<didl:DIDL xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:didl="urn:mpeg:mpeg21:2002:02-DIDL-NS" xsi:schemaLocation="urn:mpeg:mpeg21:2002:02-DIDL-NS 
			 http://standards.iso.org/ittf/PubliclyAvailableStandards/MPEG-21_schema_files/did/didmodel.xsd"><didl:Item><didl:Descriptior><didl:Statement mimeType="application/xml; charset=utf-8"><dii:Identifier xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="urn:mpeg:mpeg21:2002:01-DII-NS
		 	http://standards.iso.org/ittf/PubliclyAvailableStandards/MPEG-21_schema_files/dii/dii.xsd" xmlns:dii="urn:mpeg:mpeg21:2002:01-DII-NS">http://gdea.informatik.uni-koeln.de/705/</dii:Identifier></didl:Statement></didl:Descriptior><didl:Descriptior><didl:Statement mimeType="application/xml; charset=utf-8"><oai_dc:dc xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/">
        <dc:title>Complexity Results for Three-dimensional Orthogonal Graph Drawing</dc:title>
        <dc:creator>Patrignani, Maurizio</dc:creator>
        <dc:subject>P.600.700 Orthogonal</dc:subject>
        <dc:subject>G.999 Others</dc:subject>
        <dc:subject>P.060 3D</dc:subject>
        <dc:description>We introduce the 3SAT reduction framework which can be used to prove the NP-hardness of finding three-dimensional orthogonal drawings with specific constraints. We use it to show that finding a drawing of a graph whose edges have a fixed shape is NP-hard. Also, it is NP-hard finding a drawing of a graph with nodes at prescribed positions when a maximum of two bends per edge is allowed. We comment the impact of these results on the two open problems of determining whether a graph always admits a 3D orthogonal drawing with at most two bends per edge and of characterizing orthogonal shapes admitting a drawing without intersections.&#13;
    </dc:description>
        <dc:publisher>Springer</dc:publisher>
        <dc:contributor>Healy, Patrick</dc:contributor>
        <dc:contributor>Nikolov, Nikola S.</dc:contributor>
        <dc:date>2006</dc:date>
        <dc:type>Conference Paper</dc:type>
        <dc:type>NonPeerReviewed</dc:type>
        <dc:identifier>Patrignani, Maurizio (2006) Complexity Results for Three-dimensional Orthogonal Graph Drawing. [Conference Paper]</dc:identifier>
        <dc:relation>http://gdea.informatik.uni-koeln.de/705/</dc:relation></oai_dc:dc></didl:Statement></didl:Descriptior></didl:Item></didl:DIDL>