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Documents authored by Haddad-Zaknoon, Catherine A.


Document
On Testing Decision Tree

Authors: Nader H. Bshouty and Catherine A. Haddad-Zaknoon

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)


Abstract
In this paper, we study testing decision tree of size and depth that are significantly smaller than the number of attributes n. Our main result addresses the problem of poly(n,1/ε) time algorithms with poly(s,1/ε) query complexity (independent of n) that distinguish between functions that are decision trees of size s from functions that are ε-far from any decision tree of size ϕ(s,1/ε), for some function ϕ > s. The best known result is the recent one that follows from Blanc, Lange and Tan, [Guy Blanc et al., 2020], that gives ϕ(s,1/ε) = 2^{O((log³s)/ε³)}. In this paper, we give a new algorithm that achieves ϕ(s,1/ε) = 2^{O(log² (s/ε))}. Moreover, we study the testability of depth-d decision tree and give a distribution free tester that distinguishes between depth-d decision tree and functions that are ε-far from depth-d² decision tree.

Cite as

Nader H. Bshouty and Catherine A. Haddad-Zaknoon. On Testing Decision Tree. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bshouty_et_al:LIPIcs.STACS.2022.17,
  author =	{Bshouty, Nader H. and Haddad-Zaknoon, Catherine A.},
  title =	{{On Testing Decision Tree}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{17:1--17:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.17},
  URN =		{urn:nbn:de:0030-drops-158273},
  doi =		{10.4230/LIPIcs.STACS.2022.17},
  annote =	{Keywords: Testing decision trees}
}
Document
Optimal Randomized Group Testing Algorithm to Determine the Number of Defectives

Authors: Nader H. Bshouty, Catherine A. Haddad-Zaknoon, Raghd Boulos, Foad Moalem, Jalal Nada, Elias Noufi, and Yara Zaknoon

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)


Abstract
We study the problem of determining the exact number of defective items in an adaptive group testing by using a minimum number of tests. We improve the existing algorithm and prove a lower bound that shows that the number of tests in our algorithm is optimal up to small additive terms.

Cite as

Nader H. Bshouty, Catherine A. Haddad-Zaknoon, Raghd Boulos, Foad Moalem, Jalal Nada, Elias Noufi, and Yara Zaknoon. Optimal Randomized Group Testing Algorithm to Determine the Number of Defectives. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 18:1-18:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bshouty_et_al:LIPIcs.SWAT.2020.18,
  author =	{Bshouty, Nader H. and Haddad-Zaknoon, Catherine A. and Boulos, Raghd and Moalem, Foad and Nada, Jalal and Noufi, Elias and Zaknoon, Yara},
  title =	{{Optimal Randomized Group Testing Algorithm to Determine the Number of Defectives}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{18:1--18:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.18},
  URN =		{urn:nbn:de:0030-drops-122658},
  doi =		{10.4230/LIPIcs.SWAT.2020.18},
  annote =	{Keywords: Group Testing, Randomized Algorithm}
}
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