Reconstruction in One Dimension from Unlabeled Euclidean Lengths
Let G be a 3-connected ordered graph with n vertices and m edges. Let p be a randomly chosen mapping of these n vertices to the integer range { 1 , 2 , 3 , … , 2 b } for b ≥ m 2 . Let ℓ be the vector of m Euclidean lengths of G ’s edges under p . In this paper, we show that, with high probability ov...
Saved in:
| Published in: | Combinatorica (Budapest. 1981) Vol. 44; no. 6; pp. 1325 - 1351 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01-12-2024
Springer Nature B.V |
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Let
G
be a 3-connected ordered graph with
n
vertices and
m
edges. Let
p
be a randomly chosen mapping of these
n
vertices to the integer range
{
1
,
2
,
3
,
…
,
2
b
}
for
b
≥
m
2
. Let
ℓ
be the vector of
m
Euclidean lengths of
G
’s edges under
p
. In this paper, we show that, with high probability over
p
, we can efficiently reconstruct both
G
and
p
from
ℓ
. This reconstruction problem is NP-HARD in the worst case, even if both
G
and
ℓ
are given. We also show that our results stand in the presence of small amounts of error in
ℓ
, and in the real setting, with sufficiently accurate length measurements. Our method combines lattice reduction, which has previously been used to solve random subset sum problems, with an algorithm of Seymour that can efficiently reconstruct an ordered graph given an independence oracle for its matroid. |
|---|---|
| AbstractList | Let G be a 3-connected ordered graph with n vertices and m edges. Let p be a randomly chosen mapping of these n vertices to the integer range {1,2,3,…,2b} for b≥m2. Let ℓ be the vector of m Euclidean lengths of G’s edges under p. In this paper, we show that, with high probability over p, we can efficiently reconstruct both G and p from ℓ. This reconstruction problem is NP-HARD in the worst case, even if both G and ℓ are given. We also show that our results stand in the presence of small amounts of error in ℓ, and in the real setting, with sufficiently accurate length measurements. Our method combines lattice reduction, which has previously been used to solve random subset sum problems, with an algorithm of Seymour that can efficiently reconstruct an ordered graph given an independence oracle for its matroid. Let G be a 3-connected ordered graph with n vertices and m edges. Let $$\textbf{p}$$ p be a randomly chosen mapping of these n vertices to the integer range $$\{1, 2,3, \ldots , 2^b\}$$ { 1 , 2 , 3 , … , 2 b } for $$b\ge m^2$$ b ≥ m 2 . Let $$\ell $$ ℓ be the vector of m Euclidean lengths of G ’s edges under $$\textbf{p}$$ p . In this paper, we show that, with high probability over $$\textbf{p}$$ p , we can efficiently reconstruct both G and $$\textbf{p}$$ p from $$\ell $$ ℓ . This reconstruction problem is NP-HARD in the worst case, even if both G and $$\ell $$ ℓ are given. We also show that our results stand in the presence of small amounts of error in $$\ell $$ ℓ , and in the real setting, with sufficiently accurate length measurements. Our method combines lattice reduction, which has previously been used to solve random subset sum problems, with an algorithm of Seymour that can efficiently reconstruct an ordered graph given an independence oracle for its matroid. Let