Medians in median graphs and their cube complexes in linear time
The median of a set of vertices P of a graph G is the set of all vertices x of G minimizing the sum of distances from x to all vertices of P. In this paper, we present a linear time algorithm to compute medians in median graphs. We also present a linear time algorithm to compute medians in the assoc...
Gespeichert in:
| Veröffentlicht in: | Journal of computer and system sciences 2022-06, Vol.126, p.80-105 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 105 |
|---|---|
| container_issue | |
| container_start_page | 80 |
| container_title | Journal of computer and system sciences |
| container_volume | 126 |
| creator | Bénéteau, Laurine Chalopin, Jérémie Chepoi, Victor Vaxès, Yann |
| description | The median of a set of vertices P of a graph G is the set of all vertices x of G minimizing the sum of distances from x to all vertices of P. In this paper, we present a linear time algorithm to compute medians in median graphs. We also present a linear time algorithm to compute medians in the associated ℓ1-cube complexes. Our algorithm is based on the majority rule characterization of medians in median graphs and on a fast computation of parallelism classes of edges (Θ-classes) via Lexicographic Breadth First Search (LexBFS). We show that any LexBFS ordering of the vertices of a median graph satisfies the following fellow traveler property: the parents of any two adjacent vertices are also adjacent. Using the fast computation of the Θ-classes, we also compute the Wiener index (total distance) in linear time and the distance matrix in optimal quadratic time. |
| doi_str_mv | 10.1016/j.jcss.2022.01.001 |
| format | Article |
| fullrecord | <record><control><sourceid>elsevier_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_03547953v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0022000022000034</els_id><sourcerecordid>S0022000022000034</sourcerecordid><originalsourceid>FETCH-LOGICAL-c378t-773a90dc9567b8a5cc4392e503a297a7ddb3bae41a5b02fe81e68f111bba192a3</originalsourceid><addsrcrecordid>eNp9kMFOwzAMhiMEEmPwApxy5dASJ23TShyYJmBIQ1zgHLmpy1J17ZSUCd6edkMc8cVW8v2W_DF2DSIGAdltEzc2hFgKKWMBsRBwwmYgChFJLZNTNhPjTyTGOmcXITQjAGmmZuz-hSqHXeCu49vDyD887jaBY1fxYUPOc_tZErf9dtfSFx3I1nWEng9uS5fsrMY20NVvn7P3x4e35Spavz49LxfryCqdD5HWCgtR2SLNdJljam2iCkmpUCgLjbqqSlUiJYBpKWRNOVCW1wBQlgiFRDVnN8e9G2zNzrst-m_TozOrxdpMb0KliS5StYeRlUfW-j4ET_VfAISZfJnGTL7M5MsIMKOOMXR3DNF4xd6RN8E66uwoxZMdTNW7_-I_UcJytA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Medians in median graphs and their cube complexes in linear time</title><source>Access via ScienceDirect (Elsevier)</source><creator>Bénéteau, Laurine ; Chalopin, Jérémie ; Chepoi, Victor ; Vaxès, Yann</creator><creatorcontrib>Bénéteau, Laurine ; Chalopin, Jérémie ; Chepoi, Victor ; Vaxès, Yann</creatorcontrib><description>The median of a set of vertices P of a graph G is the set of all vertices x of G minimizing the sum of distances from x to all vertices of P. In this paper, we present a linear time algorithm to compute medians in median graphs. We also present a linear time algorithm to compute medians in the associated ℓ1-cube complexes. Our algorithm is based on the majority rule characterization of medians in median graphs and on a fast computation of parallelism classes of edges (Θ-classes) via Lexicographic Breadth First Search (LexBFS). We show that any LexBFS ordering of the vertices of a median graph satisfies the following fellow traveler property: the parents of any two adjacent vertices are also adjacent. Using the fast computation of the Θ-classes, we also compute the Wiener index (total distance) in linear time and the distance matrix in optimal quadratic time.</description><identifier>ISSN: 0022-0000</identifier><identifier>EISSN: 1090-2724</identifier><identifier>DOI: 10.1016/j.jcss.2022.01.001</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>CAT cube complex ; Combinatorics ; Computational Geometry ; Computer Science ; Data Structures and Algorithms ; Discrete Mathematics ; Event structures ; LexBFS ; Linear time algorithm ; Mathematics ; Median graph ; Median problem ; Metric Geometry</subject><ispartof>Journal of computer and system sciences, 2022-06, Vol.126, p.80-105</ispartof><rights>2022 Elsevier Inc.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c378t-773a90dc9567b8a5cc4392e503a297a7ddb3bae41a5b02fe81e68f111bba192a3</citedby><cites>FETCH-LOGICAL-c378t-773a90dc9567b8a5cc4392e503a297a7ddb3bae41a5b02fe81e68f111bba192a3</cites><orcidid>0000-0002-2988-8969</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.jcss.2022.01.001$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,780,784,885,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03547953$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Bénéteau, Laurine</creatorcontrib><creatorcontrib>Chalopin, Jérémie</creatorcontrib><creatorcontrib>Chepoi, Victor</creatorcontrib><creatorcontrib>Vaxès, Yann</creatorcontrib><title>Medians in median graphs and their cube complexes in linear time</title><title>Journal of computer and system sciences</title><description>The median of a set of vertices P of a graph G is the set of all vertices x of G minimizing the sum of distances from x to all vertices of P. In this paper, we present a linear time algorithm to compute medians in median graphs. We also present a linear time algorithm to compute medians in the associated ℓ1-cube complexes. Our algorithm is based on the majority rule characterization of medians in median graphs and on a fast computation of parallelism classes of edges (Θ-classes) via Lexicographic Breadth First Search (LexBFS). We show that any LexBFS ordering of the vertices of a median graph satisfies the following fellow traveler property: the parents of any two adjacent vertices are also adjacent. Using the fast computation of the Θ-classes, we also compute the Wiener index (total distance) in linear time and the distance matrix in optimal quadratic time.