Towards tight bounds for the streaming set cover problem

Sariel Har-Peled, Piotr Indyk, Sepideh Mahabadi, Ali Vakilian

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We consider the classic Set Cover problem in the data stream model. For n elements and m sets (m ≥ n) we give a O(1/δ)-pass algorithm with a strongly sub-linear Õ(mnδ) space and logarithmic approximation factor. This yields a significant improvement over the earlier algorithm of Demaine et al. [11] that uses exponentially larger number of passes. We complement this result by showing that the tradeoff between the number of passes and space exhibited by our algorithm is tight, at least when the approximation factor is equal to 1. Specifically, we show that any algorithm that computes set cover exactly using (1/2δ - 1) passes must use Ω(mnδ) space in the regime of m = O(n). Furthermore, we consider the problem in the geometric setting where the elements are points in ℝ2 and sets are either discs, axis-parallel rectangles, or fat triangles in the plane, and show that our algorithm (with a slight modification) uses the optimal Õ(n) space to find a logarithmic approximation in O(1/δ) passes. Finally, we show that any randomized one-pass algorithm that distinguishes between covers of size 2 and 3 must use a linear (i.e., Ω(mn)) amount of space. This is the first result showing that a randomized, approximate algorithm cannot achieve a space bound that is sublinear in the input size. This indicates that using multiple passes might be necessary in order to achieve sub-linear space bounds for this problem while guaranteeing small approximation factors.

Original languageEnglish (US)
Title of host publicationPODS 2016 - Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems
PublisherAssociation for Computing Machinery
Number of pages13
ISBN (Electronic)9781450341912
StatePublished - Jun 15 2016
Event35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2016 - San Francisco, United States
Duration: Jun 26 2016Jul 1 2016

Publication series

NameProceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems


Other35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2016
Country/TerritoryUnited States
CitySan Francisco

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Hardware and Architecture


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