We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeofs between two competing metrics, and show that this family is equivalent to a family of preferential attachment random graph models with upper cutoffs. This is first explanation of how preferential attachment can arise from a more basic underlying mechanism of local competition. We rigorously determine the degree distribution for the family of random graph models, showing that it obeys a power law up to afinite threshold and decays exponentially above this threshold. We also rigorously analyze a generalized version of our graph process, with two natural parameters, one corresponding to the cutoff and the other a \\fertility” parameter. We prove that the general model has a power-law degree distribution up to a cutoff, and establish monotonicity of the power as a function of the two parameters. Limiting cases of the general model include the standard preferential attachment model without cutoff and the uniform attachment model.<\/p>\n","protected":false},"excerpt":{"rendered":"
We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeofs between two competing metrics, and show that this family is equivalent to a family of preferential attachment random graph models with upper cutoffs. This is first explanation of how preferential attachment can arise from a more basic underlying mechanism […]<\/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":[13547],"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-314801","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-systems-and-networking","msr-locale-en_us"],"msr_publishername":"","msr_edition":"Combinatorics, Probability and Computing 14","msr_affiliation":"","msr_published_date":"2004-11-29","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"697-721","msr_chapter":"","msr_isbn":"","msr_journal":"Combinatorics, Probability and Computing 14","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"459444","msr_publicationurl":"https:\/\/arxiv.org\/abs\/cond-mat\/0502205","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"degree-distribution-of-competition-induced-preferential-attachment-graphs","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2016\/11\/Degree-Distribution-of-Competition-Induced-Preferential-Attachment-Graphs.pdf","id":459444,"label_id":0},{"type":"url","title":"https:\/\/arxiv.org\/abs\/cond-mat\/0502205","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"https:\/\/arxiv.org\/abs\/cond-mat\/0502205"}],"msr-author-ordering":[{"type":"text","value":"Noam Berger","user_id":0,"rest_url":false},{"type":"user_nicename","value":"borgs","user_id":31278,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=borgs"},{"type":"user_nicename","value":"jchayes","user_id":32200,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=jchayes"},{"type":"text","value":"Raissa M. 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