New bounds on a hypercube coloring problem
In studying the scalability of optical networks, one problem which arises involves coloring the vertices of the n-cube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of χ k ̄ (n) , the minimum number...
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| Veröffentlicht in: | Information processing letters 2002-12, Vol.84 (5), p.265-269 |
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| container_title | Information processing letters |
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| creator | Ngo, Hung Quang Du, Ding-Zhu Graham, Ronald L. |
| description | In studying the scalability of optical networks, one problem which arises involves coloring the vertices of the
n-cube with as few colors as possible such that any two vertices whose Hamming distance is at most
k are colored differently. Determining the exact value of
χ
k
̄
(n)
, the minimum number of colors needed, appears to be a difficult problem. In this note, we improve the known lower and upper bounds of
χ
k
̄
(n)
and indicate the connection of this coloring problem to linear codes. |
| doi_str_mv | 10.1016/S0020-0190(02)00301-0 |
| format | Article |
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n-cube with as few colors as possible such that any two vertices whose Hamming distance is at most
k are colored differently. Determining the exact value of
χ
k
̄
(n)
, the minimum number of colors needed, appears to be a difficult problem. In this note, we improve the known lower and upper bounds of
χ
k
̄
(n)
and indicate the connection of this coloring problem to linear codes.</description><identifier>ISSN: 0020-0190</identifier><identifier>EISSN: 1872-6119</identifier><identifier>DOI: 10.1016/S0020-0190(02)00301-0</identifier><identifier>CODEN: IFPLAT</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>[formula omitted]-cube ; Algorithmics. Computability. Computer arithmetics ; Applied sciences ; Codes ; Coloring ; Combinatorial problems ; Computer science; control theory; systems ; Exact sciences and technology ; Fiber optics ; Information retrieval. Graph ; Linear programming ; Mathematical models ; Scalability ; Studies ; Theoretical computing</subject><ispartof>Information processing letters, 2002-12, Vol.84 (5), p.265-269</ispartof><rights>2002 Elsevier Science B.V.</rights><rights>2003 INIST-CNRS</rights><rights>Copyright Elsevier Sequoia S.A. Dec 16, 2002</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c411t-4b5fc06099be47304170b7b80eb0da3364a9dd5d49e2accfab11a475d92a5b263</citedby><cites>FETCH-LOGICAL-c411t-4b5fc06099be47304170b7b80eb0da3364a9dd5d49e2accfab11a475d92a5b263</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0020019002003010$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=13968757$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Ngo, Hung Quang</creatorcontrib><creatorcontrib>Du, Ding-Zhu</creatorcontrib><creatorcontrib>Graham, Ronald L.</creatorcontrib><title>New bounds on a hypercube coloring problem</title><title>Information processing letters</title><description>In studying the scalability of optical networks, one problem which arises involves coloring the vertices of the
n-cube with as few colors as possible such that any two vertices whose Hamming distance is at most
k are colored differently. Determining the exact value of
χ
k
̄
(n)
, the minimum number of colors needed, appears to be a difficult problem. In this note, we improve the known lower and upper bounds of
χ
k
̄
(n)
and indicate the connection of this coloring problem to linear codes.</description><subject>[formula omitted]-cube</subject><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Codes</subject><subject>Coloring</subject><subject>Combinatorial problems</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Fiber optics</subject><subject>Information retrieval. Graph</subject><subject>Linear programming</subject><subject>Mathematical models</subject><subject>Scalability</subject><subject>Studies</subject><subject>Theoretical computing</subject><issn>0020-0190</issn><issn>1872-6119</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><recordid>eNqFkE1LAzEYhIMoWKs_QVgEQYXV902ym81JpPgFRQ_qOeRrdUu7qUlX6b93-4EePc3lmRlmCDlGuETA8uoFgEIOKOEM6DkAA8xhhwywEjQvEeUuGfwi--QgpQkAlJyJAbl48t-ZCV3rUhbaTGcfy7mPtjM-s2EaYtO-Z_MYzNTPDslerafJH211SN7ubl9HD_n4-f5xdDPOLUdc5NwUtYUSpDSeCwYcBRhhKvAGnGas5Fo6VzguPdXW1togai4KJ6kuDC3ZkJxscvvez86nhZqELrZ9paJM0AorVvRQsYFsDClFX6t5bGY6LhWCWr2i1q-o1WQFVK1fUdD7TrfhOlk9raNubZP-zEyWlShEz11vON8v_Wp8VMk2vrXeNdHbhXKh-afpB0twdC0</recordid><startdate>20021216</startdate><enddate>20021216</enddate><creator>Ngo, Hung Quang</creator><creator>Du, Ding-Zhu</creator><creator>Graham, Ronald L.</creator><general>Elsevier B.V</general><general>Elsevier Science</general><general>Elsevier Sequoia S.A</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>20021216</creationdate><title>New bounds on a hypercube coloring problem</title><author>Ngo, Hung Quang ; Du, Ding-Zhu ; Graham, Ronald L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c411t-4b5fc06099be47304170b7b80eb0da3364a9dd5d49e2accfab11a475d92a5b263</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2002</creationdate><topic>[formula omitted]-cube</topic><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Applied sciences</topic><topic>Codes</topic><topic>Coloring</topic><topic>Combinatorial problems</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Fiber optics</topic><topic>Information retrieval. Graph</topic><topic>Linear programming</topic><topic>Mathematical models</topic><topic>Scalability</topic><topic>Studies</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ngo, Hung Quang</creatorcontrib><creatorcontrib>Du, Ding-Zhu</creatorcontrib><creatorcontrib>Graham, Ronald L.</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>Information processing letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ngo, Hung Quang</au><au>Du, Ding-Zhu</au><au>Graham, Ronald L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New bounds on a hypercube coloring problem</atitle><jtitle>Information processing letters</jtitle><date>2002-12-16</date><risdate>2002</risdate><volume>84</volume><issue>5</issue><spage>265</spage><epage>269</epage><pages>265-269</pages><issn>0020-0190</issn><eissn>1872-6119</eissn><coden>IFPLAT</coden><abstract>In studying the scalability of optical networks, one problem which arises involves coloring the vertices of the
n-cube with as few colors as possible such that any two vertices whose Hamming distance is at most
k are colored differently. Determining the exact value of
χ
k
̄
(n)
, the minimum number of colors needed, appears to be a difficult problem. In this note, we improve the known lower and upper bounds of
χ
k
̄
(n)
and indicate the connection of this coloring problem to linear codes.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/S0020-0190(02)00301-0</doi><tpages>5</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0020-0190 |
| ispartof | Information processing letters, 2002-12, Vol.84 (5), p.265-269 |
| issn | 0020-0190 1872-6119 |
| language | eng |
| recordid | cdi_proquest_journals_237281835 |
| source | Elsevier ScienceDirect Journals |
| subjects | [formula omitted]-cube Algorithmics. Computability. Computer arithmetics Applied sciences Codes Coloring Combinatorial problems Computer science control theory systems Exact sciences and technology Fiber optics Information retrieval. Graph Linear programming Mathematical models Scalability Studies Theoretical computing |
| title | New bounds on a hypercube coloring problem |
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