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Documents authored by Rahman, Md Lutfar

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Rahman, Md Lutfar

Document
DOI: 10.4230/LIPIcs.SWAT.2022.31
Erdős-Selfridge Theorem for Nonmonotone CNFs

Authors: Md Lutfar Rahman and Thomas Watson

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
In an influential paper, Erdős and Selfridge introduced the Maker-Breaker game played on a hypergraph, or equivalently, on a monotone CNF. The players take turns assigning values to variables of their choosing, and Breaker’s goal is to satisfy the CNF, while Maker’s goal is to falsify it. The Erdős-Selfridge Theorem says that the least number of clauses in any monotone CNF with k literals per clause where Maker has a winning strategy is Θ(2^k). We study the analogous question when the CNF is not necessarily monotone. We prove bounds of Θ(√2 ^k) when Maker plays last, and Ω(1.5^k) and O(r^k) when Breaker plays last, where r = (1+√5)/2≈ 1.618 is the golden ratio.
Cite as

Md Lutfar Rahman and Thomas Watson. Erdős-Selfridge Theorem for Nonmonotone CNFs. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 31:1-31:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rahman_et_al:LIPIcs.SWAT.2022.31,
  author =	{Rahman, Md Lutfar and Watson, Thomas},
  title =	{{Erd\H{o}s-Selfridge Theorem for Nonmonotone CNFs}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{31:1--31:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.31},
  URN =		{urn:nbn:de:0030-drops-161916},
  doi =		{10.4230/LIPIcs.SWAT.2022.31},
  annote =	{Keywords: Game, nonmonotone, CNFs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2021.57
6-Uniform Maker-Breaker Game Is PSPACE-Complete

Authors: Md Lutfar Rahman and Thomas Watson

Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

Abstract
In a STOC 1976 paper, Schaefer proved that it is PSPACE-complete to determine the winner of the so-called Maker-Breaker game on a given set system, even when every set has size at most 11. Since then, there has been no improvement on this result. We prove that the game remains PSPACE-complete even when every set has size 6.
Cite as

Md Lutfar Rahman and Thomas Watson. 6-Uniform Maker-Breaker Game Is PSPACE-Complete. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 57:1-57:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{rahman_et_al:LIPIcs.STACS.2021.57,
  author =	{Rahman, Md Lutfar and Watson, Thomas},
  title =	{{6-Uniform Maker-Breaker Game Is PSPACE-Complete}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{57:1--57:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus 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.2021.57},
  URN =		{urn:nbn:de:0030-drops-137020},
  doi =		{10.4230/LIPIcs.STACS.2021.57},
  annote =	{Keywords: Game, Maker-Breaker, Complexity, Reduction, PSPACE-complete, NL-hard}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.9
Complexity of Unordered CNF Games

Authors: Md Lutfar Rahman and Thomas Watson

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
The classic TQBF problem is to determine who has a winning strategy in a game played on a given CNF formula, where the two players alternate turns picking truth values for the variables in a given order, and the winner is determined by whether the CNF gets satisfied. We study variants of this game in which the variables may be played in any order, and each turn consists of picking a remaining variable and a truth value for it. - For the version where the set of variables is partitioned into two halves and each player may only pick variables from his/her half, we prove that the problem is PSPACE-complete for 5-CNFs and in P for 2-CNFs. Previously, it was known to be PSPACE-complete for unbounded-width CNFs (Schaefer, STOC 1976). - For the general unordered version (where each variable can be picked by either player), we also prove that the problem is PSPACE-complete for 5-CNFs and in P for 2-CNFs. Previously, it was known to be PSPACE-complete for 6-CNFs (Ahlroth and Orponen, MFCS 2012) and PSPACE-complete for positive 11-CNFs (Schaefer, STOC 1976).
Cite as

Md Lutfar Rahman and Thomas Watson. Complexity of Unordered CNF Games. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 9:1-9:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{rahman_et_al:LIPIcs.ISAAC.2018.9,
  author =	{Rahman, Md Lutfar and Watson, Thomas},
  title =	{{Complexity of Unordered CNF Games}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{9:1--9:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.9},
  URN =		{urn:nbn:de:0030-drops-99574},
  doi =		{10.4230/LIPIcs.ISAAC.2018.9},
  annote =	{Keywords: CNF, Games, PSPACE-complete, SAT, Linear Time}
}

Rahman, Md. Khaledur

Document
DOI: 10.4230/LIPIcs.WABI.2018.22
A Multi-labeled Tree Edit Distance for Comparing "Clonal Trees" of Tumor Progression

Authors: Nikolai Karpov, Salem Malikic, Md. Khaledur Rahman, and S. Cenk Sahinalp

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract
We introduce a new edit distance measure between a pair of "clonal trees", each representing the progression and mutational heterogeneity of a tumor sample, constructed by the use of single cell or bulk high throughput sequencing data. In a clonal tree, each vertex represents a specific tumor clone, and is labeled with one or more mutations in a way that each mutation is assigned to the oldest clone that harbors it. Given two clonal trees, our multi-labeled tree edit distance (MLTED) measure is defined as the minimum number of mutation/label deletions, (empty) leaf deletions, and vertex (clonal) expansions, applied in any order, to convert each of the two trees to the maximal common tree. We show that the MLTED measure can be computed efficiently in polynomial time and it captures the similarity between trees of different clonal granularity well. We have implemented our algorithm to compute MLTED exactly and applied it to a variety of data sets successfully. The source code of our method can be found in: https://github.com/khaled-rahman/leafDelTED.
Cite as

Nikolai Karpov, Salem Malikic, Md. Khaledur Rahman, and S. Cenk Sahinalp. A Multi-labeled Tree Edit Distance for Comparing "Clonal Trees" of Tumor Progression. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{karpov_et_al:LIPIcs.WABI.2018.22,
  author =	{Karpov, Nikolai and Malikic, Salem and Rahman, Md. Khaledur and Sahinalp, S. Cenk},
  title =	{{A Multi-labeled Tree Edit Distance for Comparing "Clonal Trees" of Tumor Progression}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.22},
  URN =		{urn:nbn:de:0030-drops-93242},
  doi =		{10.4230/LIPIcs.WABI.2018.22},
  annote =	{Keywords: Intra-tumor heterogeneity, tumor evolution, multi-labeled tree, tree edit distance, dynamic programming}
}
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