Dynamic Planar Voronoi Diagrams for General Distance Functions and Their Algorithmic Applications
We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include L p -norms and additively weighted Euclidean distances. Our data structure supports general (convex, pairwise disjoint) sites that have constant de...
Saved in:
| Published in: | Discrete & computational geometry Vol. 64; no. 3; pp. 838 - 904 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer US
01.10.2020
Springer Nature B.V |
| Subjects: | |
| ISSN: | 0179-5376, 1432-0444 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include
L
p
-norms and additively weighted Euclidean distances. Our data structure supports general (convex, pairwise disjoint) sites that have constant description complexity (e.g., points, line segments, disks, etc.). Our structure uses
O
(
n
log
3
n
)
storage, and requires polylogarithmic update and query time, improving an earlier data structure of Agarwal, Efrat, and Sharir which required
O
(
n
ε
)
time for an update and
O
(
log
n
)
time for a query [SICOMP 1999]. Our data structure has numerous applications. In all of them, it gives faster algorithms, typically reducing an
O
(
n
ε
)
factor in the previous bounds to polylogarithmic. In addition, we give here two new applications: an efficient construction of a spanner in a disk intersection graph, and a data structure for efficient connectivity queries in a dynamic disk graph. To obtain this data structure, we combine and extend various techniques from the literature. Along the way, we obtain several side results that are of independent interest. Our data structure depends on the existence and an efficient construction of
“vertical” shallow cuttings
in arrangements of bivariate algebraic functions. We prove that an appropriate level in an arrangement of a random sample of a suitable size provides such a cutting. To compute it efficiently, we develop a randomized incremental construction algorithm for computing the lowest
k
levels in an arrangement of bivariate algebraic functions (we mostly consider here collections of functions whose lower envelope has linear complexity, as is the case in the dynamic nearest-neighbor context, under both types of norm). To analyze this algorithm, we also improve a longstanding bound on the combinatorial complexity of the vertical decomposition of these levels. Finally, to obtain our structure, we combine our vertical shallow cutting construction with Chan’s algorithm for efficiently maintaining the lower envelope of a dynamic set of planes in
R
3
. Along the way, we also revisit Chan’s technique and present a variant that uses a single binary counter, with a simpler analysis and improved amortized deletion time (by a logarithmic factor; the insertion and query costs remain asymptotically the same). |
|---|---|
| AbstractList | We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include
L
p
-norms and additively weighted Euclidean distances. Our data structure supports general (convex, pairwise disjoint) sites that have constant description complexity (e.g., points, line segments, disks, etc.). Our structure uses
O
(
n
log
3
n
)
storage, and requires polylogarithmic update and query time, improving an earlier data structure of Agarwal, Efrat, and Sharir which required
O
(
n
ε
)
time for an update and
O
(
log
n
)
time for a query [SICOMP 1999]. Our data structure has numerous applications. In all of them, it gives faster algorithms, typically reducing an
O
(
n
ε
)
factor in the previous bounds to polylogarithmic. In addition, we give here two new applications: an efficient construction of a spanner in a disk intersection graph, and a data structure for efficient connectivity queries in a dynamic disk graph. To obtain this data structure, we combine and extend various techniques from the literature. Along the way, we obtain several side results that are of independent interest. Our data structure depends on the existence and an efficient construction of
“vertical” shallow cuttings
in arrangements of bivariate algebraic functions. We prove that an appropriate level in an arrangement of a random sample of a suitable size provides such a cutting. To compute it efficiently, we develop a randomized incremental construction algorithm for computing the lowest
k
levels in an arrangement of bivariate algebraic functions (we mostly consider here collections of functions whose lower envelope has linear complexity, as is the case in the dynamic nearest-neighbor context, under both types of norm). To analyze this algorithm, we also improve a longstanding bound on the combinatorial complexity of the vertical decomposition of these levels. Finally, to obtain our structure, we combine our vertical shallow cutting construction with Chan’s algorithm for efficiently maintaining the lower envelope of a dynamic set of planes in
