Optimal simulation of full binary trees on faulty hypercubes
We study the problem of running full binary tree based algorithms on a hypercube with faulty nodes. The key to this problem is to devise a method for embedding a full binary tree into the faulty hypercube. Based on a novel embedding strategy, we present two results for embedding an (n-1) tree fa ful...
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Veröffentlicht in: | IEEE transactions on parallel and distributed systems 1995-03, Vol.6 (3), p.269-286 |
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description | We study the problem of running full binary tree based algorithms on a hypercube with faulty nodes. The key to this problem is to devise a method for embedding a full binary tree into the faulty hypercube. Based on a novel embedding strategy, we present two results for embedding an (n-1) tree fa full binary tree with 2/sup n-1/ nodes) into an n-cube (a hypercube with 2/sup n/ nodes) with unit dilation and load. For the problem where the root of the tree must be mapped to a specified hypercube node (specified root embedding problem), we show that up to n-2 (node or edge) faults can be tolerated. This result is optimal in the following sense: 1) it is time-optimal, 2) (n-1)-tree is the largest fall binary tree that can be embedded in an n-cube, and 3) n-2 faults Is the maximum number of worst-case faults that can be tolerated in the specified root problem. Furthermore, we also show that any algorithm for this problem cannot be totally recursive in nature. For the problem where the root can be mapped to any nonfaulty hypercube node (variable root embedding problem), we show that up to 2n-3-[log n] faults can be tolerated. Thus we have improved upon the previous result of n-1-[log n]. In addition, we show that the algorithm for the variable root embedding problem is optimal within a class of algorithms called recursive embedding algorithms as far as the number of tolerable faults is concerned. Finally, we show that when an O(1spl radic/n) fraction of nodes in the hypercube are faulty, it is not always possible to have an O(1)-load variable root embedding no matter how large the dilation is.< > |
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The key to this problem is to devise a method for embedding a full binary tree into the faulty hypercube. Based on a novel embedding strategy, we present two results for embedding an (n-1) tree fa full binary tree with 2/sup n-1/ nodes) into an n-cube (a hypercube with 2/sup n/ nodes) with unit dilation and load. For the problem where the root of the tree must be mapped to a specified hypercube node (specified root embedding problem), we show that up to n-2 (node or edge) faults can be tolerated. This result is optimal in the following sense: 1) it is time-optimal, 2) (n-1)-tree is the largest fall binary tree that can be embedded in an n-cube, and 3) n-2 faults Is the maximum number of worst-case faults that can be tolerated in the specified root problem. Furthermore, we also show that any algorithm for this problem cannot be totally recursive in nature. For the problem where the root can be mapped to any nonfaulty hypercube node (variable root embedding problem), we show that up to 2n-3-[log n] faults can be tolerated. Thus we have improved upon the previous result of n-1-[log n]. In addition, we show that the algorithm for the variable root embedding problem is optimal within a class of algorithms called recursive embedding algorithms as far as the number of tolerable faults is concerned. Finally, we show that when an O(1spl radic/n) fraction of nodes in the hypercube are faulty, it is not always possible to have an O(1)-load variable root embedding no matter how large the dilation is.< ></description><identifier>ISSN: 1045-9219</identifier><identifier>EISSN: 1558-2183</identifier><identifier>DOI: 10.1109/71.372776</identifier><identifier>CODEN: ITDSEO</identifier><language>eng</language><publisher>Los Alamitos, CA: IEEE</publisher><subject>Applied sciences ; Binary trees ; Computer science ; Computer science; control theory; systems ; Computer systems and distributed systems. User interface ; Exact sciences and technology ; Hypercubes ; Robustness ; Senior members ; Simulation ; Software</subject><ispartof>IEEE transactions on parallel and distributed systems, 1995-03, Vol.6 (3), p.269-286</ispartof><rights>1995 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c372t-35ba638f0e11895210f56558519b93a1d8604b5c45cd5fdc00b27e5649710a763</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/372776$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/372776$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=3469481$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Chan, B.M.Y.</creatorcontrib><creatorcontrib>Chin, F.Y.L.</creatorcontrib><creatorcontrib>Chung-Keung Poon</creatorcontrib><title>Optimal simulation of full binary trees on faulty hypercubes</title><title>IEEE transactions on parallel and distributed systems</title><addtitle>TPDS</addtitle><description>We study the problem of running full binary tree based algorithms on a hypercube with faulty nodes. The key to this problem is to devise a method for embedding a full binary tree into the faulty hypercube. Based on a novel embedding strategy, we present two results for embedding an (n-1) tree fa full binary tree with 2/sup n-1/ nodes) into an n-cube (a hypercube with 2/sup n/ nodes) with unit dilation and load. For the problem where the root of the tree must be mapped to a specified hypercube node (specified root embedding problem), we show that up to n-2 (node or edge) faults can be tolerated. This result is optimal in the following sense: 1) it is time-optimal, 2) (n-1)-tree is the largest fall binary tree