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Documents authored by Wild, Sebastian

Document
Complete Volume
DOI: 10.4230/LIPIcs.AofA.2024
LIPIcs, Volume 302, AofA 2024, Complete Volume

Authors: Cécile Mailler and Sebastian Wild

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

Abstract
LIPIcs, Volume 302, AofA 2024, Complete Volume
Cite as

35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 1-458, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Proceedings{mailler_et_al:LIPIcs.AofA.2024,
  title =	{{LIPIcs, Volume 302, AofA 2024, Complete Volume}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{1--458},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024},
  URN =		{urn:nbn:de:0030-drops-204341},
  doi =		{10.4230/LIPIcs.AofA.2024},
  annote =	{Keywords: LIPIcs, Volume 302, AofA 2024, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.AofA.2024.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Cécile Mailler and Sebastian Wild

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mailler_et_al:LIPIcs.AofA.2024.0,
  author =	{Mailler, C\'{e}cile and Wild, Sebastian},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.0},
  URN =		{urn:nbn:de:0030-drops-204353},
  doi =		{10.4230/LIPIcs.AofA.2024.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2024.17
Deterministic Cache-Oblivious Funnelselect

Authors: Gerth Stølting Brodal and Sebastian Wild

Published in: LIPIcs, Volume 294, 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)

Abstract
In the multiple-selection problem one is given an unsorted array S of N elements and an array of q query ranks r_1 < ⋯ < r_q, and the task is to return, in sorted order, the q elements in S of rank r_1, …, r_q, respectively. The asymptotic deterministic comparison complexity of the problem was settled by Dobkin and Munro [JACM 1981]. In the I/O model an optimal I/O complexity was achieved by Hu et al. [SPAA 2014]. Recently [ESA 2023], we presented a cache-oblivious algorithm with matching I/O complexity, named funnelselect, since it heavily borrows ideas from the cache-oblivious sorting algorithm funnelsort from the seminal paper by Frigo, Leiserson, Prokop and Ramachandran [FOCS 1999]. Funnelselect is inherently randomized as it relies on sampling for cheaply finding many good pivots. In this paper we present deterministic funnelselect, achieving the same optimal I/O complexity cache-obliviously without randomization. Our new algorithm essentially replaces a single (in expectation) reversed-funnel computation using random pivots by a recursive algorithm using multiple reversed-funnel computations. To meet the I/O bound, this requires a carefully chosen subproblem size based on the entropy of the sequence of query ranks; deterministic funnelselect thus raises distinct technical challenges not met by randomized funnelselect. The resulting worst-case I/O bound is O(∑_{i = 1}^{q+1} Δ_i/B ⋅ log_{M/B} N/Δ_i + N/B), where B is the external memory block size, M ≥ B^{1+ε} is the internal memory size, for some constant ε > 0, and Δ_i = r_i - r_{i-1} (assuming r_0 = 0 and r_{q+1} = N + 1).
Cite as

Gerth Stølting Brodal and Sebastian Wild. Deterministic Cache-Oblivious Funnelselect. In 19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 294, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{brodal_et_al:LIPIcs.SWAT.2024.17,
  author =	{Brodal, Gerth St{\o}lting and Wild, Sebastian},
  title =	{{Deterministic Cache-Oblivious Funnelselect}},
  booktitle =	{19th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2024)},
  pages =	{17:1--17:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-318-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{294},
  editor =	{Bodlaender, Hans L.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2024.17},
  URN =		{urn:nbn:de:0030-drops-200576},
  doi =		{10.4230/LIPIcs.SWAT.2024.17},
  annote =	{Keywords: Multiple selection, cache-oblivious algorithm, entropy bounds}
}
Document
DOI: 10.4230/LIPIcs.FUN.2024.15
Polyamorous Scheduling

Authors: Leszek Gąsieniec, Benjamin Smith, and Sebastian Wild

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)

Abstract
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the underlying optimisation problem: Polyamorous Scheduling. In Polyamorous Scheduling, we are given an edge-weighted graph and try to find a periodic schedule of matchings in this graph such that the maximal weighted waiting time between consecutive occurrences of the same edge is minimised. We show that the problem is NP-hard and that there is no efficient approximation algorithm with a better ratio than 4/3 unless P = NP. On the positive side, we obtain an O(log n)-approximation algorithm; indeed, an O(log Δ)-approximation for Δ the maximum degree, i.e., the largest number of relationships of any individual. We also define a generalisation of density from the Pinwheel Scheduling Problem, "poly density", and ask whether there exists a poly-density threshold similar to the 5/6-density threshold for Pinwheel Scheduling [Kawamura, STOC 2024]. Polyamorous Scheduling is a natural generalisation of Pinwheel Scheduling with respect to its optimisation variant, Bamboo Garden Trimming. Our work contributes the first nontrivial hardness-of-approximation reduction for any periodic scheduling problem, and opens up numerous avenues for further study of Polyamorous Scheduling.
Cite as