G be a 3-connected ordered graph with n vertices and m edges. Let p be a randomly chosen mapping of these n vertices to the integer range { 1 , 2 , 3 , … , 2 b } for b ≥ m 2 . Let ℓ be the vector of m Euclidean lengths of G ’s edges under p . In this paper, we show that, with high probability over p , we can efficiently reconstruct both G and p from ℓ . This reconstruction problem is NP-HARD in the worst case, even if both G and ℓ are given. We also show that our results stand in the presence of small amounts of error in ℓ , and in the real setting, with sufficiently accurate length measurements. Our method combines lattice reduction, which has previously been used to solve random subset sum problems, with an algorithm of Seymour that can efficiently reconstruct an ordered graph given an independence oracle for its matroid. |
| Author | Connelly, Robert Gortler, Steven J. Theran, Louis |
| Author_xml | – sequence: 1 givenname: Robert surname: Connelly fullname: Connelly, Robert organization: Department of Mathematics, Cornell University – sequence: 2 givenname: Steven J. surname: Gortler fullname: Gortler, Steven J. organization: School of Engineering and Applied Sciences, Harvard University – sequence: 3 givenname: Louis surname: Theran fullname: Theran, Louis email: lst6@st-and.ac.uk organization: School of Mathematics and Statistics, University of St Andrews |
| BookMark | eNp9kE9LAzEQxYNUsK1-AU8LnqOTpN1sbkqtf6BQEHsO2WS2btlma7IL9dubuoI3mcPA8N6bmd-EjHzrkZBrBrcMQN5FgJkSFPiMAjCm6PGMjNlMKJorxkdkDBwUVXkhLsgkxh0AFILNx-T-DW3rYxd629Wtz2qfrT1mj_UefTwNqtDus41vTIkNumzZ26Z2aHy2Qr_tPuIlOa9ME_Hqt0_J5mn5vnihq_Xz6-JhRS0H6KhEzqQwCkGaOZdcVcqy0lgnCyegysFIkOgUA1GU5dxWyMr0keXcpcsdE1NyM-QeQvvZY-z0ru2DTyu1YLxQuVCppoQPKhvaGANW-hDqvQlfmoE-kdIDKZ1I6R9S-phMYjDFJPZbDH_R_7i-AbLObU0 |
| Cites_doi | 10.1007/BF02579179 10.1007/s00454-023-00605-x 10.1145/1109557.1109641 10.1007/BF01457454 10.1016/S0092-8240(05)80259-9 10.1016/S0196-8858(03)00101-5 10.1007/s00454-004-1124-4 10.1007/11792086_18 10.1109/ACCESS.2019.2928130 10.1007/978-3-540-39763-2_9 10.1287/moor.5.3.321 10.1145/2455.2461 10.1109/TIT.2021.3113921 10.1007/978-3-642-55566-4_27 10.2307/2371182 10.2307/2371127 10.1093/acprof:oso/9780198566946.001.0001 10.1137/0215038 10.1038/nature04556 10.2307/2034435 10.1016/j.dam.2015.10.029 10.1137/0221008 10.1016/j.jctb.2004.11.002 10.1007/s10479-018-2989-6 10.1353/ajm.0.0132 10.1109/SFCS.1985.16 10.1090/dimacs/004/11 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2024 The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s) 2024 – notice: The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | C6C AAYXX CITATION |
| DOI | 10.1007/s00493-024-00119-x |
| DatabaseName | Springer Nature OA Free Journals CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1439-6912 |
| EndPage | 1351 |
| ExternalDocumentID | 10_1007_s00493_024_00119_x |
