License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.44
URN: urn:nbn:de:0030-drops-66676
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6667/
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Rao, Anup ; Sinha, Makrand

A Direct-Sum Theorem for Read-Once Branching Programs

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Abstract

We study a direct-sum question for read-once branching programs. If M(f) denotes the minimum average memory required to compute a function f(x_1,x_2, ..., x_n) how much memory is required to compute f on k independent inputs that arrive in parallel? We show that when the inputs are sampled independently from some domain X and M(f) = Omega(n), then computing the value of f on k streams requires average memory at least Omega(k * M(f)/n). Our results are obtained by defining new ways to measure the information complexity of read-once branching programs. We define two such measures: the transitional and cumulative information content. We prove that any read-once branching program with transitional information content I can be simulated using average memory O(n(I+1)). On the other hand, if every read-once branching program with cumulative information content I can be simulated with average memory O(I+1), then computing f on k inputs requires average memory at least Omega(k * (M(f)-1)).

BibTeX - Entry

@InProceedings{rao_et_al:LIPIcs:2016:6667,
  author =	{Anup Rao and Makrand Sinha},
  title =	{{A Direct-Sum Theorem for Read-Once Branching Programs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Klaus Jansen and Claire Mathieu and Jos{\'e} D. P. Rolim and Chris Umans},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6667},
  URN =		{urn:nbn:de:0030-drops-66676},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.44},
  annote =	{Keywords: Direct-sum, Information complexity, Streaming Algorithms}
}

Keywords: Direct-sum, Information complexity, Streaming Algorithms
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)
Issue Date: 2016
Date of publication: 06.09.2016


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