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Documents authored by Weiss, Armin

Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2022.127
Satisfiability Problems for Finite Groups

Authors: Paweł M. Idziak, Piotr Kawałek, Jacek Krzaczkowski, and Armin Weiß

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Over twenty years ago, Goldmann and Russell initiated the study of the complexity of the equation satisfiability problem (PolSat and the NUDFA program satisfiability problem (ProgramSat) in finite groups. They showed that these problems are in 𝖯 for nilpotent groups while they are NP-complete for non-solvable groups. In this work we completely characterize finite groups for which the problem ProgramSat can be solved in randomized polynomial time under the assumptions of the Randomized Exponential Time Hypothesis and the Constant Degree Hypothesis. We also determine the complexity of PolSat for a wide class of finite groups. As a by-product, we obtain a classification for ListPolSat, a version of PolSat where each variable can be restricted to an arbitrary subset. Finally, we also prove unconditional algorithms for these problems in certain cases.
Cite as

Paweł M. Idziak, Piotr Kawałek, Jacek Krzaczkowski, and Armin Weiß. Satisfiability Problems for Finite Groups. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 127:1-127:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{idziak_et_al:LIPIcs.ICALP.2022.127,
  author =	{Idziak, Pawe{\l} M. and Kawa{\l}ek, Piotr and Krzaczkowski, Jacek and Wei{\ss}, Armin},
  title =	{{Satisfiability Problems for Finite Groups}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{127:1--127:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.127},
  URN =		{urn:nbn:de:0030-drops-164685},
  doi =		{10.4230/LIPIcs.ICALP.2022.127},
  annote =	{Keywords: Satisifiability, Solvable groups, ProgramSat, PolSat, Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.26
The Isomorphism Problem for Plain Groups Is in Σ₃^{𝖯}

Authors: Heiko Dietrich, Murray Elder, Adam Piggott, Youming Qiao, and Armin Weiß

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

Abstract
Testing isomorphism of infinite groups is a classical topic, but from the complexity theory viewpoint, few results are known. Sénizergues and the fifth author (ICALP2018) proved that the isomorphism problem for virtually free groups is decidable in PSPACE when the input is given in terms of so-called virtually free presentations. Here we consider the isomorphism problem for the class of plain groups, that is, groups that are isomorphic to a free product of finitely many finite groups and finitely many copies of the infinite cyclic group. Every plain group is naturally and efficiently presented via an inverse-closed finite convergent length-reducing rewriting system. We prove that the isomorphism problem for plain groups given in this form lies in the polynomial time hierarchy, more precisely, in Σ₃^𝖯. This result is achieved by combining new geometric and algebraic characterisations of groups presented by inverse-closed finite convergent length-reducing rewriting systems developed in recent work of the second and third authors (2021) with classical finite group isomorphism results of Babai and Szemerédi (1984).
Cite as

Heiko Dietrich, Murray Elder, Adam Piggott, Youming Qiao, and Armin Weiß. The Isomorphism Problem for Plain Groups Is in Σ₃^{𝖯}. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 26:1-26:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dietrich_et_al:LIPIcs.STACS.2022.26,
  author =	{Dietrich, Heiko and Elder, Murray and Piggott, Adam and Qiao, Youming and Wei{\ss}, Armin},
  title =	{{The Isomorphism Problem for Plain Groups Is in \Sigma₃^\{𝖯\}}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{26:1--26:14},
  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.2022.26},
  URN =		{urn:nbn:de:0030-drops-158368},
  doi =		{10.4230/LIPIcs.STACS.2022.26},
  annote =	{Keywords: plain group, isomorphism problem, polynomial hierarchy, \Sigma₃^\{𝖯\} complexity class, inverse-closed finite convergent length-reducing rewriting system}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.74
Parallel Algorithms for Power Circuits and the Word Problem of the Baumslag Group

Authors: Caroline Mattes and Armin Weiß

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
Power circuits have been introduced in 2012 by Myasnikov, Ushakov and Won as a data structure for non-elementarily compressed integers supporting the arithmetic operations addition and (x,y) ↦ x⋅2^y. The same authors applied power circuits to give a polynomial-time solution to the word problem of the Baumslag group, which has a non-elementary Dehn function. In this work, we examine power circuits and the word problem of the Baumslag group under parallel complexity aspects. In particular, we establish that the word problem of the Baumslag group can be solved in NC - even though one of the essential steps is to compare two integers given by power circuits and this, in general, is shown to be 𝖯-complete. The key observation is that the depth of the occurring power circuits is logarithmic and such power circuits can be compared in NC.
Cite as

Caroline Mattes and Armin Weiß. Parallel Algorithms for Power Circuits and the Word Problem of the Baumslag Group. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 74:1-74:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{mattes_et_al:LIPIcs.MFCS.2021.74,
  author =	{Mattes, Caroline and Wei{\ss}, Armin},
  title =	{{Parallel Algorithms for Power Circuits and the Word Problem of the Baumslag Group}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{74:1--74:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.74},
  URN =		{urn:nbn:de:0030-drops-145148},
  doi =		{10.4230/LIPIcs.MFCS.2021.74},
  annote =	{Keywords: Word problem, Baumslag group, power circuit, parallel complexity}
}
Document
DOI: 10.4230/LIPIcs.CCC.2020.29
Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems

Authors: Laurent Bartholdi, Michael Figelius, Markus Lohrey, and Armin Weiß

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)

Abstract
We give lower bounds on the complexity of the word problem of certain non-solvable groups: for a large class of non-solvable infinite groups, including in particular free groups, Grigorchuk’s group and Thompson’s groups, we prove that their word problem is ALOGTIME-hard. For some of these groups (including Grigorchuk’s group and Thompson’s groups) we prove that the circuit value problem (which is equivalent to the circuit evaluation problem) is PSPACE-complete.
Cite as

Laurent Bartholdi, Michael Figelius, Markus Lohrey, and Armin Weiß. Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 29:1-29:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bartholdi_et_al:LIPIcs.CCC.2020.29,
  author =	{Bartholdi, Laurent and Figelius, Michael and Lohrey, Markus and Wei{\ss}, Armin},
  title =	{{Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{29:1--29:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.29},
  URN =		{urn:nbn:de:0030-drops-125814},
  doi =		{10.4230/LIPIcs.CCC.2020.29},
  annote =	{Keywords: NC^1-hardness, word problem, G-programs, straight-line programs, non-solvable groups, self-similar groups, Thompson’s groups, Grigorchuk’s group}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.102
Hardness of Equations over Finite Solvable Groups Under the Exponential Time Hypothesis

Authors: Armin Weiß

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Goldmann and Russell (2002) initiated the study of the complexity of the equation satisfiability problem in finite groups by showing that it is in 𝖯 for nilpotent groups while it is 𝖭𝖯-complete for non-solvable groups. Since then, several results have appeared showing that the problem can be solved in polynomial time in certain solvable groups of Fitting length two. In this work, we present the first lower bounds for the equation satisfiability problem in finite solvable groups: under the assumption of the exponential time hypothesis, we show that it cannot be in 𝖯 for any group of Fitting length at least four and for certain groups of Fitting length three. Moreover, the same hardness result applies to the equation identity problem.
Cite as

Armin Weiß. Hardness of Equations over Finite Solvable Groups Under the Exponential Time Hypothesis. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 102:1-102:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wei:LIPIcs.ICALP.2020.102,
  author =	{Wei{\ss}, Armin},
  title =	{{Hardness of Equations over Finite Solvable Groups Under the Exponential Time Hypothesis}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{102:1--102:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.102},
  URN =		{urn:nbn:de:0030-drops-125093},
  doi =		{10.4230/LIPIcs.ICALP.2020.102},
  annote =	{Keywords: equations in groups, solvable groups, exponential time hypothesis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.6
An Automaton Group with PSPACE-Complete Word Problem

Authors: Jan Philipp Wächter and Armin Weiß

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
We construct an automaton group with a PSPACE-complete word problem, proving a conjecture due to Steinberg. Additionally, the constructed group has a provably more difficult, namely EXPSPACE-complete, compressed word problem. Our construction directly simulates the computation of a Turing machine in an automaton group and, therefore, seems to be quite versatile. It combines two ideas: the first one is a construction used by D'Angeli, Rodaro and the first author to obtain an inverse automaton semigroup with a PSPACE-complete word problem and the second one is to utilize a construction used by Barrington to simulate circuits of bounded degree and logarithmic depth in the group of even permutations over five elements.
Cite as

Jan Philipp Wächter and Armin Weiß. An Automaton Group with PSPACE-Complete Word Problem. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wachter_et_al:LIPIcs.STACS.2020.6,
  author =	{W\"{a}chter, Jan Philipp and Wei{\ss}, Armin},
  title =	{{An Automaton Group with PSPACE-Complete Word Problem}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{6:1--6:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.6},
  URN =		{urn:nbn:de:0030-drops-118674},
  doi =		{10.4230/LIPIcs.STACS.2020.6},
  annote =	{Keywords: automaton group, word problem, PSPACE, compressed word problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.43
The Power Word Problem

Authors: Markus Lohrey and Armin Weiß

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
In this work we introduce a new succinct variant of the word problem in a finitely generated group G, which we call the power word problem: the input word may contain powers p^x, where p is a finite word over generators of G and x is a binary encoded integer. The power word problem is a restriction of the compressed word problem, where the input word is represented by a straight-line program (i.e., an algebraic circuit over G). The main result of the paper states that the power word problem for a finitely generated free group F is AC^0-Turing-reducible to the word problem for F. Moreover, the following hardness result is shown: For a wreath product G Wr Z, where G is either free of rank at least two or finite non-solvable, the power word problem is complete for coNP. This contrasts with the situation where G is abelian: then the power word problem is shown to be in TC^0.
Cite as

Markus Lohrey and Armin Weiß. The Power Word Problem. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2019.43,
  author =	{Lohrey, Markus and Wei{\ss}, Armin},
  title =	{{The Power Word Problem}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{43:1--43:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.43},
  URN =		{urn:nbn:de:0030-drops-109871},
  doi =		{10.4230/LIPIcs.MFCS.2019.43},
  annote =	{Keywords: word problem, compressed word problem, free groups}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.139
The Isomorphism Problem for Finite Extensions of Free Groups Is In PSPACE

Authors: Géraud Sénizergues and Armin Weiß

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

Abstract
We present an algorithm for the following problem: given a context-free grammar for the word problem of a virtually free group G, compute a finite graph of groups G with finite vertex groups and fundamental group G. Our algorithm is non-deterministic and runs in doubly exponential time. It follows that the isomorphism problem of context-free groups can be solved in doubly exponential space. Moreover, if, instead of a grammar, a finite extension of a free group is given as input, the construction of the graph of groups is in NP and, consequently, the isomorphism problem in PSPACE.
Cite as

Géraud Sénizergues and Armin Weiß. The Isomorphism Problem for Finite Extensions of Free Groups Is In PSPACE. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 139:1-139:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{senizergues_et_al:LIPIcs.ICALP.2018.139,
  author =	{S\'{e}nizergues, G\'{e}raud and Wei{\ss}, Armin},
  title =	{{The Isomorphism Problem for Finite Extensions of Free Groups Is In PSPACE}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{139:1--139:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.139},
  URN =		{urn:nbn:de:0030-drops-91437},
  doi =		{10.4230/LIPIcs.ICALP.2018.139},
  annote =	{Keywords: virtually free groups, context-free groups, isomorphism problem, structure tree, graph of groups}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.23
TC^0 Circuits for Algorithmic Problems in Nilpotent Groups

Authors: Alexei Myasnikov and Armin Weiß

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
Recently, Macdonald et. al. showed that many algorithmic problems for finitely generated nilpotent groups including computation of normal forms, the subgroup membership problem, the conjugacy problem, and computation of subgroup presentations can be done in LOGSPACE. Here we follow their approach and show that all these problems are complete for the uniform circuit class TC^0 - uniformly for all r-generated nilpotent groups of class at most c for fixed r and c. Moreover, if we allow a certain binary representation of the inputs, then the word problem and computation of normal forms is still in uniform TC^0, while all the other problems we examine are shown to be TC^0-Turing reducible to the problem of computing greatest common divisors and expressing them as linear combinations.
Cite as

Alexei Myasnikov and Armin Weiß. TC^0 Circuits for Algorithmic Problems in Nilpotent Groups. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{myasnikov_et_al:LIPIcs.MFCS.2017.23,
  author =	{Myasnikov, Alexei and Wei{\ss}, Armin},
  title =	{{TC^0 Circuits for Algorithmic Problems in Nilpotent Groups}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{23:1--23:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.23},
  URN =		{urn:nbn:de:0030-drops-81089},
  doi =		{10.4230/LIPIcs.MFCS.2017.23},
  annote =	{Keywords: nilpotent groups, TC^0, abelian groups, word problem, conjugacy problem, subgroup membership problem, greatest common divisors}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.38
BlockQuicksort: Avoiding Branch Mispredictions in Quicksort

Authors: Stefan Edelkamp and Armin Weiss

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
Since the work of Kaligosi and Sanders (2006), it is well-known that Quicksort - which is commonly considered as one of the fastest in-place sorting algorithms - suffers in an essential way from branch mispredictions. We present a novel approach to address this problem by partially decoupling control from data flow: in order to perform the partitioning, we split the input in blocks of constant size (we propose 128 data elements); then, all elements in one block are compared with the pivot and the outcomes of the comparisons are stored in a buffer. In a second pass, the respective elements are rearranged. By doing so, we avoid conditional branches based on outcomes of comparisons at all (except for the final Insertionsort). Moreover, we prove that for a static branch predictor the average total number of branch mispredictions is at most epsilon n log n + O(n) for some small epsilon depending on the block size when sorting n elements. Our experimental results are promising: when sorting random integer data, we achieve an increase in speed (number of elements sorted per second) of more than 80% over the GCC implementation of C++ std::sort. Also for many other types of data and non-random inputs, there is still a significant speedup over std::sort. Only in few special cases like sorted or almost sorted inputs, std::sort can beat our implementation. Moreover, even on random input permutations, our implementation is even slightly faster than an implementation of the highly tuned Super Scalar Sample Sort, which uses a linear amount of additional space.
Cite as

Stefan Edelkamp and Armin Weiss. BlockQuicksort: Avoiding Branch Mispredictions in Quicksort. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{edelkamp_et_al:LIPIcs.ESA.2016.38,
  author =	{Edelkamp, Stefan and Weiss, Armin},
  title =	{{BlockQuicksort: Avoiding Branch Mispredictions in Quicksort}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{38:1--38:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.38},
  URN =		{urn:nbn:de:0030-drops-63890},
  doi =		{10.4230/LIPIcs.ESA.2016.38},
  annote =	{Keywords: in-place sorting, Quicksort, branch mispredictions, lean programs}
}
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