R
3
. Along the way, we also revisit Chan’s technique and present a variant that uses a single binary counter, with a simpler analysis and improved amortized deletion time (by a logarithmic factor; the insertion and query costs remain asymptotically the same). We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include $$L_p$$ L p -norms and additively weighted Euclidean distances. Our data structure supports general (convex, pairwise disjoint) sites that have constant description complexity (e.g., points, line segments, disks, etc.). Our structure uses $$O(n \log ^3 n)$$ O ( n log 3 n ) storage, and requires polylogarithmic update and query time, improving an earlier data structure of Agarwal, Efrat, and Sharir which required $$O(n^{\varepsilon })$$ O ( n ε ) time for an update and $$O(\log n)$$ O ( log n ) time for a query [SICOMP 1999]. Our data structure has numerous applications. In all of them, it gives faster algorithms, typically reducing an $$O(n^{\varepsilon })$$ O ( n ε ) factor in the previous bounds to polylogarithmic. In addition, we give here two new applications: an efficient construction of a spanner in a disk intersection graph, and a data structure for efficient connectivity queries in a dynamic disk graph. To obtain this data structure, we combine and extend various techniques from the literature. Along the way, we obtain several side results that are of independent interest. Our data structure depends on the existence and an efficient construction of “vertical” shallow cuttings in arrangements of bivariate algebraic functions. We prove that an appropriate level in an arrangement of a random sample of a suitable size provides such a cutting. To compute it efficiently, we develop a randomized incremental construction algorithm for computing the lowest k levels in an arrangement of bivariate algebraic functions (we mostly consider here collections of functions whose lower envelope has linear complexity, as is the case in the dynamic nearest-neighbor context, under both types of norm). To analyze this algorithm, we also improve a longstanding bound on the combinatorial complexity of the vertical decomposition of these levels. Finally, to obtain our structure, we combine our vertical shallow cutting construction with Chan’s algorithm for efficiently maintaining the lower envelope of a dynamic set of planes in $${{\mathbb {R}}}^3$$ R 3 . Along the way, we also revisit Chan’s technique and present a variant that uses a single binary counter, with a simpler analysis and improved amortized deletion time (by a logarithmic factor; the insertion and query costs remain asymptotically the same). We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include Lp-norms and additively weighted Euclidean distances. Our data structure supports general (convex, pairwise disjoint) sites that have constant description complexity (e.g., points, line segments, disks, etc.). Our structure uses O(nlog3n) storage, and requires polylogarithmic update and query time, improving an earlier data structure of Agarwal, Efrat, and Sharir which required O(nε) time for an update and O(logn) time for a query [SICOMP 1999]. Our data structure has numerous applications. In all of them, it gives faster algorithms, typically reducing an O(nε) factor in the previous bounds to polylogarithmic. In addition, we give here two new applications: an efficient construction of a spanner in a disk intersection graph, and a data structure for efficient connectivity queries in a dynamic disk graph. To obtain this data structure, we combine and extend various techniques from the literature. Along the way, we obtain several side results that are of independent interest. Our data structure depends on the existence and an efficient construction of “vertical” shallow cuttings in arrangements of bivariate algebraic functions. We prove that an appropriate level in an arrangement of a random sample of a suitable size provides such a cutting. To compute it efficiently, we develop a randomized incremental construction algorithm for computing the lowest k levels in an arrangement of bivariate algebraic functions (we mostly consider here collections of functions whose lower envelope has linear complexity, as is the case in the dynamic nearest-neighbor context, under both types of norm). To analyze this algorithm, we also improve a longstanding bound on the combinatorial complexity of the vertical decomposition of these levels. Finally, to obtain our structure, we combine our vertical shallow cutting construction with Chan’s algorithm for efficiently maintaining the lower envelope of a dynamic set of planes in R3. Along the way, we also revisit Chan’s technique and present a variant that uses a single binary counter, with a simpler analysis and improved amortized deletion time (by a logarithmic factor; the insertion and query costs remain asymptotically the same). |
