Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space
The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding the...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ushakov, V N [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2016 |
|---|
| Rechteinformationen: |
Nutzungsrecht: © Pleiades Publishing, Ltd. 2016 |
|---|
| Schlagwörter: |
|---|
| Übergeordnetes Werk: |
Enthalten in: Proceedings of the Steklov Institute of Mathematics - Birmingham, Ala. [u.a.] : Interperiodica, 1966, 293(2016), S1, Seite 225-237 |
|---|---|
| Übergeordnetes Werk: |
volume:293 ; year:2016 ; number:S1 ; pages:225-237 |
| Links: |
|---|
| DOI / URN: |
10.1134/S0081543816050205 |
|---|
| Katalog-ID: |
OLC1980664927 |
|---|
| LEADER | 01000caa a2200265 4500 | ||
|---|---|---|---|
| 001 | OLC1980664927 | ||
| 003 | DE-627 | ||
| 005 | 20230714205816.0 | ||
| 007 | tu | ||
| 008 | 160816s2016 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1134/S0081543816050205 |2 doi | |
| 028 | 5 | 2 | |a PQ20161012 |
| 035 | |a (DE-627)OLC1980664927 | ||
| 035 | |a (DE-599)GBVOLC1980664927 | ||
| 035 | |a (PRQ)c1400-ab57c84d8078a579bf0155ff0b222c2980dd267c1017236af21a2db651c6e22e0 | ||
| 035 | |a (KEY)0279113720160000293000000225algorithmsfortheconstructionofanoptimalcoverforset | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 510 |q DE-600 |
| 100 | 1 | |a Ushakov, V N |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space |
| 264 | 1 | |c 2016 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 520 | |a The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented. | ||
| 540 | |a Nutzungsrecht: © Pleiades Publishing, Ltd. 2016 | ||
| 650 | 4 | |a Chebyshev center | |
| 650 | 4 | |a best n -net | |
| 650 | 4 | |a ball cover | |
| 650 | 4 | |a Hausdorff deviation | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematics | |
| 700 | 1 | |a Lebedev, P D |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |t Proceedings of the Steklov Institute of Mathematics |d Birmingham, Ala. [u.a.] : Interperiodica, 1966 |g 293(2016), S1, Seite 225-237 |w (DE-627)130717630 |w (DE-600)968615-0 |w (DE-576)016264665 |x 0568-6407 |
| 773 | 1 | 8 | |g volume:293 |g year:2016 |g number:S1 |g pages:225-237 |
| 856 | 4 | 1 | |u http://dx.doi.org/10.1134/S0081543816050205 |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-MAT | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_4316 | ||
| 951 | |a AR | ||
| 952 | |d 293 |j 2016 |e S1 |h 225-237 | ||
| author_variant |
v n u vn vnu |
|---|---|
| matchkey_str |
article:05686407:2016----::loihsoteosrcinfnpiacvrostitrei |
| hierarchy_sort_str |
2016 |
| publishDate |
2016 |
| allfields |
10.1134/S0081543816050205 doi PQ20161012 (DE-627)OLC1980664927 (DE-599)GBVOLC1980664927 (PRQ)c1400-ab57c84d8078a579bf0155ff0b222c2980dd267c1017236af21a2db651c6e22e0 (KEY)0279113720160000293000000225algorithmsfortheconstructionofanoptimalcoverforset DE-627 ger DE-627 rakwb eng 510 DE-600 Ushakov, V N verfasserin aut Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented. Nutzungsrecht: © Pleiades Publishing, Ltd. 2016 Chebyshev center best n -net ball cover Hausdorff deviation Mathematics, general Mathematics Lebedev, P D oth Enthalten in Proceedings of the Steklov Institute of Mathematics Birmingham, Ala. [u.a.] : Interperiodica, 1966 293(2016), S1, Seite 225-237 (DE-627)130717630 (DE-600)968615-0 (DE-576)016264665 0568-6407 volume:293 year:2016 number:S1 pages:225-237 http://dx.doi.org/10.1134/S0081543816050205 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4316 AR 293 2016 S1 225-237 |
| spelling |
10.1134/S0081543816050205 doi PQ20161012 (DE-627)OLC1980664927 (DE-599)GBVOLC1980664927 (PRQ)c1400-ab57c84d8078a579bf0155ff0b222c2980dd267c1017236af21a2db651c6e22e0 (KEY)0279113720160000293000000225algorithmsfortheconstructionofanoptimalcoverforset DE-627 ger DE-627 rakwb eng 510 DE-600 Ushakov, V N verfasserin aut Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented. Nutzungsrecht: © Pleiades Publishing, Ltd. 2016 Chebyshev center best n -net ball cover Hausdorff deviation Mathematics, general Mathematics Lebedev, P D oth Enthalten in Proceedings of the Steklov Institute of Mathematics Birmingham, Ala. [u.a.] : Interperiodica, 1966 293(2016), S1, Seite 225-237 (DE-627)130717630 (DE-600)968615-0 (DE-576)016264665 0568-6407 volume:293 year:2016 number:S1 pages:225-237 http://dx.doi.org/10.1134/S0081543816050205 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4316 AR 293 2016 S1 225-237 |
