Incidence Geometries and the Pass Complexity of Semi-Streaming Set Cover

@article{Chakrabarti2015IncidenceGA,
  title={Incidence Geometries and the Pass Complexity of Semi-Streaming Set Cover},
  author={Amit Chakrabarti and Anthony Wirth},
  journal={Electron. Colloquium Comput. Complex.},
  year={2015},
  volume={22},
  pages={113}
}
Set cover, over a universe of size n, may be modelled as a data-streaming problem, where the m sets that comprise the instance are to be read one by one. A semi-streaming algorithm is allowed only O(npoly{log n, log m}) space to process this stream. For each p ≤ 1, we give a very simple deterministic algorithm that makes p passes over the input stream and returns an appropriately certified (p + 1)n1/(p + 1)-approximation to the optimum set cover. More importantly, we proceed to show that this… Expand
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References

SHOWING 1-10 OF 36 REFERENCES
Semi-Streaming Set Cover
TLDR
A semi-streaming algorithm is designed that on input hypergraph G constructs a succinct data structure D such that for every 0 ⩽ ε < 1, an edge (1 − ε)-cover that approximates the optimal edge ( 1-)cover within a factor of f(ε, n) can be extracted from D (efficiently and with no additional space requirements). Expand
On Streaming and Communication Complexity of the Set Cover Problem
We develop the first streaming algorithm and the first two-party communication protocol that uses a constant number of passes/rounds and sublinear space/communication for logarithmic approximation toExpand
On graph problems in a semi-streaming model
TLDR
In the course of this general study, semi-streaming constant approximation algorithms for the unweighted and weighted matching problems are given, along with a further algorithmic improvement for the bipartite case. Expand
Recognizing well-parenthesized expressions in the streaming model
TLDR
It is proved that this one-pass algorithm for Dyck(2) is optimal, up to a log(n) factor, even when two-sided error is allowed, and conjecture that a similar bound holds for any constant number of passes over the input. Expand
A threshold of ln n for approximating set cover (preliminary version)
  • U. Feige
  • Mathematics, Computer Science
  • STOC '96
  • 1996
We prove that (] – o(]))lnn is a threshold below which set, cover cannot be approximated efficiently, unless NP has slightly superpolynornial time algorithms. This closes tlw gap (up to low orderExpand
Set cover algorithms for very large datasets
TLDR
In order to scale Set Cover to large datasets, this work provides a new algorithm which finds a solution that is provably close to that of greedy, but which is much more efficient to implement using modern disk technology. Expand
The Projection Games Conjecture and the NP-Hardness of ln n-Approximating Set-Cover
TLDR
It is shown that under the projection games conjecture, it is NP-hard to approximate Set-Cover on instances of size N to within (1 − α) lnN for arbitrarily small α > 0. Expand
A tight analysis of the greedy algorithm for set cover
  • P. Slavík
  • Mathematics, Computer Science
  • STOC '96
  • 1996
TLDR
The first substantial improvement of the 20 year old classical harmonic upper bound, H(m), of Johnson, Lovssz, and ChvAt al is provided, and the approximation guarantee for the greedy algorithm is better than the guarantee recently established by Srinivasan for the randomized rounding technique, thus improving the bounds on the integralit~ gap. Expand
Information Cost Tradeoffs for Augmented Index and Streaming Language Recognition
TLDR
The first passive memory checkers that verify the interaction transcripts of priority queues, stacks, and double-ended queues are presented, and tight upper and lower bounds are obtained for these problems, thereby addressing an important sub-class of the memory checking framework of Blum et al. Expand
A Tight Analysis of the Greedy Algorithm for Set Cover
TLDR
The first substantial improvement of the 20-year-old classical harmonic upper bound,H(m), of Johnson, Lovasz, and Chvatal, is provided and the approximation guarantee for the greedy algorithm is better than the guarantee recently established by Srinivasan for the randomized rounding technique, thus improving the bounds on theintegrality gap. Expand
...
1
2
3
4
...