We present a uniform approach to design e\ufb03cient distributed approximation algorithms for various network optimization problems. Our approach is randomized and based on a probabilistic tree embedding due to Fakcharoenphol, Rao, and Talwar [12] (FRT embedding). We show how to e\ufb03ciently compute an (implicit) FRT embedding in a decentralized manner and how to use the embedding to obtain expected O(logn)-approximate distributed algorithms for the generalized Steiner forest problem, the minimum routing cost spanning tree problem, and the k-source shortest paths problem in arbitrary networks. The time complexities of our algorithms are within a polylogarithmic factor of the optimum. The distributed construction of the FRT embedding is based on the computation of least elements (LE) lists, a distributed data structure that can be of independent interest. Assuming a global order on the nodes of a network, the LE list of a node stores the smallest node (with respect to the given order) within every distance d (cf. Cohen [6], Cohen and Kaplan [7]). For weighted graphs, we give an almost-optimal distributed algorithm for computing LE lists, assuming a random order on the nodes. For unweighted graphs, our LE lists computation has asymptotically optimal time complexity O(D), where D is the diameter of the network. As a byproduct, we get an improved leader election algorithm in general networks that is both time-optimal and almost message-optimal with high probability.<\/p>\n","protected":false},"excerpt":{"rendered":"
We present a uniform approach to design e\ufb03cient distributed approximation algorithms for various network optimization problems. Our approach is randomized and based on a probabilistic tree embedding due to Fakcharoenphol, Rao, and Talwar [12] (FRT embedding). We show how to e\ufb03ciently compute an (implicit) FRT embedding in a decentralized manner and how to use the […]<\/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":[{"type":"user_nicename","value":"dalia"}],"msr_publishername":"Association for Computing Machinery, Inc.","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"the 27th Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing (PODC)","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"Copyright \u00a9 2007 by the Association for Computing Machinery, Inc. 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