| Author | Roditty, Liam Sharir, Micha Mulzer, Wolfgang Seiferth, Paul Kaplan, Haim |
| Author_xml | – sequence: 1 givenname: Haim surname: Kaplan fullname: Kaplan, Haim organization: Blavatnik School of Computer Science, Tel Aviv University – sequence: 2 givenname: Wolfgang orcidid: 0000-0002-1948-5840 surname: Mulzer fullname: Mulzer, Wolfgang email: mulzer@inf.fu-berlin.de organization: Institut für Informatik, Freie Universität Berlin – sequence: 3 givenname: Liam surname: Roditty fullname: Roditty, Liam organization: Department of Computer Science, Bar-Ilan University – sequence: 4 givenname: Paul surname: Seiferth fullname: Seiferth, Paul organization: Institut für Informatik, Freie Universität Berlin – sequence: 5 givenname: Micha surname: Sharir fullname: Sharir, Micha organization: Blavatnik School of Computer Science, Tel Aviv University |
| BookMark | eNp9kEFPAjEQhRuDiYj-AU9NPK9Ot93t9khA0IRED-i1GUoXSpYW2-XAv3cBExMPnCYz-d6bl3dLej54S8gDgycGIJ8TgChEBjlkALngmbwifSZ4noEQokf6wKTKCi7LG3Kb0gY6XkHVJzg-eNw6Qz8a9BjpV4jBB0fHDlcRt4nWIdKp9TZi0x1Ti95YOtl707rgE0W_pPO1dZEOm1WIrl0fzYa7XeMMnpA7cl1jk-z97xyQz8nLfPSazd6nb6PhLDO85G0mLF-qaqkUN3yBhc0LW8pScVUxhlAuhERQWBosuMhrwSpY1EvO8wKLRbdLPiCPZ99dDN97m1q9Cfvou5c6F0IJISVjHVWdKRNDStHW2rj2FLSN6BrNQB8L1edCdVeoPhWqjw_yf9JddFuMh8sifhalDvYrG_9SXVD9AHJFie8 |
| CitedBy_id | crossref_primary_10_1016_j_comgeo_2022_101979 crossref_primary_10_1007_s00454_023_00621_x crossref_primary_10_1016_j_comgeo_2023_102053 crossref_primary_10_1016_j_comgeo_2022_101976 crossref_primary_10_1515_geo_2022_0667 crossref_primary_10_1007_s00454_023_00564_3 crossref_primary_10_1155_2021_9948543 crossref_primary_10_1137_20M1388371 crossref_primary_10_1145_3527614 |
| Cites_doi | 10.1137/S0097539795295936 10.1007/BF02187740 10.1016/0925-7721(92)90006-E 10.1145/1017460.1017461 10.1007/BF01293483 10.1007/3-540-33099-2 10.1137/S0097539703439404 10.1137/S0097539795281840 10.1006/jcss.2000.1741 10.1016/0196-8858(83)90014-3 10.1007/s00454-010-9248-1 10.1145/502090.502095 10.1016/0196-6774(80)90015-2 10.1007/s00454-016-9784-4 10.1137/0211059 10.1137/16M1059692 10.1007/BF02189314 10.1007/BF02574030 10.1007/BF02187681 10.1007/s00454-009-9177-z 10.1137/S0097539798349188 10.1007/978-3-540-77974-2 10.1016/0022-0000(81)90012-X 10.1137/090751670 10.1017/CBO9780511626371 10.1016/0012-365X(79)90084-0 10.1137/0217052 10.1145/322217.322219 10.1142/8685 10.1016/j.comgeo.2014.12.003 10.1137/0218080 10.1007/s00453-009-9322-3 10.1007/BF02574692 10.1007/978-3-319-44479-6_19 10.1145/323233.323264 10.1145/1706591.1706596 10.1145/304893.304993 10.1007/BFb0035760 10.1137/1.9781611974782.165 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2020 The Author(s) 2020. This work is published under https://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) 2020 – notice: The Author(s) 2020. This work is published under https://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 3V. 7SC 7TB 7XB 88I 8AL 8AO 8FD 8FE 8FG 8FK 8G5 ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO FR3 GNUQQ GUQSH HCIFZ JQ2 K7- KR7 L6V L7M L~C L~D M0N M2O M2P M7S MBDVC P5Z P62 PADUT PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.1007/s00454-020-00243-7 |
| DatabaseName | Springer Nature OA Free Journals CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Research Library (Alumni Edition) SciTech Premium Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Health Research Premium Collection ProQuest Central Essentials ProQuest Central Technology collection ProQuest One Community College ProQuest Central Korea Engineering Research Database ProQuest Central Student Research Library Prep SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database Civil Engineering Abstracts ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Research Library Science Database Engineering Database Research Library (Corporate) Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Research Library China ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef Research Library Prep Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College Research Library (Alumni Edition) ProQuest Pharma Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Research Library Research Library China ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection Civil Engineering Abstracts ProQuest Computing Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) |
| DatabaseTitleList | CrossRef Research Library Prep |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Computer Science |
| EISSN | 1432-0444 |
| EndPage | 904 |
| ExternalDocumentID | 10_1007_s00454_020_00243_7 |
