• Documents
  • Authors
  • Tables
  • Log in
  • Sign up
  • MetaCart
  • DMCA
  • Donate

CiteSeerX logo

Advanced Search Include Citations
Advanced Search Include Citations

DMCA

Regularity lemmas and combinatorial algorithms

Cached

  • Download as a PDF

Download Links

  • [www.cs.cmu.edu]
  • [www.cs.cmu.edu]
  • [www.stanford.edu]
  • [www.cs.cmu.edu]
  • [www.cs.cmu.edu]
  • [www.cs.cmu.edu]
  • [www.cs.cmu.edu]
  • [www.stanford.edu]
  • [theory.stanford.edu]
  • [tocmirror.cs.tau.ac.il]

  • Save to List
  • Add to Collection
  • Correct Errors
  • Monitor Changes
by Nikhil Bansal , Ryan Williams
Venue:In Proc. FOCS
Citations:19 - 3 self
  • Summary
  • Citations
  • Active Bibliography
  • Co-citation
  • Clustered Documents
  • Version History

BibTeX

@INPROCEEDINGS{Bansal_regularitylemmas,
    author = {Nikhil Bansal and Ryan Williams},
    title = {Regularity lemmas and combinatorial algorithms},
    booktitle = {In Proc. FOCS},
    year = {},
    pages = {2009}
}

Share

Facebook Twitter Reddit Bibsonomy

OpenURL

 

Abstract

Abstract — We present new combinatorial algorithms for Boolean matrix multiplication (BMM) and preprocessing a graph to answer independent set queries. We give the first asymptotic improvements on combinatorial algorithms for dense BMM in many years, improving on the “Four Russians ” O(n 3 /(w log n)) bound for machine models with wordsize w. (For a pointer machine, we can set w = log n.) The algorithms utilize notions from Regularity Lemmas for graphs in a novel way. • We give two randomized combinatorial algorithms for BMM. The first algorithm is essentially a reduction from BMM to the Triangle Removal Lemma. The best known bounds for the Triangle Removal Lemma only imply an O ` (n 3 log β)/(βw log n) ´ time algorithm for BMM where β = (log ∗ n) δ for some δ> 0, but improvements on the Triangle Removal Lemma would yield corresponding runtime improvements. The second algorithm applies the Weak Regularity Lemma of Frieze and Kannan along with “ several information compression ideas, running in O n 3 (log log n) 2 /(log n) 9/4 ”) time with probability exponentially “ close to 1. When w ≥ log n, it can be implemented in O n 3 (log log n) 2 /(w log n) 7/6 ”) time. Our results immediately imply improved combinatorial methods for CFG parsing, detecting triangle-freeness, and transitive closure. Using Weak Regularity, we also give an algorithm for answering queries of the form is S ⊆ V an independent set? in a graph. Improving on prior work, we show how to randomly preprocess a graph in O(n 2+ε) time (for all ε> 0) so that with high probability, all subsequent batches of log n independent “ set queries can be answered deterministically in O n 2 (log log n) 2 /((log n) 5/4 ”) time. When w ≥ log n, w queries can be answered in O n 2 (log log n) 2 /((log n) 7/6 ” time. In addition to its nice applications, this problem is interesting in that it is not known how to do better than O(n 2) using “algebraic ” methods. 1.

Keyphrases

combinatorial algorithm    regularity lemma    log log    triangle removal lemma    new combinatorial algorithm    algebraic method    corresponding runtime improvement    novel way    cfg parsing    high probability    log independent set query    weak regularity    many year    improved combinatorial method    transitive closure    subsequent batch    first algorithm    several information compression idea    first asymptotic improvement    independent set    weak regularity lemma    algorithm utilize notion    nice application    known bound    independent set query    time algorithm    boolean matrix multiplication    dense bmm    prior work    machine model    second algorithm    pointer machine    four russian   

Powered by: Apache Solr
  • About CiteSeerX
  • Submit and Index Documents
  • Privacy Policy
  • Help
  • Data
  • Source
  • Contact Us

Developed at and hosted by The College of Information Sciences and Technology

© 2007-2019 The Pennsylvania State University