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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">INFORMATICA</journal-id>
<journal-title-group><journal-title>Informatica</journal-title></journal-title-group>
<issn pub-type="epub">0868-4952</issn><issn pub-type="ppub">0868-4952</issn>
<publisher>
<publisher-name>VU</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">INFO1103</article-id><article-id pub-id-type="doi">10.15388/Informatica.2016.89</article-id>
<article-categories><subj-group subj-group-type="heading">
<subject>Research Article</subject></subj-group></article-categories>
<title-group>
<article-title>On Bisecting the Unit Simplex Using Various Distance Norms</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="Author">
<name><surname>Salmerón</surname><given-names>Jose M.G.</given-names></name><email xlink:href="mailto:josemanuel@ual.es">josemanuel@ual.es</email><xref ref-type="aff" rid="j_INFORMATICA_aff_000"/><xref ref-type="corresp" rid="cor1">*</xref>
</contrib>
<contrib contrib-type="Author">
<name><surname>Casado</surname><given-names>Leocadio G.</given-names></name><email xlink:href="mailto:leo@ual.es">leo@ual.es</email><xref ref-type="aff" rid="j_INFORMATICA_aff_000"/>
</contrib>
<contrib contrib-type="Author">
<name><surname>Hendrix</surname><given-names>Eligius M.T.</given-names></name><email xlink:href="mailto:eligius@uma.es">eligius@uma.es</email><xref ref-type="aff" rid="j_INFORMATICA_aff_001"/>
</contrib>
<aff id="j_INFORMATICA_aff_000">Informatics Department, University of Almería (ceiA3), Spain</aff>
<aff id="j_INFORMATICA_aff_001">Department of Computer Architecture, Universidad de Málaga, Spain</aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><label>*</label>Corresponding author.</corresp>
</author-notes>
<pub-date pub-type="epub"><day>01</day><month>01</month><year>2016</year></pub-date><volume>27</volume><issue>2</issue><fpage>351</fpage><lpage>366</lpage><history><date date-type="received"><day>01</day><month>01</month> <year>2016</year></date><date date-type="accepted"><day>01</day><month>05</month> <year>2016</year></date></history>
<permissions><copyright-statement>Vilnius University</copyright-statement><copyright-year>2016</copyright-year></permissions>
<abstract>
<p>The iterative bisection of the longest edge of the unit simplex generates a binary tree, where the specific shape depends on the chosen longest edges to be bisected. In global optimization, the use of various distance norms may be advantageous for bounding purposes. The question dealt with in this paper is how the size of a binary tree generated by the refinement process depends on heuristics for longest edge selection when various distance norms are used. We focus on the minimum size of the tree that can be reached, how selection criteria may reduce the size of the tree compared to selecting the first edge, whether a predefined grid is covered and how unique are the selection criteria. The exact numerical values are provided for the unit simplex in 4 and 5-dimensional space.</p>
</abstract>
<kwd-group>
<label>Keywords</label>
<kwd>simplex</kwd>
<kwd>Branch-and-Bound</kwd>
<kwd>longest edge bisection</kwd>
<kwd>norm</kwd>
<kwd>selection heuristics</kwd>
</kwd-group>
</article-meta>
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