Network Simplification in Half-Duplex: Building on Submodularity
This paper explores the network simplification problem in the context of Gaussian half-duplex diamond networks. Specifically, given an N -relay diamond network, this problem seeks to derive fundamental guarantees on the capacity of the best k -relay subnetwork, as a function of the full network ca...
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description | This paper explores the network simplification problem in the context of Gaussian half-duplex diamond networks. Specifically, given an N -relay diamond network, this problem seeks to derive fundamental guarantees on the capacity of the best k -relay subnetwork, as a function of the full network capacity. Simplification guarantees are presented in terms of a particular approximate capacity , termed Independent-Gaussian (IG) approximate capacity, that characterizes the network capacity to within an additive gap, which is independent of the channel coefficients and operating SNR. The main focus of this work is when k\!=\!N\!-\!1 relays are selected out of N relays in a diamond network. First, a simple algorithm is proposed which selects all relays except the one with the minimum IG approximate half-duplex capacity. It is shown that the selected (N\!-\!1) -relay subnetwork has an IG approximate half-duplex capacity that is at least 1/2 of the IG approximate half-duplex capacity of the full network and that for the proposed algorithm, this guarantee is tight. Furthermore, this work proves the following tight fundamental guarantee: there always exists a subnetwork of k\!=\!N\!-\!1 relays that have an IG approximate half-duplex capacity that is at least equal to (N-1)/N of the IG approximate half-duplex capacity of the full network. Finally, these results are extended to derive lower bounds on the fraction guarantee when k \in [1:N] relays are selected. The key steps in the proofs lie in the derivation of properties of submodular functions, which provide a combinatorial handle on the network simplification problem for Gaussian half-duplex diamond networks. |
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Specifically, given an <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>-relay diamond network, this problem seeks to derive fundamental guarantees on the capacity of the best <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>-relay subnetwork, as a function of the full network capacity. Simplification guarantees are presented in terms of a particular approximate capacity , termed Independent-Gaussian (IG) approximate capacity, that characterizes the network capacity to within an additive gap, which is independent of the channel coefficients and operating SNR. The main focus of this work is when <inline-formula> <tex-math notation="LaTeX">k\!=\!N\!-\!1 </tex-math></inline-formula> relays are selected out of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> relays in a diamond network. First, a simple algorithm is proposed which selects all relays except the one with the minimum IG approximate half-duplex capacity. It is shown that the selected <inline-formula> <tex-math notation="LaTeX">(N\!-\!1) </tex-math></inline-formula>-relay subnetwork has an IG approximate half-duplex capacity that is at least <inline-formula> <tex-math notation="LaTeX">1/2 </tex-math></inline-formula> of the IG approximate half-duplex capacity of the full network and that for the proposed algorithm, this guarantee is tight. Furthermore, this work proves the following tight fundamental guarantee: there always exists a subnetwork of <inline-formula> <tex-math notation="LaTeX">k\!=\!N\!-\!1 </tex-math></inline-formula> relays that have an IG approximate half-duplex capacity that is at least equal to <inline-formula> <tex-math notation="LaTeX">(N-1)/N </tex-math></inline-formula> of the IG approximate half-duplex capacity of the full network. Finally, these results are extended to derive lower bounds on the fraction guarantee when <inline-formula> <tex-math notation="LaTeX">k \in [1:N] </tex-math></inline-formula> relays are selected. The key steps in the proofs lie in the derivation of properties of submodular functions, which provide a combinatorial handle on the network simplification problem for Gaussian half-duplex diamond networks.]]