| GroupedDBID | -52 -5D -5G -BR -EM -ET -Y2 -~C -~X .86 .DC 06D 0R~ 0VY 199 1N0 1SB 2.D 203 28- 29F 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6J9 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAEOY AAGAY AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACREN ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEARS AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFYQB 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 ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMTXH AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA C6C CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IAO 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- MQGED N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9R PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WIP WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZWQNP ~EX AAYXX CITATION |
| ID | FETCH-LOGICAL-c200t-7e2173a9e07a52729f9c1bacd78d30f60a707ed91038bb5cfe1b493c22d209d13 |
| IEDL.DBID | AEJHL |
| ISSN | 0209-9683 |
| IngestDate | Sat Nov 16 16:51:54 EST 2024 Fri Nov 22 01:17:52 EST 2024 Sat Nov 16 01:15:34 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Keywords | Graph realization problem Rigidity theory Distance geometry |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c200t-7e2173a9e07a52729f9c1bacd78d30f60a707ed91038bb5cfe1b493c22d209d13 |
| OpenAccessLink | http://link.springer.com/10.1007/s00493-024-00119-x |
| PQID | 3128963939 |
| PQPubID | 2043757 |
| PageCount | 27 |
| ParticipantIDs | proquest_journals_3128963939 crossref_primary_10_1007_s00493_024_00119_x springer_journals_10_1007_s00493_024_00119_x |
| PublicationCentury | 2000 |
| PublicationDate | 2024-12-01 |
| PublicationDateYYYYMMDD | 2024-12-01 |
| PublicationDate_xml | – month: 12 year: 2024 text: 2024-12-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationTitle | Combinatorica (Budapest. 1981) |
| PublicationTitleAbbrev | Combinatorica |
| PublicationYear | 2024 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | SkienaSSSundaramGA partial digest approach to restriction site mappingBull. Math. Biol.199456227529410.1016/S0092-8240(05)80259-9 CrippenGMHavelTFDistance Geometry and Molecular Conformation, Volume 15 of Chemometrics Series1988ChichesterResearch Studies Press, Ltd. MoharBAlviYChartrandGOellermannORSchwenkAJThe Laplacian spectrum of graphsGraph Theory, Combinatorics, and Applications1991HobokenWiley871898 WhitneyHOn the abstract properties of linear dependenceAm. J. Math.1935573509533150709110.2307/2371182 JacksonBJordánTConnected rigidity matroids and unique realizations of graphsJ. Comb. Theory Ser. B2005941129213027810.1016/j.jctb.2004.11.002 LenstraAKLenstraHWJrLovászLFactoring polynomials with rational coefficientsMath. Ann.1982261451553468266410.1007/BF01457454 Zadik, I., Song, M.J., Wein, A.S., Bruna, J.: Lattice-based methods surpass sum-of-squares in clustering. In P.-L. Loh, M. Raginsky (eds) Proceedings of Thirty Fifth Conference on Learning Theory, volume 178 of Proceedings of Machine Learning Research, pp. 1247–1248. PMLR, 02–05 Jul 2022. arXiv:2112.03898 TutteWTAn algorithm for determining whether a given binary matroid is graphicProc. Am. Math. Soc.19601190591711717310.2307/2034435 WhitneyH2-Isomorphic graphsAm. J. Math.1933551–4245254150696110.2307/2371127 OxleyJMatroid Theory, volume 21 of Oxford Graduate Texts in Mathematics2011secondOxfordOxford University Press10.1093/acprof:oso/9780198566946.001.0001 Gortler, S.J., Theran.: Lattices without a big constant and with noise. (2022). arXiv:2204.12340 HendricksonBConditions for unique graph realizationsSIAM J. Comput.19922116584114881810.1137/0221008 