Local Algorithms for Sparse Spanning Graphs
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Rubinfeld_Local algotithms.pdf
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511.9 KB
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Adobe PDF
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Author(s)
Levi, Reut
Ron, Dana
Rubinfeld, Ronitt
Date Issued
2014
Journal
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)
Publisher
Schloss Dagstuhl
Citation
Levi, Reut, Ron, Dana, and Rubinfeld, Ronitt. “Local Algorithms for Sparse Spanning Graphs.” Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014), 2014
Version
Final published version
Abstract
We initiate the study of the problem of designing sublinear-time (local) algorithms that, given an edge (u,v) in a connected graph G = (V,E), decide whether (u,v) belongs to a sparse spanning graph G' = (V,E') of G. Namely, G' should be connected and |E'| should be upper bounded by (1 + ε)|V| for a given parameter ε > 0. To this end the algorithms may query the incidence relation of the graph G, and we seek algorithms whose query complexity and running time (per given edge (u,v)) is as small as possible. Such an algorithm may be randomized but (for a fixed choice of its random coins) its decision on different edges in the graph should be consistent with the same spanning graph G' and independent of the order of queries. We first show that for general (bounded-degree) graphs, the query complexity of any such algorithm must be Ω(√|V|). This lower bound holds for graphs that have high expansion. We then turn to design and analyze algorithms both for graphs with high expansion (obtaining a result that roughly matches the lower bound) and for graphs that are (strongly) non-expanding (obtaining results in which the complexity does not depend on |V|). The complexity of the problem for graphs that do not fall into these two categories is left as an open question.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution 4.0 International License
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DOI of Published Version
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2014.826
