NDLI: Efficient distributed approximation algorithms via probabilistic tree embeddings

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Efficient distributed approximation algorithms via probabilistic tree embeddings

Content Provider	ACM Digital Library
Author	Pandurangan, Gopal Malkhi, Dahlia Khan, Maleq Talwar, Kunal Kuhn, Fabian
Abstract	We present a uniform approach to design efficient 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 (FRT embedding). We show how to efficiently compute an (implicit) FRT embedding in a decentralized manner and how to use the embedding to obtain expected O(log n)-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 might be of independent interest. Assuming a global order on the nodes of a network, the LE list of a node stores the smallest node (w.r.t. the given order) within every distance \$d\$. Assuming a random order on the nodes, we give an almost-optimal distributed algorithm for computing LE lists on weighted graphs. 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 synchronous leader election algorithm for general networks.
Starting Page	263
Ending Page	272
Page Count	10
File Format	PDF
ISBN	9781595939890
DOI	10.1145/1400751.1400787
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2008-08-18
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Generalized steiner forests Network optimization Probabilistic tree embeddings Metric spaces Least element lists Distributed approximation
Content Type	Text
Resource Type	Article

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