that can be embedded in an n-cube, and 3) n-2 faults Is the maximum number of worst-case faults that can be tolerated in the specified root problem. Furthermore, we also show that any algorithm for this problem cannot be totally recursive in nature. For the problem where the root can be mapped to any nonfaulty hypercube node (variable root embedding problem), we show that up to 2n-3-[log n] faults can be tolerated. Thus we have improved upon the previous result of n-1-[log n]. In addition, we show that the algorithm for the variable root embedding problem is optimal within a class of algorithms called recursive embedding algorithms as far as the number of tolerable faults is concerned. Finally, we show that when an O(1spl radic/n) fraction of nodes in the hypercube are faulty, it is not always possible to have an O(1)-load variable root embedding no matter how large the dilation is.< ></description><subject>Applied sciences</subject><subject>Binary trees</subject><subject>Computer science</subject><subject>Computer science; control theory; systems</subject><subject>Computer systems and distributed systems. User interface</subject><subject>Exact sciences and technology</subject><subject>Hypercubes</subject><subject>Robustness</subject><subject>Senior members</subject><subject>Simulation</subject><subject>Software</subject><issn>1045-9219</issn><issn>1558-2183</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><recordid>eNqFkM1LxDAQxYMouK4evHrKQQQPXTP5DniRxS9Y2IueS5pNsJJta9Ie-t_bpaJHTzPM_ObN4yF0CWQFQMydghVTVCl5hBYghC4oaHY89YSLwlAwp-gs509CgAvCF-h-2_X13kac6_0QbV-3DW4DDkOMuKobm0bcJ-8znubBDrEf8cfY-eSGyudzdBJszP7ipy7R-9Pj2_ql2GyfX9cPm8JNXvqCicpKpgPxANoICiQIOXkTYCrDLOy0JLwSjgu3E2HnCKmo8kJyo4BYJdkS3cy6XWq_Bp_7cl9n52O0jW-HXFItpNQc_geF4YTRg-LtDLrU5px8KLs0xZDGEkh5CLJUUM5BTuz1j6jNzsaQbOPq_HvAuDRcH35fzVjtvf_bzhrf2xV4fg</recordid><startdate>19950301</startdate><enddate>19950301</enddate><creator>Chan, B.M.Y.</creator><creator>Chin, F.Y.L.</creator><creator>Chung-Keung Poon</creator><general>IEEE</general><general>IEEE Computer Society</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19950301</creationdate><title>Optimal simulation of full binary trees on faulty hypercubes</title><author>Chan, B.M.Y. ; Chin, F.Y.L. ; Chung-Keung Poon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c372t-35ba638f0e11895210f56558519b93a1d8604b5c45cd5fdc00b27e5649710a763</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1995</creationdate><topic>Applied sciences</topic><topic>Binary trees</topic><topic>Computer science</topic><topic>Computer science; control theory; systems</topic><topic>Computer systems and distributed systems. User interface</topic><topic>Exact sciences and technology</topic><topic>Hypercubes</topic><topic>Robustness</topic><topic>Senior members</topic><topic>Simulation</topic><topic>Software</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chan, B.M.Y.</creatorcontrib><creatorcontrib>Chin, F.Y.L.</creatorcontrib><creatorcontrib>Chung-Keung Poon</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on parallel and distributed systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Chan, B.M.Y.</au><au>Chin, F.Y.L.</au><au>Chung-Keung Poon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal simulation of full binary trees on faulty hypercubes</atitle><jtitle>IEEE transactions on parallel and distributed systems</jtitle><stitle>TPDS</stitle><date>1995-03-01</date><risdate>1995</risdate><volume>6</volume><issue>3</issue><spage>269</spage><epage>286</epage><pages>269-286</pages><issn>1045-9219</issn><eissn>1558-2183</eissn><coden>ITDSEO</coden><abstract>We study the problem of running full binary tree based algorithms on a hypercube with faulty nodes. The key to this problem is to devise a method for embedding a full binary tree into the faulty hypercube. Based on a novel embedding strategy, we present two results for embedding an (n-1) tree fa full binary tree with 2/sup n-1/ nodes) into an n-cube (a hypercube with 2/sup n/ nodes) with unit dilation and load. For the problem where the root of the tree must be mapped to a specified hypercube node (specified root embedding problem), we show that up to n-2 (node or edge) faults can be tolerated. This result is optimal in the following sense: 1) it is time-optimal, 2) (n-1)-tree is the largest fall binary tree that can be embedded in an n-cube, and 3) n-2 faults Is the maximum number of worst-case faults that can be tolerated in the specified root problem. Furthermore, we also show that any algorithm for this problem cannot be totally recursive in nature. For the problem where the root can be mapped to any nonfaulty hypercube node (variable root embedding problem), we show that up to 2n-3-[log n] faults can be tolerated. Thus we have improved upon the previous result of n-1-[log n]. In addition, we show that the algorithm for the variable root embedding problem is optimal within a class of algorithms called recursive embedding algorithms as far as the number of tolerable faults is concerned. Finally, we show that when an O(1spl radic/n) fraction of nodes in the hypercube are faulty, it is not always possible to have an O(1)-load variable root embedding no matter how large the dilation is.< ></abstract><cop>Los Alamitos, CA</cop><pub>IEEE</pub><doi>10.1109/71.372776</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record> |
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subjects | Applied sciences Binary trees Computer science Computer science control theory systems Computer systems and distributed systems. User interface Exact sciences and technology Hypercubes Robustness Senior members Simulation Software |
title | Optimal simulation of full binary trees on faulty hypercubes |
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