| GrantInformation_xml | – fundername: Israel Science Foundation grantid: 892/13 funderid: http://dx.doi.org/10.13039/501100003977 – fundername: Israel Science Foundation grantid: 822-10; 1841-14 funderid: http://dx.doi.org/10.13039/501100003977 – fundername: German-Israeli Foundation for Scientific Research and Development grantid: 1161/2011; 1367/2016 funderid: http://dx.doi.org/10.13039/501100001736 – fundername: Israeli Centers for Research Excellence grantid: 4/11 funderid: http://dx.doi.org/10.13039/501100005386 – fundername: Deutsche Forschungsgemeinschaft grantid: MU/3501/1 funderid: http://dx.doi.org/10.13039/501100001659 – fundername: European Research Council grantid: StG 757609 funderid: http://dx.doi.org/10.13039/501100000781 – fundername: United States - Israel Binational Science Foundation grantid: 2012/229 funderid: http://dx.doi.org/10.13039/100006221 |
| GroupedDBID | -52 -5D -5G -BR -DZ -EM -Y2 -~C -~X .4S .86 .DC 06D 0R~ 0VY 199 1N0 1SB 203 28- 29G 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2WC 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 692 6NX 78A 88I 8AO 8FE 8FG 8FW 8G5 8TC 8UJ 95- 95. 95~ 96X AABHQ AACDK AAGAY AAHNG AAIAL AAJBT AAJKR AAKPC AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYOK AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIHN ACIPV ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACREN ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEAQA AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFKRA 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 AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMTXH AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. BA0 BAPOH BBWZM BDATZ BENPR BGLVJ BGNMA BPHCQ BSONS C1A C6C CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBD EBLON EBS EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GUQSH GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K6V K7- KDC KOV KOW KQ8 L6V LAS LLZTM LO0 M0N M2O M2P M4Y M7S MA- MQGED N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OK1 P19 P62 P9R PADUT PF0 PKN PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I REI RHV RIG RNI RNS ROL RPX RSV RYB RZK RZZ S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WK8 YIN YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZWQNP ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7SC 7TB 7XB 8AL 8FD 8FK FR3 JQ2 KR7 L7M L~C L~D MBDVC PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c363t-4e3d98d993c3ba5e25e676939811a06b47a09a6ca5342f4180bfd3325a5b2f473 |
| IEDL.DBID | M2P |
| ISICitedReferencesCount | 22 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000572038400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0179-5376 |
| IngestDate | Thu Nov 27 13:41:48 EST 2025 Sat Nov 29 02:58:48 EST 2025 Tue Nov 18 22:20:54 EST 2025 Fri Feb 21 02:43:19 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | 68Q25 Voronoi diagram 68W40 General distance functions Dynamic structure |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c363t-4e3d98d993c3ba5e25e676939811a06b47a09a6ca5342f4180bfd3325a5b2f473 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-1948-5840 |
| OpenAccessLink | https://link.springer.com/10.1007/s00454-020-00243-7 |
| PQID | 2449447711 |
| PQPubID | 31658 |
| PageCount | 67 |
| ParticipantIDs | proquest_journals_2449447711 crossref_citationtrail_10_1007_s00454_020_00243_7 crossref_primary_10_1007_s00454_020_00243_7 springer_journals_10_1007_s00454_020_00243_7 |
| PublicationCentury | 2000 |
| PublicationDate | 20201000 2020-10-00 20201001 |
| PublicationDateYYYYMMDD | 2020-10-01 |
| PublicationDate_xml | – month: 10 year: 2020 text: 20201000 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Discrete & computational geometry |
| PublicationTitleAbbrev | Discrete Comput Geom |
| PublicationYear | 2020 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Agarwal, de Berg, Matoušek, Schwarzkopf (CR2) 1998; 27 Chan (CR11) 2000; 30 Sharir, Agarwal (CR49) 1995 Mulzer (CR43) 2018; 124 Agarwal, Efrat, Sharir (CR3) 2000; 29 Cabello, Jejčič (CR10) 2015; 48 Mulmuley (CR42) 1994 Chan, Pǎtraşcu, Roditty (CR15) 2011; 40 CR36 CR35 CR33 CR32 Roditty, Segal (CR46) 2011; 59 Chazelle (CR18) 2000 Mulmuley (CR41) 1991; 6 Fürer, Kasiviswanathan (CR27) 2012; 3 Har-Peled, Sharir (CR30) 2011; 45 Chazelle (CR17) 1993; 9 Lee (CR38) 1980; 27 Matoušek (CR40) 1992; 2 Vaidya (CR50) 1989; 18 Eppstein (CR25) 1995; 13 Afshani, Chan (CR1) 2009; 42 CR48 CR45 Overmars, van Leeuwen (CR44) 1981; 23 Clarkson (CR22) 1988; 17 Yao (CR52) 1982; 11 CR19 Edelsbrunner, Seidel (CR24) 1986; 1 CR14 CR13 Har-Peled (CR28) 2011 Holm, de Lichtenberg, Thorup (CR31) 2001; 48 Aurenhammer, Klein, Lee (CR5) 2013 CR51 Chan, Tsakalidis (CR16) 2016; 56 Kaplan, Mulzer, Roditty, Seiferth (CR34) 2018; 47 Bentley, Saxe (CR7) 1980; 1 Schwartz, Sharir (CR47) 1983; 4 CR29 Li, Long, Srinivasan (CR39) 2001; 62 CR26 Clarkson, Shor (CR23) 1989; 4 Boissonnat, Teillaud (CR9) 2007 Koltun (CR37) 2004; 51 de Berg, Cheong, van Kreveld, Overmars (CR8) 2008 CR20 Chvátal (CR21) 1979; 25 Chan (CR12) 2005; 34 Agarwal, Matoušek (CR4) 1995; 13 Basu, Pollack, Roy (CR6) 2006 243_CR14 243_CR19 Y Li (243_CR39) 2001; 62 J Holm (243_CR31) 2001; 48 K Mulmuley (243_CR41) 1991; 6 TM Chan (243_CR15) 2011; 40 (243_CR9) 2007 243_CR20 H Edelsbrunner (243_CR24) 1986; 1 DT Lee (243_CR38) 1980; 27 PK Agarwal (243_CR2) 1998; 27 243_CR48 PK Agarwal (243_CR4) 1995; 13 M Sharir (243_CR49) 1995 MH Overmars (243_CR44) 1981; 23 JT Schwartz (243_CR47) 1983; 4 B Chazelle (243_CR17) 1993; 9 KL Clarkson (243_CR23) 1989; 4 D Eppstein (243_CR25) 1995; 13 W Mulzer (243_CR43) 2018; 124 TM Chan (243_CR16) 2016; 56 243_CR51 P Afshani (243_CR1) 2009; 42 H Kaplan (243_CR34) 2018; 47 243_CR13 TM Chan (243_CR12) 2005; 34 243_CR36 S Basu (243_CR6) 2006 F Aurenhammer (243_CR5) 2013 M Fürer (243_CR27) 2012; 3 V Chvátal (243_CR21) 1979; 25 JL Bentley (243_CR7) 1980; 1 PM Vaidya (243_CR50) 1989; 18 L Roditty (243_CR46) 2011; 59 K Mulmuley (243_CR42) 1994 S Cabello (243_CR10) 2015; 48 PK Agarwal (243_CR3) 2000; 29 243_CR45 S Har-Peled (243_CR28) 2011 B Chazelle (243_CR18) 2000 243_CR26 243_CR29 ACC Yao (243_CR52) 1982; 11 TM Chan (243_CR11) 2000; 30 J Matoušek (243_CR40) 1992; 2 KL Clarkson (243_CR22) 1988; 17 V Koltun (243_CR37) 2004; 51 M de Berg (243_CR8) 2008 243_CR32 243_CR33 S Har-Peled (243_CR30) 2011; 45 243_CR35 |
| References_xml | – ident: CR45 – volume: 29 start-page: 912 issue: 3 year: 2000 end-page: 953 ident: CR3 article-title: Vertical decomposition of shallow levels in -dimensional arrangements and its applications publication-title: SIAM J. Comput. doi: 10.1137/S0097539795295936 – volume: 4 start-page: 387 issue: 5 year: 1989 end-page: 421 ident: CR23 article-title: Applications of random sampling in computational geometry, II publication-title: Discrete Comput. Geom. doi: 10.1007/BF02187740 – year: 2011 ident: CR28 publication-title: Geometric Approximation Algorithms. Mathematical Surveys and Monographs – ident: CR51 – volume: 2 start-page: 169 issue: 3 year: 1992 end-page: 186 ident: CR40 article-title: Reporting points in halfspaces publication-title: Comput. Geom. doi: 10.1016/0925-7721(92)90006-E – ident: CR35 – ident: CR29 – volume: 51 start-page: 699 issue: 5 year: 2004 end-page: 730 ident: CR37 article-title: Almost tight upper bounds for vertical decompositions in four dimensions publication-title: J. ACM doi: 10.1145/1017460.1017461 – volume: 13 start-page: 325 issue: 4 year: 1995 end-page: 345 ident: CR4 article-title: Dynamic half-space range reporting and its applications publication-title: Algorithmica doi: 10.1007/BF01293483 – year: 2006 ident: CR6 publication-title: Algorithms in Real Algebraic Geometry. Algorithms and Computation in Mathematics doi: 10.1007/3-540-33099-2 – ident: CR19 – volume: 34 start-page: 879 issue: 4 year: 2005 end-page: 893 ident: CR12 article-title: Low-dimensional linear programming with violations publication-title: SIAM J. Comput. doi: 10.1137/S0097539703439404 – volume: 27 start-page: 654 issue: 3 year: 1998 end-page: 667 ident: CR2 article-title: Constructing levels in arrangements and higher order Voronoi diagrams publication-title: SIAM J. Comput. doi: 10.1137/S0097539795281840 – volume: 62 start-page: 516 issue: 3 year: 2001 end-page: 527 ident: CR39 article-title: Improved bounds on the sample complexity of learning publication-title: J. Comput. System Sci. doi: 10.1006/jcss.2000.1741 – volume: 4 start-page: 298 issue: 3 year: 1983 end-page: 351 ident: CR47 article-title: On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds publication-title: Adv. Appl. Math. doi: 10.1016/0196-8858(83)90014-3 – volume: 45 start-page: 462 issue: 3 year: 2011 end-page: 496 ident: CR30 article-title: Relative -approximations in geometry publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-010-9248-1 – ident: CR32 – ident: CR36 – volume: 48 start-page: 723 issue: 4 year: 2001 end-page: 760 ident: CR31 article-title: Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, -edge, and biconnectivity publication-title: J. ACM doi: 10.1145/502090.502095 – ident: CR26 – year: 2007 ident: CR9 publication-title: Effective Computational Geometry for Curves and Surfaces. Mathematics and Visualization – volume: 1 start-page: 301 issue: 4 year: 1980 end-page: 358 ident: CR7 article-title: Decomposable searching problems I. Static-to-dynamic transformation publication-title: J. Algorithms doi: 10.1016/0196-6774(80)90015-2 – volume: 56 start-page: 866 issue: 4 year: 2016 end-page: 881 ident: CR16 article-title: Optimal deterministic