</description><subject>CAT cube complex</subject><subject>Combinatorics</subject><subject>Computational Geometry</subject><subject>Computer Science</subject><subject>Data Structures and Algorithms</subject><subject>Discrete Mathematics</subject><subject>Event structures</subject><subject>LexBFS</subject><subject>Linear time algorithm</subject><subject>Mathematics</subject><subject>Median graph</subject><subject>Median problem</subject><subject>Metric Geometry</subject><issn>0022-0000</issn><issn>1090-2724</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kMFOwzAMhiMEEmPwApxy5dASJ23TShyYJmBIQ1zgHLmpy1J17ZSUCd6edkMc8cVW8v2W_DF2DSIGAdltEzc2hFgKKWMBsRBwwmYgChFJLZNTNhPjTyTGOmcXITQjAGmmZuz-hSqHXeCu49vDyD887jaBY1fxYUPOc_tZErf9dtfSFx3I1nWEng9uS5fsrMY20NVvn7P3x4e35Spavz49LxfryCqdD5HWCgtR2SLNdJljam2iCkmpUCgLjbqqSlUiJYBpKWRNOVCW1wBQlgiFRDVnN8e9G2zNzrst-m_TozOrxdpMb0KliS5StYeRlUfW-j4ET_VfAISZfJnGTL7M5MsIMKOOMXR3DNF4xd6RN8E66uwoxZMdTNW7_-I_UcJytA</recordid><startdate>202206</startdate><enddate>202206</enddate><creator>Bénéteau, Laurine</creator><creator>Chalopin, Jérémie</creator><creator>Chepoi, Victor</creator><creator>Vaxès, Yann</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0002-2988-8969</orcidid></search><sort><creationdate>202206</creationdate><title>Medians in median graphs and their cube complexes in linear time</title><author>Bénéteau, Laurine ; Chalopin, Jérémie ; Chepoi, Victor ; Vaxès, Yann</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c378t-773a90dc9567b8a5cc4392e503a297a7ddb3bae41a5b02fe81e68f111bba192a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>CAT cube complex</topic><topic>Combinatorics</topic><topic>Computational Geometry</topic><topic>Computer Science</topic><topic>Data Structures and Algorithms</topic><topic>Discrete Mathematics</topic><topic>Event structures</topic><topic>LexBFS</topic><topic>Linear time algorithm</topic><topic>Mathematics</topic><topic>Median graph</topic><topic>Median problem</topic><topic>Metric Geometry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bénéteau, Laurine</creatorcontrib><creatorcontrib>Chalopin, Jérémie</creatorcontrib><creatorcontrib>Chepoi, Victor</creatorcontrib><creatorcontrib>Vaxès, Yann</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Journal of computer and system sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bénéteau, Laurine</au><au>Chalopin, Jérémie</au><au>Chepoi, Victor</au><au>Vaxès, Yann</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Medians in median graphs and their cube complexes in linear time</atitle><jtitle>Journal of computer and system sciences</jtitle><date>2022-06</date><risdate>2022</risdate><volume>126</volume><spage>80</spage><epage>105</epage><pages>80-105</pages><issn>0022-0000</issn><eissn>1090-2724</eissn><abstract>The median of a set of vertices P of a graph G is the set of all vertices x of G minimizing the sum of distances from x to all vertices of P. In this paper, we present a linear time algorithm to compute medians in median graphs. We also present a linear time algorithm to compute medians in the associated ℓ1-cube complexes. Our algorithm is based on the majority rule characterization of medians in median graphs and on a fast computation of parallelism classes of edges (Θ-classes) via Lexicographic Breadth First Search (LexBFS). We show that any LexBFS ordering of the vertices of a median graph satisfies the following fellow traveler property: the parents of any two adjacent vertices are also adjacent. Using the fast computation of the Θ-classes, we also compute the Wiener index (total distance) in linear time and the distance matrix in optimal quadratic time.</abstract><pub>Elsevier Inc</pub><doi>10.1016/j.jcss.2022.01.001</doi><tpages>26</tpages><orcidid>https://orcid.org/0000-0002-2988-8969</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-0000 |
| ispartof | Journal of computer and system sciences, 2022-06, Vol.126, p.80-105 |
| issn | 0022-0000 1090-2724 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_03547953v1 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | CAT cube complex Combinatorics Computational Geometry Computer Science Data Structures and Algorithms Discrete Mathematics Event structures LexBFS Linear time algorithm Mathematics Median graph Median problem Metric Geometry |
| title | Medians in median graphs and their cube complexes in linear time |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-30T21%3A30%3A29IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-elsevier_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Medians%20in%20median%20graphs%20and%20their%20cube%20complexes%20in%20linear%20time&rft.jtitle=Journal%20of%20computer%20and%20system%20sciences&rft.au=B%C3%A9n%C3%A9teau,%20Laurine&rft.date=2022-06&rft.volume=126&rft.spage=80&rft.epage=105&rft.pages=80-105&rft.issn=0022-0000&rft.eissn=1090-2724&rft_id=info:doi/10.1016/j.jcss.2022.01.001&rft_dat=%3Celsevier_hal_p%3ES0022000022000034%3C/elsevier_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_els_id=S0022000022000034&rfr_iscdi=true |