2 Search Results for "Sorrell, Jessica"

Document
DOI: 10.4230/LIPIcs.IPEC.2019.16
On the Fine-Grained Complexity of Least Weight Subsequence in Multitrees and Bounded Treewidth DAGs

Authors: Jiawei Gao

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

Abstract
This paper introduces a new technique that generalizes previously known fine-grained reductions from linear structures to graphs. Least Weight Subsequence (LWS) [Hirschberg and Larmore, 1987] is a class of highly sequential optimization problems with form F(j) = min_{i < j} [F(i) + c_{i,j}] . They can be solved in quadratic time using dynamic programming, but it is not known whether these problems can be solved faster than n^{2-o(1)} time. Surprisingly, each such problem is subquadratic time reducible to a highly parallel, non-dynamic programming problem [Marvin Künnemann et al., 2017]. In other words, if a "static" problem is faster than quadratic time, so is an LWS problem. For many instances of LWS, the sequential versions are equivalent to their static versions by subquadratic time reductions. The previous result applies to LWS on linear structures, and this paper extends this result to LWS on paths in sparse graphs, the Least Weight Subpath (LWSP) problems. When the graph is a multitree (i.e. a DAG where any pair of vertices can have at most one path) or when the graph is a DAG whose underlying undirected graph has constant treewidth, we show that LWSP on this graph is still subquadratically reducible to their corresponding static problems. For many instances, the graph versions are still equivalent to their static versions. Moreover, this paper shows that if we can decide a property of form Exists x Exists y P(x,y) in subquadratic time, where P is a quickly checkable property on a pair of elements, then on these classes of graphs, we can also in subquadratic time decide whether there exists a pair x,y in the transitive closure of the graph that also satisfy P(x,y).
Cite as

Jiawei Gao. On the Fine-Grained Complexity of Least Weight Subsequence in Multitrees and Bounded Treewidth DAGs. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{gao:LIPIcs.IPEC.2019.16,
  author =	{Gao, Jiawei},
  title =	{{On the Fine-Grained Complexity of Least Weight Subsequence in Multitrees and Bounded Treewidth DAGs}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.16},
  URN =		{urn:nbn:de:0030-drops-114778},
  doi =		{10.4230/LIPIcs.IPEC.2019.16},
  annote =	{Keywords: fine-grained complexity, dynamic programming, graph reachability}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.100
Ring Packing and Amortized FHEW Bootstrapping

Authors: Daniele Miccianco and Jessica Sorrell

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
The FHEW fully homomorphic encryption scheme (Ducas and Micciancio, Eurocrypt 2015) offers very fast homomorphic NAND-gate computations (on encrypted data) and a relatively fast refreshing procedure that allows to homomorphically evaluate arbitrary NAND boolean circuits. Unfortunately, the refreshing procedure needs to be executed after every single NAND computation, and each refreshing operates on a single encrypted bit, greatly decreasing the overall throughput of the scheme. We give a new refreshing procedure that simultaneously refreshes n FHEW ciphertexts, at a cost comparable to a single-bit FHEW refreshing operation. As a result, the cost of each refreshing is amortized over n encrypted bits, improving the throughput for the homomorphic evaluation of boolean circuits roughly by a factor n.
Cite as

Daniele Miccianco and Jessica Sorrell. Ring Packing and Amortized FHEW Bootstrapping. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 100:1-100:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{miccianco_et_al:LIPIcs.ICALP.2018.100,
  author =	{Miccianco, Daniele and Sorrell, Jessica},
  title =	{{Ring Packing and Amortized FHEW Bootstrapping}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{100:1--100:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.100},
  URN =		{urn:nbn:de:0030-drops-91047},
  doi =		{10.4230/LIPIcs.ICALP.2018.100},
  annote =	{Keywords: homomorphic encryption, bootstrapping, lattice-based cryptography}
}
  • Refine by Author
  • 1 Gao, Jiawei
  • 1 Miccianco, Daniele
  • 1 Sorrell, Jessica

  • Refine by Classification
  • 1 Security and privacy → Cryptography
  • 1 Theory of computation → Problems, reductions and completeness

  • Refine by Keyword
  • 1 bootstrapping
  • 1 dynamic programming
  • 1 fine-grained complexity
  • 1 graph reachability
  • 1 homomorphic encryption
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2018
  • 1 2019

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact