{"id":156444,"date":"1996-01-01T00:00:00","date_gmt":"1996-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/natural-cycletrees-flexible-interconnection-graphs\/"},"modified":"2018-10-16T20:23:05","modified_gmt":"2018-10-17T03:23:05","slug":"natural-cycletrees-flexible-interconnection-graphs","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/natural-cycletrees-flexible-interconnection-graphs\/","title":{"rendered":"Natural cycletrees: Flexible interconnection graphs"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Natural cycletrees, formally defined in this paper, is a subclass of Hamiltonian graphs with maximum degree 3 that contain a binary spanning tree. A natural cycletree used as an interconnection network thus supports directly broadcasting through the binary tree as well as nearest-neighbor communication through the cycle. Natural cycletrees have several other interesting properties; e.g., they are planar, easily extensible, and can be contracted using the same methods as for binary trees. The main results of the paper are: (i) Given an arbitrary basic binary spanning treeT, there exists a natural cycletree with a minimal number of edges forT. (ii) A natural cycletree has a very simple router. We give a superfast parallel algorithm that can establish near optimal router data for that router.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Natural cycletrees, formally defined in this paper, is a subclass of Hamiltonian graphs with maximum degree 3 that contain a binary spanning tree. A natural cycletree used as an interconnection network thus supports directly broadcasting through the binary tree as well as nearest-neighbor communication through the cycle. Natural cycletrees have several other interesting properties; e.g., [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-156444","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"","msr_edition":"Journal of Parallel and Distributed 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