Cieliebak, M., Eidenbenz, S., Penna, P..: Noisy data make the partial digest problem np-hard. In: International Workshop on Algorithms in Bioinformatics, pp. 111–123. Springer (2003) GortlerSJHealyADThurstonDPCharacterizing generic global rigidityAm. J. Math.20101324897939266364410.1353/ajm.0.0132 BillingeSJDuxburyPMGonçalvesDSLavorCMucherinoARecent results on assigned and unassigned distance geometry with applications to protein molecules and nanostructuresAnn. Oper. Res.2018271161203387108210.1007/s10479-018-2989-6 Saxe, J.B.: Embeddability of weighted graphs in k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-space is strongly NP-hard. In: Proceedings of the 17th Allerton Conference in Communications, Control and Computing, pp. 480–489 (1979) BixbyRECunninghamWHConverting linear programs to network problemsMath. Oper. Res.19805332135759484910.1287/moor.5.3.321 FriezeAMOn the Lagarias–Odlyzko algorithm for the subset sum problemSIAM J. Comput.198615253653983760210.1137/0215038 SongMJZadikIBrunaJOn the cryptographic hardness of learning single periodic neuronsAdv. Neural. Inf. Process. Syst.2021342960229615 Dattorro, J.: Convex optimization and Euclidean distance geometry. Online book. (2015). https://ccrma.stanford.edu/~dattorro/0976401304_v2015.04.11.pdf LagariasJCOdlyzkoAMSolving low-density subset sum problemsJ. Assoc. Comput. Mach.198532122924683234110.1145/2455.2461 Lovasz, L.: Computing ears and branchings in parallel. In: 26th Annual Symposium on Foundations of Computer Science (SFCS 1985), pp. 464–467. (1985). https://doi.org/10.1109/SFCS.1985.16 SeymourPDRecognizing graphic matroidsCombinatorica198111757860241810.1007/BF02579179 Diakonikolas, I., Kane, D.: Non-gaussian component analysis via lattice basis reduction. In: Conference on Learning Theory, PMLR. pp. 4535–4547 (2022) NguyenLTKimJShimBLow-rank matrix completion: a contemporary surveyIEEE Access20197942159423710.1109/ACCESS.2019.2928130 DuxburyPMGranlundLGujarathiSJuhasPBillingeSJThe unassigned distance geometry problemDiscret. Appl. Math.2016204117132347716710.1016/j.dam.2015.10.029 Andoni, A., Hsu, D., Shi, K., Sun, X.: Correspondence retrieval. In: Conference on Learning Theory, pp. 105–126. PMLR (2017) ConnellyRGeneric global rigidityDiscrete Comput. Geom.2005334549563213229010.1007/s00454-004-1124-4 So, A.M.-C., Ye, Y.: A semidefinite programming approach to tensegrity theory and realizability of graphs. In: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm. Society for Industrial and Applied Mathematics. pp. 766–775 (2006) BoutinMKemperGOn reconstructing n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-point configurations from the distribution of distances or areasAdv. Appl. Math.2004324709735205384210.1016/S0196-8858(03)00101-5 Nguyen, P.Q., Stehlé, D.: LLL on the average. In: International Algorithmic Number Theory Symposium. Springer, pp. 238–256 (2006) Connelly, R.: On generic global rigidity. In: Applied geometry and discrete mathematics, volume 4 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci. Amer. Math. Soc., Providence, RI. pp. 147–155. (1991) https://doi.org/10.1090/dimacs/004/11 JuhásPCherbaDDuxburyPPunchWBillingeSAb initio determination of solid-state nanostructureNature2006440708465565810.1038/nature04556 