algorithms for 2-d and 3-d shallow cuttings publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-016-9784-4 – volume: 11 start-page: 721 issue: 4 year: 1982 end-page: 736 ident: CR52 article-title: On constructing minimum spanning trees in -dimensional spaces and related problems publication-title: SIAM J. Comput. doi: 10.1137/0211059 – volume: 47 start-page: 1585 issue: 4 year: 2018 end-page: 1609 ident: CR34 article-title: Spanners for directed transmission graphs publication-title: SIAM J. Comput. doi: 10.1137/16M1059692 – ident: CR14 – volume: 9 start-page: 145 issue: 2 year: 1993 end-page: 158 ident: CR17 article-title: Cutting hyperplanes for divide-and-conquer publication-title: Discrete Comput. Geom. doi: 10.1007/BF02189314 – ident: CR33 – volume: 13 start-page: 111 issue: 1 year: 1995 end-page: 122 ident: CR25 article-title: Dynamic Euclidean minimum spanning trees and extrema of binary functions publication-title: Discrete Comput. Geom. doi: 10.1007/BF02574030 – volume: 1 start-page: 25 issue: 1 year: 1986 end-page: 44 ident: CR24 article-title: Voronoi diagrams and arrangements publication-title: Discrete Comput. Geom. doi: 10.1007/BF02187681 – volume: 42 start-page: 3 issue: 1 year: 2009 end-page: 21 ident: CR1 article-title: On approximate range counting and depth publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-009-9177-z – volume: 30 start-page: 561 issue: 2 year: 2000 end-page: 575 ident: CR11 article-title: Random sampling, halfspace range reporting, and construction of -levels in three dimensions publication-title: SIAM J. Comput. doi: 10.1137/S0097539798349188 – volume: 3 start-page: 31 issue: 1 year: 2012 end-page: 64 ident: CR27 article-title: Spanners for geometric intersection graphs with applications publication-title: J. Comput. Geom. – volume: 124 start-page: 59 year: 2018 end-page: 76 ident: CR43 article-title: Five proofs of Chernoff’s bound with applications publication-title: Bull. Eur. Assoc. Theor. Comput. Sci. – year: 1994 ident: CR42 publication-title: Computational Geometry. An Introduction Through Randomized Algorithms – ident: CR48 – year: 1995 ident: CR49 publication-title: Davenport–Schinzel Sequences and their Geometric Applications – year: 2008 ident: CR8 publication-title: Computational Geometry. Algorithms and Applications doi: 10.1007/978-3-540-77974-2 – volume: 23 start-page: 166 issue: 2 year: 1981 end-page: 204 ident: CR44 article-title: Maintenance of configurations in the plane publication-title: J. Comput. System Sci. doi: 10.1016/0022-0000(81)90012-X – volume: 40 start-page: 333 issue: 2 year: 2011 end-page: 349 ident: CR15 article-title: Dynamic connectivity: connecting to networks and geometry publication-title: SIAM J. Comput. doi: 10.1137/090751670 – year: 2000 ident: CR18 publication-title: The Discrepancy Method doi: 10.1017/CBO9780511626371 – volume: 25 start-page: 285 issue: 3 year: 1979 end-page: 287 ident: CR21 article-title: The tail of the hypergeometric distribution publication-title: Discrete Math. doi: 10.1016/0012-365X(79)90084-0 – volume: 17 start-page: 830 issue: 4 year: 1988 end-page: 847 ident: CR22 article-title: A randomized algorithm for closest-point queries publication-title: SIAM J. Comput. doi: 10.1137/0217052 – ident: CR13 – volume: 27 start-page: 604 issue: 4 year: 1980 end-page: 618 ident: CR38 article-title: Two-dimensional Voronoi diagrams in the -metric publication-title: J. ACM doi: 10.1145/322217.322219 – year: 2013 ident: CR5 publication-title: Voronoi Diagrams and Delaunay Triangulations doi: 10.1142/8685 – volume: 48 start-page: 360 issue: 4 year: 2015 end-page: 367 ident: CR10 article-title: Shortest paths in intersection graphs of unit disks publication-title: Comput. Geom. doi: 10.1016/j.comgeo.2014.12.003 – volume: 18 start-page: 1201 issue: 6 year: 1989 end-page: 1225 ident: CR50 article-title: Geometry helps in matching publication-title: SIAM J. Comput. doi: 10.1137/0218080 – volume: 59 start-page: 583 issue: 4 year: 2011 end-page: 600 ident: CR46 article-title: On bounded leg shortest paths problems publication-title: Algorithmica doi: 10.1007/s00453-009-9322-3 – volume: 6 start-page: 307 issue: 4 year: 1991 end-page: 338 ident: CR41 article-title: On levels in arrangements and Voronoi diagrams publication-title: Discrete Comput. Geom. doi: 10.1007/BF02574692 – ident: CR20 – volume-title: Computational Geometry. Algorithms and Applications year: 2008 ident: 243_CR8 doi: 10.1007/978-3-540-77974-2 – ident: 243_CR14 – volume: 27 start-page: 604 issue: 4 year: 1980 ident: 243_CR38 publication-title: J. ACM doi: 10.1145/322217.322219 – volume: 1 start-page: 301 issue: 4 year: 1980 ident: 243_CR7 publication-title: J. Algorithms doi: 10.1016/0196-6774(80)90015-2 – volume: 42 start-page: 3 issue: 1 year: 