15 Search Results for "Pratt, Simon"

Document
DOI: 10.4230/LIPIcs.AFT.2025.25
The Exchange Problem

Authors: Mohit Garg and Suneel Sarswat

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract
Auctions are widely used in exchanges to match buy and sell requests. Once the buyers and sellers place their requests, the exchange determines how these requests are to be matched. The two most popular objectives used while determining the matching are maximizing volume with dynamic pricing and maximizing volume at a uniform price. In this work, we study the algorithmic complexity of the problems arising from these matching tasks. For dynamic-price matching, we establish a lower bound of Ω(n log n) on the running time, thereby proving that the currently best-known O(n log n) algorithm is time-optimal. In contrast, for uniform-price matching, we present a linear-time algorithm, improving upon previous methods that require O(n log n) time to match n requests.
Cite as

Mohit Garg and Suneel Sarswat. The Exchange Problem. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garg_et_al:LIPIcs.AFT.2025.25,
  author =	{Garg, Mohit and Sarswat, Suneel},
  title =	{{The Exchange Problem}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.25},
  URN =		{urn:nbn:de:0030-drops-247449},
  doi =		{10.4230/LIPIcs.AFT.2025.25},
  annote =	{Keywords: Exchanges, Double Auctions, Matching Algorithms, Element Distinctness, Time Complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.42
(Multivariate) k-SUM as Barrier to Succinct Computation

Authors: Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
How does the time complexity of a problem change when the input is given succinctly rather than explicitly? We study this question for several geometric problems defined on a set X of N points in ℤ^d. As succinct representation, we choose a sumset (or Minkowski sum) representation: Instead of receiving X explicitly, we are given sets A,B of n points that define X as A+B = {a+b∣ a ∈ A,b ∈ B}. We investigate the fine-grained complexity of this succinct version for several Õ(N)-time computable geometric primitives. Remarkably, we can tie their complexity tightly to the complexity of corresponding k-SUM problems. Specifically, we introduce as All-ints 3-SUM(n,n,k) the following multivariate, multi-output variant of 3-SUM: given sets A,B of size n and set C of size k, determine for all c ∈ C whether there are a ∈ A and b ∈ B with a+b = c. We obtain the following results: 1) Succinct closest L_∞-pair requires time N^{1-o(1)} under the 3-SUM hypothesis, while succinct furthest L_∞-pair can be solved in time Õ(n). 2) Succinct bichromatic closest L_∞-Pair requires time N^{1-o(1)} iff the 4-SUM hypothesis holds. 3) The following problems are fine-grained equivalent to All-ints 3-SUM(n,n,k): succinct skyline computation in 2D with output size k and succinct batched orthogonal range search with k given ranges. This establishes conditionally tight Õ(min{nk, N})-time algorithms for these problems. We obtain further connections with All-ints 3-SUM(n,n,k) for succinctly computing independent sets in unit interval graphs. Thus, (Multivariate) k-SUM problems precisely capture the barrier for enabling sumset-succinct computation for various geometric primitives.
Cite as

Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel. (Multivariate) k-SUM as Barrier to Succinct Computation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 42:1-42:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gokaj_et_al:LIPIcs.ESA.2025.42,
  author =	{Gokaj, Geri and K\"{u}nnemann, Marvin and Storandt, Sabine and Truschel, Carina},
  title =	{{(Multivariate) k-SUM as Barrier to Succinct Computation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{42:1--42:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.42},
  URN =		{urn:nbn:de:0030-drops-245101},
  doi =		{10.4230/LIPIcs.ESA.2025.42},
  annote =	{Keywords: Fine-grained complexity theory, sumsets, additive combinatorics, succinct inputs, computational geometry}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.10
An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems

Authors: Dohan Kim

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We present a formalized framework for semi-Thue and conditional semi-Thue systems for studying monoids and their word problem using the Isabelle/HOL proof assistant. We provide a formalized decision procedure for the word problem of monoids if they are finitely presented by complete semi-Thue systems. In particular, we present a new formalized method for checking confluence using (conditional) critical pairs for certain conditional semi-Thue systems. We propose and formalize an inference system for generating conditional equational theories and Thue congruences using conditional semi-Thue systems. Then we provide a new formalized decision procedure for the word problem of monoids which have finite complete (reductive) conditional presentations.
Cite as

Dohan Kim. An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kim:LIPIcs.ITP.2025.10,
  author =	{Kim, Dohan},
  title =	{{An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.10},
  URN =		{urn:nbn:de:0030-drops-246081},
  doi =		{10.4230/LIPIcs.ITP.2025.10},
  annote =	{Keywords: semi-Thue systems, conditional semi-Thue systems, conditional string rewriting, monoids, word problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.87
Lazy B-Trees