| allfields_unstemmed |
10.1134/S0081543816050205 doi PQ20161012 (DE-627)OLC1980664927 (DE-599)GBVOLC1980664927 (PRQ)c1400-ab57c84d8078a579bf0155ff0b222c2980dd267c1017236af21a2db651c6e22e0 (KEY)0279113720160000293000000225algorithmsfortheconstructionofanoptimalcoverforset DE-627 ger DE-627 rakwb eng 510 DE-600 Ushakov, V N verfasserin aut Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented. Nutzungsrecht: © Pleiades Publishing, Ltd. 2016 Chebyshev center best n -net ball cover Hausdorff deviation Mathematics, general Mathematics Lebedev, P D oth Enthalten in Proceedings of the Steklov Institute of Mathematics Birmingham, Ala. [u.a.] : Interperiodica, 1966 293(2016), S1, Seite 225-237 (DE-627)130717630 (DE-600)968615-0 (DE-576)016264665 0568-6407 volume:293 year:2016 number:S1 pages:225-237 http://dx.doi.org/10.1134/S0081543816050205 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4316 AR 293 2016 S1 225-237 |
| allfieldsGer |
10.1134/S0081543816050205 doi PQ20161012 (DE-627)OLC1980664927 (DE-599)GBVOLC1980664927 (PRQ)c1400-ab57c84d8078a579bf0155ff0b222c2980dd267c1017236af21a2db651c6e22e0 (KEY)0279113720160000293000000225algorithmsfortheconstructionofanoptimalcoverforset DE-627 ger DE-627 rakwb eng 510 DE-600 Ushakov, V N verfasserin aut Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented. Nutzungsrecht: © Pleiades Publishing, Ltd. 2016 Chebyshev center best n -net ball cover Hausdorff deviation Mathematics, general Mathematics Lebedev, P D oth Enthalten in Proceedings of the Steklov Institute of Mathematics Birmingham, Ala. [u.a.] : Interperiodica, 1966 293(2016), S1, Seite 225-237 (DE-627)130717630 (DE-600)968615-0 (DE-576)016264665 0568-6407 volume:293 year:2016 number:S1 pages:225-237 http://dx.doi.org/10.1134/S0081543816050205 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4316 AR 293 2016 S1 225-237 |
| allfieldsSound |
10.1134/S0081543816050205 doi PQ20161012 (DE-627)OLC1980664927 (DE-599)GBVOLC1980664927 (PRQ)c1400-ab57c84d8078a579bf0155ff0b222c2980dd267c1017236af21a2db651c6e22e0 (KEY)0279113720160000293000000225algorithmsfortheconstructionofanoptimalcoverforset DE-627 ger DE-627 rakwb eng 510 DE-600 Ushakov, V N verfasserin aut Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented. Nutzungsrecht: © Pleiades Publishing, Ltd. 2016 Chebyshev center best n -net ball cover Hausdorff deviation Mathematics, general Mathematics Lebedev, P D oth Enthalten in Proceedings of the Steklov Institute of Mathematics Birmingham, Ala. [u.a.] : Interperiodica, 1966 293(2016), S1, Seite 225-237 (DE-627)130717630 (DE-600)968615-0 (DE-576)016264665 0568-6407 volume:293 year:2016 number:S1 pages:225-237 http://dx.doi.org/10.1134/S0081543816050205 Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4316 AR 293 2016 S1 225-237 |
| language |
English |
| source |
Enthalten in Proceedings of the Steklov Institute of Mathematics 293(2016), S1, Seite 225-237 volume:293 year:2016 number:S1 pages:225-237 |
| sourceStr |
Enthalten in Proceedings of the Steklov Institute of Mathematics 293(2016), S1, Seite 225-237 volume:293 year:2016 number:S1 pages:225-237 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Chebyshev center best n -net ball cover Hausdorff deviation Mathematics, general Mathematics |
| dewey-raw |
510 |
| isfreeaccess_bool |
false |
| container_title |
Proceedings of the Steklov Institute of Mathematics |
| authorswithroles_txt_mv |
Ushakov, V N @@aut@@ Lebedev, P D @@oth@@ |
| publishDateDaySort_date |
2016-01-01T00:00:00Z |
| hierarchy_top_id |
130717630 |
| dewey-sort |
3510 |
| id |
