A polynomial-time approximation scheme for the maximal overlap of two independent Erd\H{o}s-R\'enyi graphs
For two independent Erd\H{o}s-R\'enyi graphs $\mathbf G(n,p)$, we study the maximal overlap (i.e., the number of common edges) of these two graphs over all possible vertex correspondence. We present a polynomial-time algorithm which finds a vertex correspondence whose overlap approximates the m...
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| creator | Ding, Jian Du, Hang Gong, Shuyang |
| description | For two independent Erd\H{o}s-R\'enyi graphs $\mathbf G(n,p)$, we study the
maximal overlap (i.e., the number of common edges) of these two graphs over all
possible vertex correspondence. We present a polynomial-time algorithm which
finds a vertex correspondence whose overlap approximates the maximal overlap up
to a multiplicative factor that is arbitrarily close to 1. As a by-product, we
prove that the maximal overlap is asymptotically $\frac{n}{2\alpha-1}$ for
$p=n^{-\alpha}$ with some constant $\alpha\in (1/2,1)$. |
| doi_str_mv | 10.48550/arxiv.2210.07823 |
| format | Article |
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maximal overlap (i.e., the number of common edges) of these two graphs over all
possible vertex correspondence. We present a polynomial-time algorithm which
finds a vertex correspondence whose overlap approximates the maximal overlap up
to a multiplicative factor that is arbitrarily close to 1. As a by-product, we
prove that the maximal overlap is asymptotically $\frac{n}{2\alpha-1}$ for
$p=n^{-\alpha}$ with some constant $\alpha\in (1/2,1)$.</description><identifier>DOI: 10.48550/arxiv.2210.07823</identifier><language>eng</language><subject>Mathematics - Optimization and Control ; Mathematics - Probability</subject><creationdate>2022-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2210.07823$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2210.07823$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Ding, Jian</creatorcontrib><creatorcontrib>Du, Hang</creatorcontrib><creatorcontrib>Gong, Shuyang</creatorcontrib><title>A polynomial-time approximation scheme for the maximal overlap of two independent Erd\H{o}s-R\'enyi graphs</title><description>For two independent Erd\H{o}s-R\'enyi graphs $\mathbf G(n,p)$, we study the
maximal overlap (i.e., the number of common edges) of these two graphs over all
possible vertex correspondence. We present a polynomial-time algorithm which
finds a vertex correspondence whose overlap approximates the maximal overlap up
to a multiplicative factor that is arbitrarily close to 1. As a by-product, we
prove that the maximal overlap is asymptotically $\frac{n}{2\alpha-1}$ for
$p=n^{-\alpha}$ with some constant $\alpha\in (1/2,1)$.</description><subject>Mathematics - Optimization and Control</subject><subject>Mathematics - Probability</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFjrEKwjAYhLM4iPoATv6bU2ttLXYVqXQWx0IJNrWRJH9IQm0R3920uLvcwd1xfISs91F4yNI02lHT8y6MYx9ExyxO5uR5Ao1iUCg5FYHjkgHV2mDPJXUcFdh7y3zYoAHXMpB0bARgx4ygGrAB90LgqmaaeVEOclOXxRs_NriWW6YGDg9DdWuXZNZQYdnq5wuyueS3cxFMVJU2_tgM1UhXTXTJ_8UXtMJGxg</recordid><startdate>20221014</startdate><enddate>20221014</enddate><creator>Ding, Jian</creator><creator>Du, Hang</creator><creator>Gong, Shuyang</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20221014</creationdate><title>A polynomial-time approximation scheme for the maximal overlap of two independent Erd\H{o}s-R\'enyi graphs</title><author>Ding, Jian ; Du, Hang ; Gong, Shuyang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2210_078233</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Optimization and Control</topic><topic>Mathematics - Probability</topic><toplevel>online_resources</toplevel><creatorcontrib>Ding, Jian</creatorcontrib><creatorcontrib>Du, Hang</creatorcontrib><creatorcontrib>Gong, Shuyang</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ding, Jian</au><au>Du, Hang</au><au>Gong, Shuyang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A polynomial-time approximation scheme for the maximal overlap of two independent Erd\H{o}s-R\'enyi graphs</atitle><date>2022-10-14</date><risdate>2022</risdate><abstract>For two independent Erd\H{o}s-R\'enyi graphs $\mathbf G(n,p)$, we study the
maximal overlap (i.e., the number of common edges) of these two graphs over all
possible vertex correspondence. We present a polynomial-time algorithm which
finds a vertex correspondence whose overlap approximates the maximal overlap up
to a multiplicative factor that is arbitrarily close to 1. As a by-product, we
prove that the maximal overlap is asymptotically $\frac{n}{2\alpha-1}$ for
$p=n^{-\alpha}$ with some constant $\alpha\in (1/2,1)$.</abstract><doi>10.48550/arxiv.2210.07823</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Optimization and Control Mathematics - Probability |
| title | A polynomial-time approximation scheme for the maximal overlap of two independent Erd\H{o}s-R\'enyi graphs |
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