markov chain for binary search trees, Ann. Appl. Probab. 5, 20-36 (1995). H. M. Mahmoud, Evolution of Random Search Trees, Wiley, New York, 1992. 1995; 5 1992 |
| References_xml | – volume: 5 start-page: 20 year: 1995 end-page: 36 article-title: Rates of convergence for the move‐to‐root Markov chain for binary search trees publication-title: Ann. Appl. Probab. – volume: 5 start-page: 1 year: 1995 end-page: 19 article-title: On the Markov chain for the move‐to‐root rule for binary search trees publication-title: Ann. Appl. Probab. – year: 1992 |
| SSID | ssj0007323 |
| Score | 1.602811 |
| Snippet | We study the distribution Q on the set Bn of binary search trees over a linearly ordered set of n records under the standard random permutation model. This... |
| SourceID | crossref wiley istex |
| SourceType | Aggregation Database Publisher |
| StartPage | 1 |
| Title | On the distribution of binary search trees under the random permutation model |
| URI | https://api.istex.fr/ark:/67375/WNG-F61X7QPN-G/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2F%28SICI%291098-2418%28199601%298%3A1%3C1%3A%3AAID-RSA1%3E3.0.CO%3B2-1 |
| Volume | 8 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwxV3dT9swELf4kBB7GB9jGmNDfgAED4E4TuK4TJMgtNBJtIwyjbdTnTgvEy1qqbY_f3d2mwkx8YSEokh2ZPkX3dl3_rqfGdspTKLJkRD1pQ1im6SB1lZjqsQGVlXKOLLni57q3GZnTaLJ-T2LhfH8EPWCG_UMZ6-pg_fN-OgfaSgOwHrtvI0TZkGcmOiJMqI2IrYRtAE6Iy6CXZnjSyvVJ-2z4LpHX5ryMDzMu7vyFH8QbTfOMFzoh7yqLbiSkT-YH0eBxia_xPQU92ifMA9qxH2Pd5A1xBfRaMxQvnqMY0R45O8WSXV_Ho-DnSNrrbyaCFbZ2-nYl5_4xrrG5uxgnb25rIljx-_YZXfAMctL4vOdXsXFhxU3LmyY-37JaSd9zCn8beRKo78th3f8Hr3MxB8t4O6Gnw32o9W8yS-C6Y0PQSGlFoE01mihjZAmTnHimaDntEapIkpLJY0yYRrpqKhwXNSn-xDTAsvESVEKYYs0UfI9WxgMB_YD4zjVSjNtSok2Js50aERc2dgWOqpCW2qxyb7N9AL3ntgDPIVzBEBSpb35DEim4CUKmMAHUI5AcgQJIeRdiAAr23OarWvqj37RiTmVwM_OObRScau-X3XgHFGdQp9APof4H0CX__iSlW2xZX8gnVaXPrGFh9HEfmbz43Ky7TrHX7TACFs |
| link.rule.ids | 315,782,786,1408,27933,27934,46064,46488 |
| linkProvider | Wiley-Blackwell |
| linkToHtml | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwxV3db9MwELfYJsF44Hsa48sPDG0P2eI4seOCkEbWroW13egQezvNifMyrZ1aKu3P585ugyYQT0goimRHln_Rne3zx_l3jL0tbWbIkBD1pYtSl6nIGGcwVWEDq2ttPdlzd6QH5_lhm2hybpZ3YQI_RLPhRj3Dj9fUwWlDev8XayjOwEa9oocrZkGkmGiKcuI2IroRHARMTmQE27LAl7aqD3qH0dcRfWnLvXivGG7LT_iHK2wtVdiI6fKHPGnGcC2T4JqfJpHBRn-XmQXw_g6B7jaQOwFwN2-JD6LVWsJ8DCDvEeKWxVsj5d3cngl7U9Z5-P-E8Ig9WEx_-UFor4_ZHTd-wu73G-7Y2VPWH445ZnlFlL6LaFx8UnPrbw7z0DU5HabPON2Am_rSaHKryRW_RkMzD94F3Af5eca-ddpnRTdaBH2ISimNiKR11ghjhbSpwrVnhsbTWa3LRFVaWm1jlZikrHFqdEEhEVWJZdKsrIRwpcq03GCr48nYbTKOqy2VG1tJHGbS3MRWpLVLXWmSOnaVEc_Z56Vi4Dpwe0BgcU4ASKp0PJ8DyRSCRAET-ADKEUiOICGGYggJYGXvvGqbmi6ml-Q0pzP4PjiCjhLn-vRkAEeI6jX6G-TfEP8A6PNb_7KyN-xe96x_DMe9wZcXbD34p9Nm00u2-mM6d6_Yyqyav_Y95SeobAyD |
| linkToPdf | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwxV3db9MwELfYJk3wsPGpMb78wND2kC2OkzguCGmk7VZgbUdB29tpjp0XRFu1VOzP585ugyYQT0goimRHln_Rne072-efGXtZmUyTISHqSxelLssjrZ3GlMUGVtfKeLLn05HqXxbtDtHk_FidhQn8EM2CG_UMP15TB5_a-ugXaSg6YKNe2cMJsyBOTLREBVEbEdsIjgG6IC6CPVniSyvVx7129GlEXzryMD4sB3vyHf7gGttI0YUn0n0ph80QrmQSIvPTJNLY5jeZXgIf7RPoQQO5HwAPipZ4I1qtFczbAPIaIW4YvA3S3fVNR9hbsu72f5PBXba1dH75cWit99gtN77P7pw1zLHzB-xsMOaY5ZYIfZd3cfFJzY0_N8xDx-S0lT7ndP5t5kujwbWTb3yKZmYRYgu4v-LnIfvS7XwuT6PllQ9RJaUWkTTOaKGNkAb1otMMTaczSlVJbpU0ysR5opOqRsfoii5EzCssk2aVFcJVeabkI7Y-nozdDuM418oLbazEQSYtdGxEWrvUVTqpY2e1eMzer_QC08DsAYHDOQEgqdLmfAEkUwgSBUzgAyhHIDmChBjKASSAlb3ymm1qupp9pZA5lcFF_wS6ubhU58M-nCCqV-hvkH9D_AOgz-_-y8pesM1huwsfe_0PT9jtEJxOK01P2fr32cI9Y2tzu3ju-8lPIgYLKQ |
| 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=On+the+distribution+of+binary+search+trees+under+the+random+permutation+model&rft.jtitle=Random+structures+%26+algorithms&rft.au=Fill%2C+James+Allen&rft.date=1996-01-01&rft.pub=Wiley+Subscription+Services%2C+Inc.%2C+A+Wiley+Company&rft.issn=1042-9832&rft.eissn=1098-2418&rft.volume=8&rft.issue=1&rft.spage=1&rft.epage=25&rft_id=info:doi/10.1002%2F%28SICI%291098-2418%28199601%298%3A1%3C1%3A%3AAID-RSA1%3E3.0.CO%3B2-1&rft.externalDBID=10.1002%252F%2528SICI%25291098-2418%2528199601%25298%253A1%253C1%253A%253AAID-RSA1%253E3.0.CO%253B2-1&rft.externalDocID=RSA1 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1042-9832&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1042-9832&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1042-9832&client=summon |