Abstract
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by examining only a small part of the input; yet, answers must be globally consistent and independent of prior queries.
Unfortunately, maximally sparse spanning subgraphs, i.e., spanning trees, cannot be constructed efficiently in this model. Therefore, we settle for a spanning subgraph containing at most (1+epsilon)n edges (where n is the number of vertices and epsilon is a given approximation/sparsity parameter). We achieve a query complexity of O(poly(Delta/epsilon)n^(2/3)) (up to polylogarithmic factors in n) where Delta is the maximum degree of the input graph. Our algorithm is the first to do so on arbitrary bounded degree graphs. Moreover, we achieve the additional property that our algorithm outputs a spanner, i.e., distances are approximately preserved. With high probability, for each deleted edge there is a path of O(log n (Delta+log n)/epsilon) hops in the output that connects its endpoints.
BibTeX  Entry
@InProceedings{lenzen_et_al:LIPIcs:2017:8006,
author = {Christoph Lenzen and Reut Levi},
title = {{Brief Announcement: A Centralized Local Algorithm for the Sparse Spanning Graph Problem}},
booktitle = {31st International Symposium on Distributed Computing (DISC 2017)},
pages = {57:157:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770538},
ISSN = {18688969},
year = {2017},
volume = {91},
editor = {Andr{\'e}a W. Richa},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8006},
URN = {urn:nbn:de:0030drops80064},
doi = {10.4230/LIPIcs.DISC.2017.57},
annote = {Keywords: local, spanning graph, sparse}
}
Keywords: 

local, spanning graph, sparse 
Collection: 

31st International Symposium on Distributed Computing (DISC 2017) 
Issue Date: 

2017 
Date of publication: 

12.10.2017 