OLC1980664927 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC1980664927</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230714205816.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">160816s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S0081543816050205</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20161012</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC1980664927</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC1980664927</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)c1400-ab57c84d8078a579bf0155ff0b222c2980dd267c1017236af21a2db651c6e22e0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0279113720160000293000000225algorithmsfortheconstructionofanoptimalcoverforset</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ushakov, V N</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented.</subfield></datafield><datafield tag="540" ind1=" " ind2=" "><subfield code="a">Nutzungsrecht: © Pleiades Publishing, Ltd. 2016</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Chebyshev center</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">best n -net</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ball cover</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hausdorff deviation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lebedev, P D</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Proceedings of the Steklov Institute of Mathematics</subfield><subfield code="d">Birmingham, Ala. [u.a.] : Interperiodica, 1966</subfield><subfield code="g">293(2016), S1, Seite 225-237</subfield><subfield code="w">(DE-627)130717630</subfield><subfield code="w">(DE-600)968615-0</subfield><subfield code="w">(DE-576)016264665</subfield><subfield code="x">0568-6407</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:293</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:S1</subfield><subfield code="g">pages:225-237</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">http://dx.doi.org/10.1134/S0081543816050205</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4316</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">293</subfield><subfield code="j">2016</subfield><subfield code="e">S1</subfield><subfield code="h">225-237</subfield></datafield></record></collection>
|
| author |
Ushakov, V N |
| spellingShingle |
Ushakov, V N ddc 510 misc Chebyshev center misc best n -net misc ball cover misc Hausdorff deviation misc Mathematics, general misc Mathematics Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space |
| authorStr |
Ushakov, V N |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)130717630 |
| format |
Article |
| dewey-ones |
510 - Mathematics |
| delete_txt_mv |
keep |
| author_role |
aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
0568-6407 |
| topic_title |
510 DE-600 Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space Chebyshev center best n -net ball cover Hausdorff deviation Mathematics, general Mathematics |
| topic |
ddc 510 misc Chebyshev center misc best n -net misc ball cover misc Hausdorff deviation misc Mathematics, general misc Mathematics |
| topic_unstemmed |
ddc 510 misc Chebyshev center misc best n -net misc ball cover misc Hausdorff deviation misc Mathematics, general misc Mathematics |
| topic_browse |
ddc 510 misc Chebyshev center misc best n -net misc ball cover misc Hausdorff deviation misc Mathematics, general misc Mathematics |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| author2_variant |
p d l pd pdl |
| hierarchy_parent_title |
Proceedings of the Steklov Institute of Mathematics |
| hierarchy_parent_id |
130717630 |
| dewey-tens |
510 - Mathematics |
| hierarchy_top_title |
Proceedings of the Steklov Institute of Mathematics |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)130717630 (DE-600)968615-0 (DE-576)016264665 |
| title |
Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space |
| ctrlnum |
(DE-627)OLC1980664927 (DE-599)GBVOLC1980664927 (PRQ)c1400-ab57c84d8078a579bf0155ff0b222c2980dd267c1017236af21a2db651c6e22e0 (KEY)0279113720160000293000000225algorithmsfortheconstructionofanoptimalcoverforset |
| title_full |
Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space |
| author_sort |
Ushakov, V N |
| journal |
Proceedings of the Steklov Institute of Mathematics |
| journalStr |
Proceedings of the Steklov Institute of Mathematics |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2016 |
| contenttype_str_mv |
txt |
| container_start_page |
225 |
| author_browse |
Ushakov, V N |
| container_volume |
293 |
| class |
510 DE-600 |
| format_se |
Aufsätze |
| author-letter |