GkioulekasIGortlerSJTheranLZicklerTTrilateration using unlabeled path or loop lengthsDiscret. Comput. Geom.2024712399441470031110.1007/s00454-023-00605-x DiestelRGraph Theory, Volume 173 of Graduate Texts in Mathematics2017BerlinSpringer GortlerSJTheranLThurstonDPKirbyRGeneric unlabeled global rigidityForum of Mathematics, Sigma2019CambridgeCambridge University Press LemkeP SkienaSSSmithWDLemkePSkienaSSSmithWDReconstructing sets from interpoint distancesDiscrete and Computational Geometry2003BerlinSpringer59763110.1007/978-3-642-55566-4_27 GamarnikDKızıldağECZadikIInference in high-dimensional linear regression via lattice basis reduction and integer relation detectionIEEE Trans. Inf. Theory2021671281098139434608010.1109/TIT.2021.3113921 SJ Gortler (119_CR18) 2019 SS Skiena (119_CR32) 1994; 56 119_CR1 I Gkioulekas (119_CR15) 2024; 71 RE Bixby (119_CR3) 1980; 5 D Gamarnik (119_CR14) 2021; 67 P Juhás (119_CR21) 2006; 440 SJ Billinge (119_CR2) 2018; 271 PD Seymour (119_CR31) 1981; 1 119_CR25 PM Duxbury (119_CR12) 2016; 204 R Diestel (119_CR11) 2017 119_CR27 AM Frieze (119_CR13) 1986; 15 B Hendrickson (119_CR19) 1992; 21 AK Lenstra (119_CR24) 1982; 261 H Whitney (119_CR36) 1935; 57 GM Crippen (119_CR8) 1988 H Whitney (119_CR37) 1933; 55 LT Nguyen (119_CR28) 2019; 7 JC Lagarias (119_CR22) 1985; 32 SJ Gortler (119_CR16) 2010; 132 R Connelly (119_CR7) 2005; 33 B Jackson (119_CR20) 2005; 94 119_CR17 WT Tutte (119_CR35) 1960; 11 119_CR38 M Boutin (119_CR4) 2004; 32 MJ Song (119_CR34) 2021; 34 J Oxley (119_CR29) 2011 119_CR9 B Mohar (119_CR26) 1991 119_CR30 119_CR33 119_CR10 P Lemke (119_CR23) 2003 119_CR5 119_CR6 |
| References_xml | – volume: 1 start-page: 75 issue: 1 year: 1981 ident: 119_CR31 publication-title: Combinatorica doi: 10.1007/BF02579179 contributor: fullname: PD Seymour – ident: 119_CR30 – volume: 71 start-page: 399 issue: 2 year: 2024 ident: 119_CR15 publication-title: Discret. Comput. Geom. doi: 10.1007/s00454-023-00605-x contributor: fullname: I Gkioulekas – ident: 119_CR33 doi: 10.1145/1109557.1109641 – volume: 261 start-page: 515 issue: 4 year: 1982 ident: 119_CR24 publication-title: Math. Ann. doi: 10.1007/BF01457454 contributor: fullname: AK Lenstra – volume: 56 start-page: 275 issue: 2 year: 1994 ident: 119_CR32 publication-title: Bull. Math. Biol. doi: 10.1016/S0092-8240(05)80259-9 contributor: fullname: SS Skiena – volume: 32 start-page: 709 issue: 4 year: 2004 ident: 119_CR4 publication-title: Adv. Appl. Math. doi: 10.1016/S0196-8858(03)00101-5 contributor: fullname: M Boutin – volume: 33 start-page: 549 issue: 4 year: 2005 ident: 119_CR7 publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-004-1124-4 contributor: fullname: R Connelly – volume-title: Forum of Mathematics, Sigma year: 2019 ident: 119_CR18 contributor: fullname: SJ Gortler – ident: 119_CR27 doi: 10.1007/11792086_18 – volume: 7 start-page: 94215 year: 2019 ident: 119_CR28 publication-title: IEEE Access doi: 10.1109/ACCESS.2019.2928130 contributor: fullname: LT Nguyen – ident: 119_CR5 doi: 10.1007/978-3-540-39763-2_9 – volume-title: Distance Geometry and Molecular Conformation, Volume 15 of Chemometrics Series year: 1988 ident: 119_CR8 contributor: fullname: GM Crippen – volume: 5 start-page: 321 issue: 3 year: 1980 ident: 119_CR3 