2009 ident: 243_CR1 publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-009-9177-z – volume: 17 start-page: 830 issue: 4 year: 1988 ident: 243_CR22 publication-title: SIAM J. Comput. doi: 10.1137/0217052 – ident: 243_CR33 – volume: 48 start-page: 360 issue: 4 year: 2015 ident: 243_CR10 publication-title: Comput. Geom. doi: 10.1016/j.comgeo.2014.12.003 – volume: 47 start-page: 1585 issue: 4 year: 2018 ident: 243_CR34 publication-title: SIAM J. Comput. doi: 10.1137/16M1059692 – volume: 48 start-page: 723 issue: 4 year: 2001 ident: 243_CR31 publication-title: J. ACM doi: 10.1145/502090.502095 – volume: 27 start-page: 654 issue: 3 year: 1998 ident: 243_CR2 publication-title: SIAM J. Comput. doi: 10.1137/S0097539795281840 – volume: 18 start-page: 1201 issue: 6 year: 1989 ident: 243_CR50 publication-title: SIAM J. Comput. doi: 10.1137/0218080 – volume: 29 start-page: 912 issue: 3 year: 2000 ident: 243_CR3 publication-title: SIAM J. Comput. doi: 10.1137/S0097539795295936 – volume: 45 start-page: 462 issue: 3 year: 2011 ident: 243_CR30 publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-010-9248-1 – volume: 3 start-page: 31 issue: 1 year: 2012 ident: 243_CR27 publication-title: J. Comput. Geom. – ident: 243_CR29 doi: 10.1007/978-3-319-44479-6_19 – volume-title: Computational Geometry. An Introduction Through Randomized Algorithms year: 1994 ident: 243_CR42 – volume: 124 start-page: 59 year: 2018 ident: 243_CR43 publication-title: Bull. Eur. Assoc. Theor. Comput. Sci. – volume: 59 start-page: 583 issue: 4 year: 2011 ident: 243_CR46 publication-title: Algorithmica doi: 10.1007/s00453-009-9322-3 – ident: 243_CR51 – ident: 243_CR48 – volume: 34 start-page: 879 issue: 4 year: 2005 ident: 243_CR12 publication-title: SIAM J. Comput. doi: 10.1137/S0097539703439404 – volume: 30 start-page: 561 issue: 2 year: 2000 ident: 243_CR11 publication-title: SIAM J. Comput. doi: 10.1137/S0097539798349188 – volume: 2 start-page: 169 issue: 3 year: 1992 ident: 243_CR40 publication-title: Comput. Geom. doi: 10.1016/0925-7721(92)90006-E – volume: 1 start-page: 25 issue: 1 year: 1986 ident: 243_CR24 publication-title: Discrete Comput. Geom. doi: 10.1007/BF02187681 – volume: 6 start-page: 307 issue: 4 year: 1991 ident: 243_CR41 publication-title: Discrete Comput. Geom. doi: 10.1007/BF02574692 – volume: 13 start-page: 111 issue: 1 year: 1995 ident: 243_CR25 publication-title: Discrete Comput. Geom. doi: 10.1007/BF02574030 – volume: 9 start-page: 145 issue: 2 year: 1993 ident: 243_CR17 publication-title: Discrete Comput. Geom. doi: 10.1007/BF02189314 – ident: 243_CR20 doi: 10.1145/323233.323264 – volume-title: Effective Computational Geometry for Curves and Surfaces. Mathematics and Visualization year: 2007 ident: 243_CR9 – volume: 4 start-page: 387 issue: 5 year: 1989 ident: 243_CR23 publication-title: Discrete Comput. Geom. doi: 10.1007/BF02187740 – ident: 243_CR26 – ident: 243_CR13 doi: 10.1145/1706591.1706596 – ident: 243_CR45 doi: 10.1145/304893.304993 – volume-title: Voronoi Diagrams and Delaunay Triangulations year: 2013 ident: 243_CR5 doi: 10.1142/8685 – ident: 243_CR19 doi: 10.1007/BFb0035760 – ident: 243_CR36 – volume: 56 start-page: 866 issue: 4 year: 2016 ident: 243_CR16 publication-title: Discrete Comput. Geom. doi: 10.1007/s00454-016-9784-4 – volume: 25 start-page: 285 issue: 3 year: 1979 ident: 243_CR21 publication-title: Discrete Math. doi: 10.1016/0012-365X(79)90084-0 – volume: 51 start-page: 699 issue: 5 year: 2004 ident: 243_CR37 publication-title: J. ACM doi: 10.1145/1017460.1017461 – volume: 13 start-page: 325 issue: 4 year: 1995 ident: 243_CR4 publication-title: Algorithmica doi: 10.1007/BF01293483 – volume-title: Algorithms in Real Algebraic Geometry. Algorithms and Computation in Mathematics year: 2006 ident: 243_CR6 doi: 10.1007/3-540-33099-2 – volume: 62 start-page: 516 issue: 3 year: 2001 ident: 243_CR39 publication-title: J. Comput. System Sci. doi: 10.1006/jcss.2000.1741 – volume: 11 start-page: 721 issue: 4 year: 1982 ident: 243_CR52 publication-title: SIAM J. Comput. doi: 10.1137/0211059 – volume: 23 start-page: 166 issue: 2 year: 1981 ident: 243_CR44 publication-title: J. Comput. System Sci. doi: 10.1016/0022-0000(81)90012-X – volume-title: Davenport–Schinzel Sequences and their Geometric Applications year: 1995 ident: 243_CR49 – ident: 243_CR32 – volume: 4 start-page: 298 issue: 3 year: 1983 ident: 243_CR47 publication-title: Adv. Appl. Math. doi: 10.1016/0196-8858(83)90014-3 – volume-title: Geometric Approximation Algorithms. Mathematical Surveys and Monographs year: 2011 ident: 243_CR28 – volume: 40 start-page: 333 issue: 2 year: 2011 ident: 243_CR15 publication-title: SIAM J. Comput. doi: 10.1137/090751670 – volume-title: The Discrepancy Method year: 2000 ident: 243_CR18 doi: 10.1017/CBO9780511626371 – ident: 243_CR35 doi: 10.1137/1.9781611974782.165 |
