Tree Spanners for Bipartite Graphs and Probe Interval Graphs
A tree t-spanner T in a graph G is a spanning tree of G such that the distance between every pair of vertices in T is at most t times their distance in G. The tree t-spanner problem asks whether a graph admits a tree t-spanner, given t. We first substantially strengthen the known results for biparti...
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| creator | Brandstädt, Andreas Dragan, Feodor F. Le, Hoang-Oanh Le, Van Bang Uehara, Ryuhei |
| description | A tree t-spanner T in a graph G is a spanning tree of G such that the distance between every pair of vertices in T is at most t times their distance in G. The tree t-spanner problem asks whether a graph admits a tree t-spanner, given t. We first substantially strengthen the known results for bipartite graphs. We prove that the tree t-spanner problem is NP-complete even for chordal bipartite graphs for t ≥ 5, and every bipartite ATE–free graph has a tree 3-spanner, which can be found in linear time. The best known before results were NP-completeness for general bipartite graphs, and that every convex graph has a tree 3-spanner. We next focus on the tree t-spanner problem for probe interval graphs and related graph classes. The graph classes were introduced to deal with the physical mapping of DNA. From a graph theoretical point of view, the classes are natural generalizations of interval graphs. We show that these classes are tree 7-spanner admissible, and a tree 7-spanner can be constructed in O(m log n) time. |
| doi_str_mv | 10.1007/978-3-540-39890-5_10 |
| format | Conference Proceeding |
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The tree t-spanner problem asks whether a graph admits a tree t-spanner, given t. We first substantially strengthen the known results for bipartite graphs. We prove that the tree t-spanner problem is NP-complete even for chordal bipartite graphs for t ≥ 5, and every bipartite ATE–free graph has a tree 3-spanner, which can be found in linear time. The best known before results were NP-completeness for general bipartite graphs, and that every convex graph has a tree 3-spanner. We next focus on the tree t-spanner problem for probe interval graphs and related graph classes. The graph classes were introduced to deal with the physical mapping of DNA. From a graph theoretical point of view, the classes are natural generalizations of interval graphs. We show that these classes are tree 7-spanner admissible, and a tree 7-spanner can be constructed in O(m log n) time.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 3540204520</identifier><identifier>ISBN: 9783540204527</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 3540398902</identifier><identifier>EISBN: 9783540398905</identifier><identifier>DOI: 10.1007/978-3-540-39890-5_10</identifier><language>eng</language><publisher>Berlin, Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied sciences ; Chordal bipartite graph ; Computer science; control theory; systems ; Exact sciences and technology ; Information retrieval. Graph ; Interval bigraph ; NP-completeness ; Probe interval graph ; Theoretical computing ; Tree spanner</subject><ispartof>Graph-Theoretic Concepts in Computer Science, 2003, p.106-118</ispartof><rights>Springer-Verlag Berlin Heidelberg 2003</rights><rights>2004 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/978-3-540-39890-5_10$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/978-3-540-39890-5_10$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,775,776,780,785,786,789,4036,4037,27902,38232,41418,42487</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15758857$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Bodlaender, Hans L.</contributor><creatorcontrib>Brandstädt, Andreas</creatorcontrib><creatorcontrib>Dragan, Feodor F.</creatorcontrib><creatorcontrib>Le, Hoang-Oanh</creatorcontrib><creatorcontrib>Le, Van Bang</creatorcontrib><creatorcontrib>Uehara, Ryuhei</creatorcontrib><title>Tree Spanners for Bipartite Graphs and Probe Interval Graphs</title><title>Graph-Theoretic Concepts in Computer Science</title><description>A tree t-spanner T in a graph G is a spanning tree of G such that the distance between every pair of vertices in T is at most t times their distance in G. The tree t-spanner problem asks whether a graph admits a tree t-spanner, given t. We first substantially strengthen the known results for bipartite graphs. We prove that the tree t-spanner problem is NP-complete even for chordal bipartite graphs for t ≥ 5, and every bipartite ATE–free graph has a tree 3-spanner, which can be found in linear time. The best known before results were NP-completeness for general bipartite graphs, and that every convex graph has a tree 3-spanner. We next focus on the tree t-spanner problem for probe interval graphs and related graph classes. The graph classes were introduced to deal with the physical mapping of DNA. From a graph theoretical point of view, the classes are natural generalizations of interval graphs. We show that these classes are tree 7-spanner admissible, and a tree 7-spanner can be constructed in O(m log n) time.