Ushakov, V N |
| doi_str_mv |
10.1134/S0081543816050205 |
| dewey-full |
510 |
| title_sort |
algorithms for the construction of an optimal cover for sets in three-dimensional euclidean space |
| title_auth |
Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space |
| abstract |
The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented. |
| abstractGer |
The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented. |
| abstract_unstemmed |
The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented. |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2088 GBV_ILN_4316 |
| container_issue |
S1 |
| title_short |
Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space |
| url |
http://dx.doi.org/10.1134/S0081543816050205 |
| remote_bool |
false |
| author2 |
Lebedev, P D |
| author2Str |
Lebedev, P D |
| ppnlink |
130717630 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| author2_role |
oth |
| doi_str |
10.1134/S0081543816050205 |
| up_date |
2024-07-04T03:31:51.845Z |
| _version_ |
1803617736443559936 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a2200265 4500</leader><controlfield tag="001">OLC1980664927</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230714205816.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">160816s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S0081543816050205</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">PQ20161012</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC1980664927</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBVOLC1980664927</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(PRQ)c1400-ab57c84d8078a579bf0155ff0b222c2980dd267c1017236af21a2db651c6e22e0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(KEY)0279113720160000293000000225algorithmsfortheconstructionofanoptimalcoverforset</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">DE-600</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ushakov, V N</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algorithms for the construction of an optimal cover for sets in three-dimensional Euclidean space</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The problem of an optimal cover of sets in three-dimensional Euclidian space by the union of a fixed number of equal balls, where the optimality criterion is the radius of the balls, is studied. Analytical and numerical algorithms based on the division of a set into Dirichlet domains and finding their Chebyshev centers are suggested for this problem. Stochastic iterative procedures are used. Bounds for the asymptotics of the radii of the balls as their number tends to infinity are obtained. The simulation of several examples is performed and their visualization is presented.</subfield></datafield><datafield tag="540" ind1=" " ind2=" "><subfield code="a">Nutzungsrecht: © Pleiades Publishing, Ltd. 2016</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Chebyshev center</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">best n -net</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ball cover</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hausdorff deviation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lebedev, P D</subfield><subfield code="4">oth</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Proceedings of the Steklov Institute of Mathematics</subfield><subfield code="d">Birmingham, Ala. [u.a.] : Interperiodica, 1966</subfield><subfield code="g">293(2016), S1, Seite 225-237</subfield><subfield code="w">(DE-627)130717630</subfield><subfield code="w">(DE-600)968615-0</subfield><subfield code="w">(DE-576)016264665</subfield><subfield code="x">0568-6407</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:293</subfield><subfield code="g">year:2016</subfield><subfield code="g">number:S1</subfield><subfield code="g">pages:225-237</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">http://dx.doi.org/10.1134/S0081543816050205</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4316</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">293</subfield><subfield code="j">2016</subfield><subfield code="e">S1</subfield><subfield code="h">225-237</subfield></datafield></record></collection>
|
| score |
7.3975716 |