></description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.2019.2923994</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Additives ; Algorithms ; approximate capacity ; Approximation algorithms ; Combinatorial analysis ; Diamond ; Diamonds ; Guarantees ; Half-duplex relay networks ; Lower bounds ; Network topology ; Relay ; Relay networks (telecommunications) ; relay scheduling ; relay selection ; Simplification ; submodularity ; Topology</subject><ispartof>IEEE transactions on information theory, 2019-10, Vol.65 (10), p.6801-6818</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c333t-fe647052247ff92189383854b93435c6d7c4319430f91e657acb30c22bf17afc3</citedby><cites>FETCH-LOGICAL-c333t-fe647052247ff92189383854b93435c6d7c4319430f91e657acb30c22bf17afc3</cites><orcidid>0000-0002-4238-5362 ; 0000-0003-2989-4880 ; 0000-0003-1880-4798 ; 0000-0003-1002-5829</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/8742589$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/8742589$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Ezzeldin, Yahya H.</creatorcontrib><creatorcontrib>Cardone, Martina</creatorcontrib><creatorcontrib>Fragouli, Christina</creatorcontrib><creatorcontrib>Tuninetti, Daniela</creatorcontrib><title>Network Simplification in Half-Duplex: Building on Submodularity</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description><![CDATA[This paper explores the network simplification problem in the context of Gaussian half-duplex diamond networks. Specifically, given an <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>-relay diamond network, this problem seeks to derive fundamental guarantees on the capacity of the best <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>-relay subnetwork, as a function of the full network capacity. Simplification guarantees are presented in terms of a particular approximate capacity , termed Independent-Gaussian (IG) approximate capacity, that characterizes the network capacity to within an additive gap, which is independent of the channel coefficients and operating SNR. The main focus of this work is when <inline-formula> <tex-math notation="LaTeX">k\!=\!N\!-\!1 </tex-math></inline-formula> relays are selected out of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> relays in a diamond network. First, a simple algorithm is proposed which selects all relays except the one with the minimum IG approximate half-duplex capacity. It is shown that the selected <inline-formula> <tex-math notation="LaTeX">(N\!-\!1) </tex-math></inline-formula>-relay subnetwork has an IG approximate half-duplex capacity that is at least <inline-formula> <tex-math notation="LaTeX">1/2 </tex-math></inline-formula> of the IG approximate half-duplex capacity of the full network and that for the proposed algorithm, this guarantee is tight. Furthermore, this work proves the following tight fundamental guarantee: there always exists a subnetwork of <inline-formula> <tex-math notation="LaTeX">k\!=\!N\!-\!1 </tex-math></inline-formula> relays that have an IG approximate half-duplex capacity that is at least equal to <inline-formula> <tex-math notation="LaTeX">(N-1)/N </tex-math></inline-formula> of the IG approximate half-duplex capacity of the full network. Finally, these results are extended to derive lower bounds on the fraction guarantee when <inline-formula> <tex-math notation="LaTeX">k \in [1:N] </tex-math></inline-formula> relays are selected. The key steps in the proofs lie in the derivation of properties of submodular functions, which provide a combinatorial handle on the network simplification problem for Gaussian half-duplex diamond networks.]]></description><subject>Additives</subject><subject>Algorithms</subject><subject>approximate capacity</subject><subject>Approximation algorithms</subject><subject>Combinatorial analysis</subject><subject>Diamond</subject><subject>Diamonds</subject><subject>Guarantees</subject><subject>Half-duplex relay networks</subject><subject>Lower bounds</subject><subject>Network topology</subject><subject>Relay</subject><subject>Relay networks (telecommunications)</subject><subject>relay scheduling</subject><subject>relay selection</subject><subject>Simplification</subject><subject>submodularity</subject><subject>Topology</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kEtPwzAQhC0EEqVwR-ISiXOKn7GXE1AerVTBoeVsOa6NXNIkOImg_x5XRZxWq53Znf0QuiR4QgiGm9V8NaGYwIQCZQD8CI2IEDKHQvBjNMKYqBw4V6forOs2qeWC0BG6e3X9dxM_s2XYtlXwwZo-NHUW6mxmKp8_Dm3lfm6zhyFU61B_ZGm2HMptsx4qE0O_O0cn3lSdu_irY_T-_LSazvLF28t8er_ILWOsz70ruMSCUi69B0oUMMWU4CUwzoQt1tJyRoAz7IG4QkhjS4YtpaUn0njLxuj6sLeNzdfgul5vmiHW6aSm6WVQVBY4qfBBZWPTddF53cawNXGnCdZ7Tjpx0ntO-o9TslwdLME59y9XklORQv4CSPliVA</recordid><startdate>20191001</startdate><enddate>20191001</enddate><creator>Ezzeldin, Yahya H.