</description><subject>Applied sciences</subject><subject>Chordal bipartite graph</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Information retrieval. Graph</subject><subject>Interval bigraph</subject><subject>NP-completeness</subject><subject>Probe interval graph</subject><subject>Theoretical computing</subject><subject>Tree spanner</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>3540204520</isbn><isbn>9783540204527</isbn><isbn>3540398902</isbn><isbn>9783540398905</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2003</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNot0EtLxDAUBeD4AmdG_4GLbFxGb26SpgE3Oug4MKDguA63barVsS1JEfz3dh6rC-cc7uJj7ErCjQSwt87mQgmjQSiXOxDGSzhiUzUmuwCP2URmUgqltDvZFwjaIJyyCShA4axW52ya0hcAoHU4YXfrGAJ_66ltQ0y87iJ_aHqKQzMEvojUfyZObcVfY1cEvmyHEH9pc2gu2FlNmxQuD3fG3p8e1_NnsXpZLOf3K9EjZoPAKljQZFxh0FgoS6xQ1UE6Z4kw6KzIMCBhRpnUVpGtylKaslI5FlY6o2bsev-3p1TSpo7Ulk3yfWx-KP55aazJc2PHHe53aazajxB90XXfaXTyW0E_CnrlRxa_A_NbQfUPP6leBA</recordid><startdate>2003</startdate><enddate>2003</enddate><creator>Brandstädt, Andreas</creator><creator>Dragan, Feodor F.</creator><creator>Le, Hoang-Oanh</creator><creator>Le, Van Bang</creator><creator>Uehara, Ryuhei</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>IQODW</scope></search><sort><creationdate>2003</creationdate><title>Tree Spanners for Bipartite Graphs and Probe Interval Graphs</title><author>Brandstädt, Andreas ; Dragan, Feodor F. ; Le, Hoang-Oanh ; Le, Van Bang ; Uehara, Ryuhei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p226t-2de704a59b52570cc2d23fe1997aa2e46b62e2a26a61473a7dcc15cd382b71953</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2003</creationdate><topic>Applied sciences</topic><topic>Chordal bipartite graph</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Information retrieval. Graph</topic><topic>Interval bigraph</topic><topic>NP-completeness</topic><topic>Probe interval graph</topic><topic>Theoretical computing</topic><topic>Tree spanner</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Brandstädt, Andreas</creatorcontrib><creatorcontrib>Dragan, Feodor F.</creatorcontrib><creatorcontrib>Le, Hoang-Oanh</creatorcontrib><creatorcontrib>Le, Van Bang</creatorcontrib><creatorcontrib>Uehara, Ryuhei</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Brandstädt, Andreas</au><au>Dragan, Feodor F.</au><au>Le, Hoang-Oanh</au><au>Le, Van Bang</au><au>Uehara, Ryuhei</au><au>Bodlaender, Hans L.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Tree Spanners for Bipartite Graphs and Probe Interval Graphs</atitle><btitle>Graph-Theoretic Concepts in Computer Science</btitle><date>2003</date><risdate>2003</risdate><spage>106</spage><epage>118</epage><pages>106-118</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>3540204520</isbn><isbn>9783540204527</isbn><eisbn>3540398902</eisbn><eisbn>9783540398905</eisbn><abstract>A tree t-spanner T in a graph G is a spanning tree of G such that the distance between every pair of vertices in T is at most t times their distance in G. The tree t-spanner problem asks whether a graph admits a tree t-spanner, given t. We first substantially strengthen the known results for bipartite graphs. We prove that the tree t-spanner problem is NP-complete even for chordal bipartite graphs for t ≥ 5, and every bipartite ATE–free graph has a tree 3-spanner, which can be found in linear time. The best known before results were NP-completeness for general bipartite graphs, and that every convex graph has a tree 3-spanner. We next focus on the tree t-spanner problem for probe interval graphs and related graph classes. The graph classes were introduced to deal with the physical mapping of DNA. From a graph theoretical point of view, the classes are natural generalizations of interval graphs. We show that these classes are tree 7-spanner admissible, and a tree 7-spanner can be constructed in O(m log n) time.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/978-3-540-39890-5_10</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Graph-Theoretic Concepts in Computer Science, 2003, p.106-118 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_15758857 |
| source | Springer Books |
| subjects | Applied sciences Chordal bipartite graph Computer science control theory systems Exact sciences and technology Information retrieval. Graph Interval bigraph NP-completeness Probe interval graph Theoretical computing Tree spanner |
| title | Tree Spanners for Bipartite Graphs and Probe Interval Graphs |
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