Leszek Gąsieniec, Benjamin Smith, and Sebastian Wild. Polyamorous Scheduling. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gasieniec_et_al:LIPIcs.FUN.2024.15,
  author =	{G\k{a}sieniec, Leszek and Smith, Benjamin and Wild, Sebastian},
  title =	{{Polyamorous Scheduling}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.15},
  URN =		{urn:nbn:de:0030-drops-199234},
  doi =		{10.4230/LIPIcs.FUN.2024.15},
  annote =	{Keywords: Periodic scheduling, Pinwheel scheduling, Edge-coloring, Chromatic index, Approximation algorithms, Hardness of approximation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.25
Funnelselect: Cache-Oblivious Multiple Selection

Authors: Gerth Stølting Brodal and Sebastian Wild

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We present the algorithm funnelselect, the first optimal randomized cache-oblivious algorithm for the multiple-selection problem. The algorithm takes as input an unsorted array of N elements and q query ranks r_1 < ⋯ < r_q, and returns in sorted order the q input elements of rank r_1, …, r_q, respectively. The algorithm uses expected and with high probability O(∑_{i = 1}^{q+1} Δ_i/B ⋅ log_{M/B} N/(Δ_i) + N/B) I/Os, where B is the external memory block size, M ≥ B^{1+ε} is the internal memory size, for some constant ε > 0, and Δ_i = r_i - r_{i-1} (assuming r_0 = 0 and r_{q+1} = N + 1). This is the best possible I/O bound in the cache-oblivious and external memory models. The result is achieved by reversing the computation of the cache-oblivious sorting algorithm funnelsort by Frigo, Leiserson, Prokop and Ramachandran [FOCS 1999], using randomly selected pivots for distributing elements, and pruning computations that with high probability are not expected to contain any query ranks.
Cite as

Gerth Stølting Brodal and Sebastian Wild. Funnelselect: Cache-Oblivious Multiple Selection. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{brodal_et_al:LIPIcs.ESA.2023.25,
  author =	{Brodal, Gerth St{\o}lting and Wild, Sebastian},
  title =	{{Funnelselect: Cache-Oblivious Multiple Selection}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.25},
  URN =		{urn:nbn:de:0030-drops-186789},
  doi =		{10.4230/LIPIcs.ESA.2023.25},
  annote =	{Keywords: Multiple selection, cache-oblivious algorithm, randomized algorithm, entropy bounds}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.70
Hypersuccinct Trees - New Universal Tree Source Codes for Optimal Compressed Tree Data Structures and Range Minima

Authors: J. Ian Munro, Patrick K. Nicholson, Louisa Seelbach Benkner, and Sebastian Wild

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We present a new universal source code for distributions of unlabeled binary and ordinal trees that achieves optimal compression to within lower order terms for all tree sources covered by existing universal codes. At the same time, it supports answering many navigational queries on the compressed representation in constant time on the word-RAM; this is not known to be possible for any existing tree compression method. The resulting data structures, "hypersuccinct trees", hence combine the compression achieved by the best known universal codes with the operation support of the best succinct tree data structures. We apply hypersuccinct trees to obtain a universal compressed data structure for range-minimum queries. It has constant query time and the optimal worst-case space usage of 2n+o(n) bits, but the space drops to 1.736n + o(n) bits on average for random permutations of n elements, and 2lg binom{n}{r} + o(n) for arrays with r increasing runs, respectively. Both results are optimal; the former answers an open problem of Davoodi et al. (2014) and Golin et al. (2016). Compared to prior work on succinct data structures, we do not have to tailor our data structure to specific applications; hypersuccinct trees automatically adapt to the trees at hand. We show that they simultaneously achieve the optimal space usage to within lower order terms for a wide range of distributions over tree shapes, including: binary search trees (BSTs) generated by insertions in random order / Cartesian trees of random arrays, random fringe-balanced BSTs, binary trees with a given number of binary/unary/leaf nodes, random binary tries generated from memoryless sources, full binary trees, unary paths, as well as uniformly chosen weight-balanced BSTs, AVL trees, and left-leaning red-black trees.
Cite as

