Submodular optimization has received significant attention in both practice and theory, as a wide array of problems in machine learning, auction theory, and combinatorial optimization have submodular structure. In practice, these problems often involve large amounts of data, and must be solved in a distributed way. One popular framework for running such distributed algorithms is MapReduce. In this paper, we present two simple algorithms for cardinality constrained submodular optimization in the MapReduce model: the first is a (1/2-o(1))-approximation in 2 MapReduce rounds, and the second is a (1-1/e-epsilon)-approximation in (1+o(1))/epsilon MapReduce rounds.
@InProceedings{liu_et_al:OASIcs.SOSA.2019.18, author = {Liu, Paul and Vondrak, Jan}, title = {{Submodular Optimization in the MapReduce Model}}, booktitle = {2nd Symposium on Simplicity in Algorithms (SOSA 2019)}, pages = {18:1--18:10}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-099-6}, ISSN = {2190-6807}, year = {2019}, volume = {69}, editor = {Fineman, Jeremy T. and Mitzenmacher, Michael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.18}, URN = {urn:nbn:de:0030-drops-100447}, doi = {10.4230/OASIcs.SOSA.2019.18}, annote = {Keywords: mapreduce, submodular, optimization, approximation algorithms} }
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