publication-title: Math. Oper. Res. doi: 10.1287/moor.5.3.321 contributor: fullname: RE Bixby – volume: 32 start-page: 229 issue: 1 year: 1985 ident: 119_CR22 publication-title: J. Assoc. Comput. Mach. doi: 10.1145/2455.2461 contributor: fullname: JC Lagarias – volume: 67 start-page: 8109 issue: 12 year: 2021 ident: 119_CR14 publication-title: IEEE Trans. Inf. Theory doi: 10.1109/TIT.2021.3113921 contributor: fullname: D Gamarnik – start-page: 597 volume-title: Discrete and Computational Geometry year: 2003 ident: 119_CR23 doi: 10.1007/978-3-642-55566-4_27 contributor: fullname: P Lemke – volume: 57 start-page: 509 issue: 3 year: 1935 ident: 119_CR36 publication-title: Am. J. Math. doi: 10.2307/2371182 contributor: fullname: H Whitney – ident: 119_CR10 – volume: 55 start-page: 245 issue: 1–4 year: 1933 ident: 119_CR37 publication-title: Am. J. Math. doi: 10.2307/2371127 contributor: fullname: H Whitney – volume-title: Matroid Theory, volume 21 of Oxford Graduate Texts in Mathematics year: 2011 ident: 119_CR29 doi: 10.1093/acprof:oso/9780198566946.001.0001 contributor: fullname: J Oxley – volume: 15 start-page: 536 issue: 2 year: 1986 ident: 119_CR13 publication-title: SIAM J. Comput. doi: 10.1137/0215038 contributor: fullname: AM Frieze – volume: 34 start-page: 29602 year: 2021 ident: 119_CR34 publication-title: Adv. Neural. Inf. Process. Syst. contributor: fullname: MJ Song – ident: 119_CR9 – volume: 440 start-page: 655 issue: 7084 year: 2006 ident: 119_CR21 publication-title: Nature doi: 10.1038/nature04556 contributor: fullname: P Juhás – start-page: 871 volume-title: Graph Theory, Combinatorics, and Applications year: 1991 ident: 119_CR26 contributor: fullname: B Mohar – volume: 11 start-page: 905 year: 1960 ident: 119_CR35 publication-title: Proc. Am. Math. Soc. doi: 10.2307/2034435 contributor: fullname: WT Tutte – volume: 204 start-page: 117 year: 2016 ident: 119_CR12 publication-title: Discret. Appl. Math. doi: 10.1016/j.dam.2015.10.029 contributor: fullname: PM Duxbury – volume: 21 start-page: 65 issue: 1 year: 1992 ident: 119_CR19 publication-title: SIAM J. Comput. doi: 10.1137/0221008 contributor: fullname: B Hendrickson – volume: 94 start-page: 1 issue: 1 year: 2005 ident: 119_CR20 publication-title: J. Comb. Theory Ser. B doi: 10.1016/j.jctb.2004.11.002 contributor: fullname: B Jackson – ident: 119_CR38 – volume: 271 start-page: 161 year: 2018 ident: 119_CR2 publication-title: Ann. Oper. Res. doi: 10.1007/s10479-018-2989-6 contributor: fullname: SJ Billinge – ident: 119_CR17 – ident: 119_CR1 – volume-title: Graph Theory, Volume 173 of Graduate Texts in Mathematics year: 2017 ident: 119_CR11 contributor: fullname: R Diestel – volume: 132 start-page: 897 issue: 4 year: 2010 ident: 119_CR16 publication-title: Am. J. Math. doi: 10.1353/ajm.0.0132 contributor: fullname: SJ Gortler – ident: 119_CR25 doi: 10.1109/SFCS.1985.16 – ident: 119_CR6 doi: 10.1090/dimacs/004/11 |
| SSID | ssj0008315 |
| Score | 2.4143333 |
| Snippet | Let
G
be a 3-connected ordered graph with
n
vertices and
m
edges. Let
p
be a randomly chosen mapping of these
n
vertices to the integer range
{
1
,
2
,
3
,
…