J. Ian Munro, Patrick K. Nicholson, Louisa Seelbach Benkner, and Sebastian Wild. Hypersuccinct Trees - New Universal Tree Source Codes for Optimal Compressed Tree Data Structures and Range Minima. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 70:1-70:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{munro_et_al:LIPIcs.ESA.2021.70,
  author =	{Munro, J. Ian and Nicholson, Patrick K. and Benkner, Louisa Seelbach and Wild, Sebastian},
  title =	{{Hypersuccinct Trees - New Universal Tree Source Codes for Optimal Compressed Tree Data Structures and Range Minima}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{70:1--70:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.70},
  URN =		{urn:nbn:de:0030-drops-146512},
  doi =		{10.4230/LIPIcs.ESA.2021.70},
  annote =	{Keywords: analysis of algorithms, universal source code, compressed trees, succinct data structure, succinct trees, tree covering, random binary search trees, range-minimum queries}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.25
Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees

Authors: Meng He, J. Ian Munro, Yakov Nekrich, Sebastian Wild, and Kaiyu Wu

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
We present the first succinct distance oracles for (unweighted) interval graphs and related classes of graphs, using a novel succinct data structure for ordinal trees that supports the mapping between preorder (i.e., depth-first) ranks and level-order (breadth-first) ranks of nodes in constant time. Our distance oracles for interval graphs also support navigation queries - testing adjacency, computing node degrees, neighborhoods, and shortest paths - all in optimal time. Our technique also yields optimal distance oracles for proper interval graphs (unit-interval graphs) and circular-arc graphs. Our tree data structure supports all operations provided by different approaches in previous work, as well as mapping to and from level-order ranks and retrieving the last (first) internal node before (after) a given node in a level-order traversal, all in constant time.
Cite as

Meng He, J. Ian Munro, Yakov Nekrich, Sebastian Wild, and Kaiyu Wu. Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{he_et_al:LIPIcs.ISAAC.2020.25,
  author =	{He, Meng and Munro, J. Ian and Nekrich, Yakov and Wild, Sebastian and Wu, Kaiyu},
  title =	{{Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.25},
  URN =		{urn:nbn:de:0030-drops-133693},
  doi =		{10.4230/LIPIcs.ISAAC.2020.25},
  annote =	{Keywords: succinct data structures, distance oracles, ordinal tree, level order, breadth-first order, interval graphs, proper interval graphs, succinct graph representation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.63
Nearly-Optimal Mergesorts: Fast, Practical Sorting Methods That Optimally Adapt to Existing Runs

Authors: J. Ian Munro and Sebastian Wild

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
We present two stable mergesort variants, "peeksort" and "powersort", that exploit existing runs and find nearly-optimal merging orders with negligible overhead. Previous methods either require substantial effort for determining the merging order (Takaoka 2009; Barbay & Navarro 2013) or do not have an optimal worst-case guarantee (Peters 2002; Auger, Nicaud & Pivoteau 2015; Buss & Knop 2018) . We demonstrate that our methods are competitive in terms of running time with state-of-the-art implementations of stable sorting methods.
Cite as

J. Ian Munro and Sebastian Wild. Nearly-Optimal Mergesorts: Fast, Practical Sorting Methods That Optimally Adapt to Existing Runs. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 63:1-63:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{munro_et_al:LIPIcs.ESA.2018.63,
  author =	{Munro, J. Ian and Wild, Sebastian},
  title =	{{Nearly-Optimal Mergesorts: Fast, Practical Sorting Methods That Optimally Adapt to Existing Runs}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{63:1--63:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.63},
  URN =		{urn:nbn:de:0030-drops-95265},
  doi =		{10.4230/LIPIcs.ESA.2018.63},
  annote =	{Keywords: adaptive sorting, nearly-optimal binary search trees, Timsort}
}
Document
DOI: 10.4230/LIPIcs.AofA.2018.36
Average Cost of QuickXsort with Pivot Sampling

Authors: Sebastian Wild

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)

Abstract
QuickXsort is a strategy to combine Quicksort with another sorting method X so that the result has essentially the same comparison cost as X in isolation, but sorts in place even when X requires a linear-size buffer. We solve the recurrence for QuickXsort precisely up to the linear term including the optimization to choose pivots from a sample of k elements. This allows to immediately obtain overall average costs using only the average costs of sorting method X (as if run in isolation). We thereby extend and greatly simplify the analysis of QuickHeapsort and QuickMergesort with practically efficient pivot selection, and give the first tight upper bounds including the linear term for such methods.
Cite as

Sebastian Wild. Average Cost of QuickXsort with Pivot Sampling. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{wild:LIPIcs.AofA.2018.36,
  author =	{Wild, Sebastian},
  title =	{{Average Cost of QuickXsort with Pivot Sampling}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{36:1--36:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.36},
  URN =		{urn:nbn:de:0030-drops-89295},
  doi =		{10.4230/LIPIcs.AofA.2018.36},
  annote =	{Keywords: in-situ sorting, constant-factor optimal sorting, pivot sampling, QuickMergesort, QuickHeapsort, Quicksort recurrence, average-case analysis}
}
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