</creator><creator>Cardone, Martina</creator><creator>Fragouli, Christina</creator><creator>Tuninetti, Daniela</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-4238-5362</orcidid><orcidid>https://orcid.org/0000-0003-2989-4880</orcidid><orcidid>https://orcid.org/0000-0003-1880-4798</orcidid><orcidid>https://orcid.org/0000-0003-1002-5829</orcidid></search><sort><creationdate>20191001</creationdate><title>Network Simplification in Half-Duplex: Building on Submodularity</title><author>Ezzeldin, Yahya H. ; Cardone, Martina ; Fragouli, Christina ; Tuninetti, Daniela</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c333t-fe647052247ff92189383854b93435c6d7c4319430f91e657acb30c22bf17afc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Additives</topic><topic>Algorithms</topic><topic>approximate capacity</topic><topic>Approximation algorithms</topic><topic>Combinatorial analysis</topic><topic>Diamond</topic><topic>Diamonds</topic><topic>Guarantees</topic><topic>Half-duplex relay networks</topic><topic>Lower bounds</topic><topic>Network topology</topic><topic>Relay</topic><topic>Relay networks (telecommunications)</topic><topic>relay scheduling</topic><topic>relay selection</topic><topic>Simplification</topic><topic>submodularity</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ezzeldin, Yahya H.</creatorcontrib><creatorcontrib>Cardone, Martina</creatorcontrib><creatorcontrib>Fragouli, Christina</creatorcontrib><creatorcontrib>Tuninetti, Daniela</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications 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 information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Ezzeldin, Yahya H.</au><au>Cardone, Martina</au><au>Fragouli, Christina</au><au>Tuninetti, Daniela</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Network Simplification in Half-Duplex: Building on Submodularity</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>2019-10-01</date><risdate>2019</risdate><volume>65</volume><issue>10</issue><spage>6801</spage><epage>6818</epage><pages>6801-6818</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract><![CDATA[This paper explores the network simplification problem in the context of Gaussian half-duplex diamond networks. Specifically, given an <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula>-relay diamond network, this problem seeks to derive fundamental guarantees on the capacity of the best <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>-relay subnetwork, as a function of the full network capacity. Simplification guarantees are presented in terms of a particular approximate capacity , termed Independent-Gaussian (IG) approximate capacity, that characterizes the network capacity to within an additive gap, which is independent of the channel coefficients and operating SNR. The main focus of this work is when <inline-formula> <tex-math notation="LaTeX">k\!=\!N\!-\!1 </tex-math></inline-formula> relays are selected out of <inline-formula> <tex-math notation="LaTeX">N </tex-math></inline-formula> relays in a diamond network. First, a simple algorithm is proposed which selects all relays except the one with the minimum IG approximate half-duplex capacity. It is shown that the selected <inline-formula> <tex-math notation="LaTeX">(N\!-\!1) </tex-math></inline-formula>-relay subnetwork has an IG approximate half-duplex capacity that is at least <inline-formula> <tex-math notation="LaTeX">1/2 </tex-math></inline-formula> of the IG approximate half-duplex capacity of the full network and that for the proposed algorithm, this guarantee is tight. Furthermore, this work proves the following tight fundamental guarantee: there always exists a subnetwork of <inline-formula> <tex-math notation="LaTeX">k\!=\!N\!-\!1 </tex-math></inline-formula> relays that have an IG approximate half-duplex capacity that is at least equal to <inline-formula> <tex-math notation="LaTeX">(N-1)/N </tex-math></inline-formula> of the IG approximate half-duplex capacity of the full network. Finally, these results are extended to derive lower bounds on the fraction guarantee when <inline-formula> <tex-math notation="LaTeX">k \in [1:N] </tex-math></inline-formula> relays are selected. The key steps in the proofs lie in the derivation of properties of submodular functions, which provide a combinatorial handle on the network simplification problem for Gaussian half-duplex diamond networks.]]></abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TIT.2019.2923994</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0002-4238-5362</orcidid><orcidid>https://orcid.org/0000-0003-2989-4880</orcidid><orcidid>https://orcid.org/0000-0003-1880-4798</orcidid><orcidid>https://orcid.org/0000-0003-1002-5829</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Additives Algorithms approximate capacity Approximation algorithms Combinatorial analysis Diamond Diamonds Guarantees Half-duplex relay networks Lower bounds Network topology Relay Relay networks (telecommunications) relay scheduling relay selection Simplification submodularity Topology |
title | Network Simplification in Half-Duplex: Building on Submodularity |
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