,... Let G be a 3-connected ordered graph with n vertices and m edges. Let $$\textbf{p}$$ p be a randomly chosen mapping of these n vertices to the integer range... Let G be a 3-connected ordered graph with n vertices and m edges. Let p be a randomly chosen mapping of these n vertices to the integer range {1,2,3,…,2b} for... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Publisher |
| StartPage | 1325 |
| SubjectTerms | Algorithms Apexes Combinatorics Error analysis Euclidean geometry Graph theory Mathematics Mathematics and Statistics Original Paper Reconstruction |
| Title | Reconstruction in One Dimension from Unlabeled Euclidean Lengths |
| URI | https://link.springer.com/article/10.1007/s00493-024-00119-x https://www.proquest.com/docview/3128963939 |
| Volume | 44 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07T8MwELagXWDgjSgU5IENjJI4D3ujokEVKjBApXaK_ApUIIOUVuLnc06TVCAYYMqQxEo-n-87-3yfETplnlLcRDERTEQkFDQkImYR0bEAsleh9Kmrdx48JHdj1k-dTA5tli7sy0WdkSwddVPr5mJZl3IMSalTRiBwbAP3RGDc7V56Mxg2DphVBxcEnhOfZLSqlfm5la98tAwyv-VFS7q53vzXh26hjSq6xL2FOWyjFWN30PptI81a7KJLN-FcysbiqcX31uC-U_l3K2fYFZzgkQXrAEbSOJ2r16k2wuKhsU-z52IPja7Tx6sBqY5RIAqGwIwkBqYdVHDjJSIKIJjOufKlUDphmnp57InES4zmTipdykjlxpfwByoINCCofbqPWvbNmgOEObwkpQyNFH5oAsNVxGAaqkUuvVCqpIPOajCz94VaRtboIpe4ZIBLuY-OZx8d1K3xzqqRU2QUCBOcAqe8g85rgJe3f2_t8G-PH6G1wPVRuTOli1oAuzlGq4Wen1T25K7jyaT_CX42xmw |
| link.rule.ids | 315,782,786,27933,27934,41073,42142,48344,48347,49649,49652,52153 |
| linkProvider | Springer Nature |
| linkToHtml | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV07T8MwED5BOwADb0ShgAc2sJTEedgbFS0qoi0DrdROkV-BSsggpZX4-dhp0goEA8xJrPjz-R6-u88Al9STkukoxpzyCIechJjHNMIq5tbYy1D4xPU7d5-SwZi2O44mJ6x6YYpq9yolWWjqZbObc2ZdzjHEBVEZtp5j3bGdBzWot8aTSXupgWl5c0HgOfZJSspmmZ9H-WqQVl7mt8RoYW_udv73p7uwXfqXqLUQiD1Y02YftvpLctb8AG5cyLkijkVTgx6NRm3H8-_OzpBrOUEjY-XD2iSFOnP5OlWaG9TT5nn2kh_C6K4zvO3i8iIFLO0mmOFE28CDcKa9hEeBdaczJn3BpUqoIl4WezzxEq2YI0sXIpKZ9oWdgQwCZSFUPjmCmnkz-hgQsx8JIUItuB_qQDMZURuIKp4JLxQyacBVhWb6vuDLSJfMyAUuqcWlqKRj6UcDmhXgabl38pRYk2nVAiOsAdcVwKvHv4928rfXL2CjO-z30t794OEUNgO3XkWdShNqdgn0Gaznan5eCtcnf_HI7A |
| linkToPdf | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEF60BdGDb7FadQ_edDGPzWNvFptStVZBC97CvqIFWQtpwZ_vbJqkKHoQz0mW5NvZnZnMfN8idBo7UjIdhITHPCCU-5TwMA6ICjk4e0mF61u-c_8xGj7H3cTK5NQs_qLbvSpJzjkNVqXJTC8mKruoiW82sLX1R0oK0TICUWSTQiYDlt7sJDf9Qb0bx-UpBp5jlShjvyTO_DzKV-e0iDi_FUkL39Pb-P9bb6L1Mu7EnbmhbKElbbbR2l0t2prvoEubii4EZfHY4Hujcdfq_9t_athSUfDIgN2Ar1I4mcm3sdLc4IE2L9PXfBeNesnTVZ-UBywQCYtjSiINCYnPmXYiHngQZmdMuoJLFcXKd7LQ4ZETacWsiLoQgcy0K-ALpOcpgFO5_h5qmHej9xFm8JAQgmrBXao9zWQQQ4KqeCYcKmTUQmcVsulkrqOR1orJBS4p4FJ02LH0o4XaFfhpuaby1AdXCtsF81kLnVdgLy7_PtrB324_QSsP3V46uB7eHqJVz05X0b7SRg2YAX2ElnM1Oy7t7BPc7tFt |
| 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=Reconstruction+in+One+Dimension+from+Unlabeled+Euclidean+Lengths&rft.jtitle=Combinatorica+%28Budapest.+1981%29&rft.au=Connelly%2C+Robert&rft.au=Gortler%2C+Steven+J.&rft.au=Theran%2C+Louis&rft.date=2024-12-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0209-9683&rft.eissn=1439-6912&rft.volume=44&rft.issue=6&rft.spage=1325&rft.epage=1351&rft_id=info:doi/10.1007%2Fs00493-024-00119-x&rft.externalDocID=10_1007_s00493_024_00119_x |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0209-9683&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0209-9683&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0209-9683&client=summon |