| SSID | ssj0004908 |
| Score | 2.4317849 |
| Snippet | We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include
L
p... We describe a new data structure for dynamic nearest neighbor queries in the plane with respect to a general family of distance functions. These include... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 838 |
| SubjectTerms | Algebra Algorithms Bivariate analysis Combinatorial analysis Combinatorics Complexity Computational Mathematics and Numerical Analysis Cutting parameters Data structures Disks Mathematics Mathematics and Statistics Norms Queries Ricky Pollack Memorial Issue Supports Voronoi graphs |
| SummonAdditionalLinks | – databaseName: Springer Nature Link Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3PT8MgFCY6PejB-TNOp-HgTZu00AI9Ls7Fgy5G57JbA5Rpk6UzbfXvFxjt1KiJHkuBNPDo-8h77_sAOEOYSA3a9EGaEuGFgmOPhZEpzlGSRJGYYpvyP76hwyGbTOI7VxRW1tnudUjS_qmbYjfLFueZ646l0fPoKljT7o4ZwYb7h_GyGjK2OnTG1DxDVuJKZb6f47M7WmLML2FR620G7f995zbYcugS9hbmsANWVL4L2rVyA3QHeRds3jZsreUe4P2FLD00Cka8gGPDajDPYD_jJnerhBrYQsdPrRsNnpQKDrRHtEYLeZ7CkQk4wN7saV5k1bOZrPchNL4PHgdXo8trz0kveBITXHmhwmnMUg1eJBY8UihSVjUxZkHAfSJCyv2YE8kjHKJpGDBfTFOMUcQjoZ8pPgCtfJ6rQwAJQoGiiEhz-WESCYFY4AtT86qhA6cdENQ7kEjHS27kMWZJw6hsVzTRK5rYFU30mPNmzMuClePX3t16YxN3QstEw5o4DCkNgg64qDdy-frn2Y7-1v0YbCBjCzb_rwtaVfGqTsC6fKuysji1lvsOZLPkNw priority: 102 providerName: Springer Nature |
| Title | Dynamic Planar Voronoi Diagrams for General Distance Functions and Their Algorithmic Applications |
| URI | https://link.springer.com/article/10.1007/s00454-020-00243-7 https://www.proquest.com/docview/2449447711 |
| Volume | 64 |
| WOSCitedRecordID | wos000572038400001&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: Springer Nature Link Contemporary 1997-Present customDbUrl: eissn: 1432-0444 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004908 issn: 0179-5376 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/eLvHCXMwpV1LTxsxEB7xOtADr4JKC5EP3MBqbK_Xu6cqLURIQLoCGqFeVrbXoZFQQrMpv78ex5u0SHDhYmkftizN2DP2zHwfwBEXqfVOm19Ig9TQxGhBs0RicY6zqZRmIELKf_9S9XrZ3V1exAu3OqZVNnti2KirscU78s_eDOVJohRjXx5_U2SNwuhqpNBYhlXv2TBM6brixaIuMg-MdKh0FGFLYtFMKJ0L2HMUD08BlI-q_w3Twtt8FiANdqe7-dYZb8FG9DhJZ6Yi27DkRjuw2bA5kLi4d-Dd1RzBtX4P-nRGVU-Q1UhPSB-RDsZDcjrUmM9VE-_skohZ7V-ij2kd6XorGRSZ6FFFbjEIQToP935W0184WOefcPku_Oie3X47p5GOgVqRiilNnKjyrPIOjRVGS8elC0yKecaYbqcmUbqd69RqKRI-SFjWNoNKCC61NP5ZiT1YGY1H7gOQlHPmFE8tHogyy43hGWsbrIP17oRW-8AaWZQ2YpUjZcZDOUdZDvIrvfzKIL_S9zme93mcIXW8-vdBI7Qyrtq6XEhsH04asS8-vzzax9dH-wTrHDUt5AAewMp08scdwpp9mg7rSQtWv571iusWLF8o2kIN_h7aAlt149tC_vTt9U3_L0Pj9M4 |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LTxsxEB5RQGo5FBqoCoXWBzi1Flnb-zqgKmqIQHkohxDlttheh0aiG5oNrfhT_EY8zm5CkZpbDj3uwyOt_c3D65lvAI4ZD7QN2qwiDQNFhZKcRsLH4hyjA99XQ-5S_vutsNOJBoO4uwaPZS0MplWWNtEZ6nSs8R_5qXVDsRBh6Hnf7n5R7BqFp6tlC40ZLJrm4Y_dsuVnl3W7vieMNc573y9o0VWAah7wKRWGp3GUWr-suZK-Yb5xDQHjyPNkNVAilNVYBlr6XLCh8KKqGqacM1_6yl6H3Mp9BRsCmcUwVZB1F3WYseuAhyCnSJNSFOm4Uj3HdUdxs-ZIAGn4tyNcRLcvDmSdn2ts_28ztANvi4ia1GYq8A7WTFaB7bJbBSmMVwW22nOG2nwXZP0hkz9HmmDXJjkhfWRyGI9IfSQxXy0nNpgnBSe3vYkxtDakYaMAp6hEZinp4SELqd3e2FmY_kBhtWfpAHtwtZLPfg_r2TgzH4AEjHkmZIHGDV-kmVIs8qoK63xtuCTDffDKtU90wcWOLUFukzmLtMNLYvGSOLwkdsyX-Zi7GRPJ0rcPS5AkhVXKkwVC9uFrCbPF439LO1gu7TO8vui1W0nrstP8CG8YotzlOx7C-nRyb45gU_-ejvLJJ6cvBK5XDb8ngrBJZg |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NT9RAFH9BMAYPoggRBJ2DnnTCdqbTaQ_GbFg2EnCzByTES52ZTmET7OJ2lfCv-df53my7qyZy4-CxXy_p9Pe-Ou_9HsArIROHQRsqUplYHlsjeRoras7xLlHKljKU_J8e68EgPTvLhkvws-2FobLK1iYGQ12MHf0j30M3lMWx1lG0VzZlEcNe__3VN04TpGintR2nMYPIkb-5xvStfnfYw2_9Woj-wcn-B95MGOBOJnLKYy-LLC3QRztpjfJC-TAcMEujyHQSG2vTyUzijJKxKOMo7diykFIooywea4ly78GKxhyTygmH6vOiJzML0_AI8JwoU5qGndC2F3jvOCVugRCQ6z-d4iLS_WtzNvi8_tr_vFqP4VETabPuTDWewJKv1mGtnWLBGqO2Dg8_zplr66dgejeV-TpyjKY5mQk7JYaH8Yj1Robq2GqGQT5ruLrxJMXWzrM-RgdBgZmpCnZCmy-se3mOqzC9IGHd38oENuDTnbz2JixX48o_A5YIEXktEkeJYOqEtSKNOpb6fzGMMnoLohYHuWs42mlUyGU-Z5cO2MkRO3nATo7PvJk_czVjKLn17p0WMHljrep8gZYteNtCbnH539K2b5f2Eh4g6vLjw8HRc1gVBPhQBrkDy9PJd78L992P6aievAiqw-DLXaPvF8UdUlI |
| 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=Dynamic+Planar+Voronoi+Diagrams+for+General+Distance+Functions+and+Their+Algorithmic+Applications&rft.jtitle=Discrete+%26+computational+geometry&rft.au=Kaplan%2C+Haim&rft.au=Mulzer+Wolfgang&rft.au=Roditty+Liam&rft.au=Seiferth%2C+Paul&rft.date=2020-10-01&rft.pub=Springer+Nature+B.V&rft.issn=0179-5376&rft.eissn=1432-0444&rft.volume=64&rft.issue=3&rft.spage=838&rft.epage=904&rft_id=info:doi/10.1007%2Fs00454-020-00243-7&rft.externalDBID=HAS_PDF_LINK |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0179-5376&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0179-5376&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0179-5376&client=summon |