{"id":157842,"date":"2012-09-01T00:00:00","date_gmt":"2012-09-01T07:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/a-compact-routing-scheme-and-approximate-distance-oracle-for-power-law-graphs\/"},"modified":"2018-10-16T20:57:37","modified_gmt":"2018-10-17T03:57:37","slug":"a-compact-routing-scheme-and-approximate-distance-oracle-for-power-law-graphs","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/a-compact-routing-scheme-and-approximate-distance-oracle-for-power-law-graphs\/","title":{"rendered":"A Compact Routing Scheme and Approximate Distance Oracle for Power-Law Graphs"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Compact routing addresses the tradeoff between table sizes and stretch, which is the worst-case ratio between the length of the path a packet is routed through by the scheme and the length of a shortest path from source to destination. We adapt the compact routing scheme by Thorup and Zwick to optimize it for power-law graphs. We analyze our adapted routing scheme based on the theory of unweighted random power-law graphs with fixed expected degree sequence by Aiello, Chung, and Lu. Our result is the first theoretical bound coupled to the parameter of the power-law graph model for a compact routing scheme. In particular, we prove that, for stretch 3, instead of routing tables with <i>\u02dcO(n<sup>1\/2<\/sup>)<\/i> bits as in the general scheme by Thorup and Zwick, expected sizes of <i>O(n<sup>\u03b3<\/sup>log n)<\/i> bits are sufficient, and that all the routing tables can be constructed at once in expected time <i>O(n<sup>1+\u03b3<\/sup>log n)<\/i>, with <i>\u03b3=(\u03c4-2)\/(2\u03c4-3)+\u03b5<\/i>, where <i>\u03c4<\/i> in (2,3) is the power-law exponent and <i>\u03b5>0<\/i> (which implies <i>\u03b5 < \u03b3 < 1\/3 + \u03b5<\/i>). Both bounds also hold with probability at least 1-1\/n (independent of <i>\u03b5<\/i>). The routing scheme is a labeled scheme, requiring a stretch-5 handshaking step and using addresses and message headers with <i>O(log nlog log n)<\/i> bits, with probability at least 1-o(1). We further demonstrate the effectiveness of our scheme by simulations on real-world graphs as well as synthetic power-law graphs. With the same techniques as for the compact routing scheme, we also adapt the approximate distance oracle by Thorup and Zwick for stretch 3 and obtain a new upper bound of expected <i>\u02dcO(n<sup>1+\u03b3<\/sup>)<\/i> for space and preprocessing for random power-law graphs.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Compact routing addresses the tradeoff between table sizes and stretch, which is the worst-case ratio between the length of the path a packet is routed through by the scheme and the length of a shortest path from source to destination. We adapt the compact routing scheme by Thorup and Zwick to optimize it for power-law [&hellip;]<\/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":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"ACM Transactions on Algorithms 9(1): 4 (2012). Extended abstract published in Distributed Computing (DISC), 2009.","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"ACM Transactions on Algorithms 9(1): 4 (2012). 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