Optimal Offline Dynamic \(2,3\)-Edge/Vertex Connectivity

We give offline algorithms for processing a sequence of \(2\) and \(3\) edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for \(3\)-edge and \(3\)-vertex connectivity require \(O(n^{2/3})\) and \(O(n)\) time per upda...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2019-03
Hauptverfasser: Peng, Richard, Sandlund, Bryce, Sleator, Daniel D
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Peng, Richard
Sandlund, Bryce
Sleator, Daniel D
description We give offline algorithms for processing a sequence of \(2\) and \(3\) edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for \(3\)-edge and \(3\)-vertex connectivity require \(O(n^{2/3})\) and \(O(n)\) time per update, respectively, our per-operation cost is only \(O(\log n)\), optimal due to the dynamic connectivity lower bound of Patrascu and Demaine. Our approach utilizes a divide and conquer scheme that transforms a graph into smaller equivalents that preserve connectivity information. This construction of equivalents is closely-related to the development of vertex sparsifiers, and shares important connections to several upcoming results in dynamic graph data structures, outside of just the offline model.
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2075686960</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2075686960</sourcerecordid><originalsourceid>FETCH-proquest_journals_20756869603</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSw8C8oycxNzFHwT0vLycxLVXCpzEvMzUxWiNEw0jGO0dR1TUlP1Q9LLSpJrVBwzs_LS00uySzLLKnkYWBNS8wpTuWF0twMym6uIc4eugVF-YWlqcUl8Vn5pUV5QKl4IwNzUzMLM0szA2PiVAEAqDo05Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2075686960</pqid></control><display><type>article</type><title>Optimal Offline Dynamic \(2,3\)-Edge/Vertex Connectivity</title><source>Free E- Journals</source><creator>Peng, Richard ; Sandlund, Bryce ; Sleator, Daniel D</creator><creatorcontrib>Peng, Richard ; Sandlund, Bryce ; Sleator, Daniel D</creatorcontrib><description>We give offline algorithms for processing a sequence of \(2\) and \(3\) edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for \(3\)-edge and \(3\)-vertex connectivity require \(O(n^{2/3})\) and \(O(n)\) time per update, respectively, our per-operation cost is only \(O(\log n)\), optimal due to the dynamic connectivity lower bound of Patrascu and Demaine. Our approach utilizes a divide and conquer scheme that transforms a graph into smaller equivalents that preserve connectivity information. This construction of equivalents is closely-related to the development of vertex sparsifiers, and shares important connections to several upcoming results in dynamic graph data structures, outside of just the offline model.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algorithms ; Connectivity ; Data structures ; Equivalence ; Lower bounds</subject><ispartof>arXiv.org, 2019-03</ispartof><rights>2019. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>776,780</link.rule.ids></links><search><creatorcontrib>Peng, Richard</creatorcontrib><creatorcontrib>Sandlund, Bryce</creatorcontrib><creatorcontrib>Sleator, Daniel D</creatorcontrib><title>Optimal Offline Dynamic \(2,3\)-Edge/Vertex Connectivity</title><title>arXiv.org</title><description>We give offline algorithms for processing a sequence of \(2\) and \(3\) edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for \(3\)-edge and \(3\)-vertex connectivity require \(O(n^{2/3})\) and \(O(n)\) time per update, respectively, our per-operation cost is only \(O(\log n)\), optimal due to the dynamic connectivity lower bound of Patrascu and Demaine. Our approach utilizes a divide and conquer scheme that transforms a graph into smaller equivalents that preserve connectivity information. This construction of equivalents is closely-related to the development of vertex sparsifiers, and shares important connections to several upcoming results in dynamic graph data structures, outside of just the offline model.</description><subject>Algorithms</subject><subject>Connectivity</subject><subject>Data structures</subject><subject>Equivalence</subject><subject>Lower bounds</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSw8C8oycxNzFHwT0vLycxLVXCpzEvMzUxWiNEw0jGO0dR1TUlP1Q9LLSpJrVBwzs_LS00uySzLLKnkYWBNS8wpTuWF0twMym6uIc4eugVF-YWlqcUl8Vn5pUV5QKl4IwNzUzMLM0szA2PiVAEAqDo05Q</recordid><startdate>20190321</startdate><enddate>20190321</enddate><creator>Peng, Richard</creator><creator>Sandlund, Bryce</creator><creator>Sleator, Daniel D</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20190321</creationdate><title>Optimal Offline Dynamic \(2,3\)-Edge/Vertex Connectivity</title><author>Peng, Richard ; Sandlund, Bryce ; Sleator, Daniel D</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20756869603</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algorithms</topic><topic>Connectivity</topic><topic>Data structures</topic><topic>Equivalence</topic><topic>Lower bounds</topic><toplevel>online_resources</toplevel><creatorcontrib>Peng, Richard</creatorcontrib><creatorcontrib>Sandlund, Bryce</creatorcontrib><creatorcontrib>Sleator, Daniel D</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Peng, Richard</au><au>Sandlund, Bryce</au><au>Sleator, Daniel D</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Optimal Offline Dynamic \(2,3\)-Edge/Vertex Connectivity</atitle><jtitle>arXiv.org</jtitle><date>2019-03-21</date><risdate>2019</risdate><eissn>2331-8422</eissn><abstract>We give offline algorithms for processing a sequence of \(2\) and \(3\) edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for \(3\)-edge and \(3\)-vertex connectivity require \(O(n^{2/3})\) and \(O(n)\) time per update, respectively, our per-operation cost is only \(O(\log n)\), optimal due to the dynamic connectivity lower bound of Patrascu and Demaine. Our approach utilizes a divide and conquer scheme that transforms a graph into smaller equivalents that preserve connectivity information. This construction of equivalents is closely-related to the development of vertex sparsifiers, and shares important connections to several upcoming results in dynamic graph data structures, outside of just the offline model.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2019-03
issn 2331-8422
language eng
recordid cdi_proquest_journals_2075686960
source Free E- Journals
subjects Algorithms
Connectivity
Data structures
Equivalence
Lower bounds
title Optimal Offline Dynamic \(2,3\)-Edge/Vertex Connectivity
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T23%3A41%3A10IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Optimal%20Offline%20Dynamic%20%5C(2,3%5C)-Edge/Vertex%20Connectivity&rft.jtitle=arXiv.org&rft.au=Peng,%20Richard&rft.date=2019-03-21&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2075686960%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2075686960&rft_id=info:pmid/&rfr_iscdi=true