We consider four problems on distance estimation and object location which share the common\ufb02avor of capturing global information via informative node labels: low-stretch routing schemes [47], distance labeling [24], searchable small worlds [30], and triangulation-based distance estimation [33]. Focusing on metrics of low doubling dimension, we approach these problems with a common technique called rings of neighbors, which refers to a sparse distributed data structure that underlies all our constructions. Apart from improving the previously known bounds for these problems, our contributions include extending Kleinberg\u2019s small world model to doubling metrics, and a short proof of the main result in Chan et al. [14]. Doubling dimension is a notion of dimensionality for general metrics that has recently become a useful algorithmic concept in the theoretical computer science literature.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider four problems on distance estimation and object location which share the common\ufb02avor of capturing global information via informative node labels: low-stretch routing schemes [47], distance labeling [24], searchable small worlds [30], and triangulation-based distance estimation [33]. Focusing on metrics of low doubling dimension, we approach these problems with a common technique called rings […]<\/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":"","msr-author-ordering":null,"msr_publishername":"Association for Computing Machinery, Inc.","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"24th Annual ACM SIGACT-SIGOPS Symp. on Principles Of Distributed Computing (PODC)","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"41-50","msr_page_range_start":"41","msr_page_range_end":"50","msr_series":"","msr_volume":"","msr_copyright":"Copyright \u00a9 2007 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and\/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or permissions@acm.org. 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