Authors: Casper Moldrup Rysgaard and Sebastian Wild

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Lazy search trees (Sandlund & Wild FOCS 2020, Sandlund & Zhang SODA 2022) are sorted dictionaries whose update and query performance smoothly interpolates between that of efficient priority queues and binary search trees - automatically, depending on actual use; no adjustments are necessary to the data structure to realize the cost savings. In this paper, we design lazy B-trees, a variant of lazy search trees suitable for external memory that generalizes the speedup of B-trees over binary search trees wrt. input/output operations to the same smooth interpolation regime. A key technical difficulty to overcome is the lack of a (fully satisfactory) external variant of biased search trees, on which lazy search trees crucially rely. We give a construction for a subset of performance guarantees sufficient to realize external-memory lazy search trees, which we deem of independent interest. As one special case, lazy B-trees can be used as an external-memory priority queue, in which case they are competitive with some tailor-made heaps; indeed, they offer faster decrease-key and insert operations than known data structures.
Cite as

Casper Moldrup Rysgaard and Sebastian Wild. Lazy B-Trees. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 87:1-87:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rysgaard_et_al:LIPIcs.MFCS.2025.87,
  author =	{Rysgaard, Casper Moldrup and Wild, Sebastian},
  title =	{{Lazy B-Trees}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{87:1--87:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.87},
  URN =		{urn:nbn:de:0030-drops-241949},
  doi =		{10.4230/LIPIcs.MFCS.2025.87},
  annote =	{Keywords: B-tree, lazy search trees, lazy updates, external memory, deferred data structures, database cracking}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.14
Specific Patterns Against Reference Sequences

Authors: Marie-Pierre Béal and Maxime Crochemore

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
We design alignment-free techniques for comparing a set of sequences or just a word, called a target, against another set of words, called a reference. This is done with the detection of factor patterns that distinguish the target from the reference. A target-specific factor of a target T against a reference R is then a factor w of a word in T that is not a factor of a word in R but whose proper factors of w are factors of a word in R. The strategy is based on the notion of minimal absent/forbidden words. We first address the computation of the set of target-specific factors of a target T against a reference R, where T and R are finite sets of sequences. The result is the construction of an automaton accepting the set of all considered target-specific factors. The construction algorithm runs in linear time according to the size of T ∪ R. The second result is the design of an algorithm to compute all the occurrences in a single sequence T of its target-specific factors against a reference R. The algorithm runs in real-time on the target sequence, independently of the number of occurrences of target-specific factors.
Cite as

Marie-Pierre Béal and Maxime Crochemore. Specific Patterns Against Reference Sequences. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 14:1-14:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{beal_et_al:OASIcs.Grossi.14,
  author =	{B\'{e}al, Marie-Pierre and Crochemore, Maxime},
  title =	{{Specific Patterns Against Reference Sequences}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{14:1--14:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.14},
  URN =		{urn:nbn:de:0030-drops-238130},
  doi =		{10.4230/OASIcs.Grossi.14},
  annote =	{Keywords: Specific pattern, Minimal absent word, Minimal forbidden word, Directed Acyclic Word Graph (DAWG), Suffix automaton}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.12
Shortest Undirected Paths in de Bruijn Graphs

Authors: Wiktor Zuba, Oded Lachish, and Solon P. Pissis

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
Computing shortest directed paths in de Bruijn graphs is well studied and well understood. This is not the case for computing undirected paths, which is much more challenging algorithmically. In this paper, we present a general framework for computing shortest undirected paths in arbitrary de Bruijn graphs, that is, arbitrary subgraphs of the complete de Bruijn graph. We then present an application of our techniques for making any arbitrary order-k de Bruijn graph G(V,E) weakly connected by adding a set of edges of minimum total cost. This improves the running time of the recent (2-2/d)-approximation algorithm by Bernardini et al. [CPM 2024] from 𝒪(k|V|²) to 𝒪(k|V|log d) time, where d is the number of weakly connected components of graph G.
Cite as

Wiktor Zuba, Oded Lachish, and Solon P. Pissis. Shortest Undirected Paths in de Bruijn Graphs. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 12:1-12:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{zuba_et_al:LIPIcs.CPM.2025.12,
  author =	{Zuba, Wiktor and Lachish, Oded and Pissis, Solon P.},
  title =	{{Shortest Undirected Paths in de Bruijn Graphs}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{12:1--12:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.12},
  URN =		{urn:nbn:de:0030-drops-231060},
  doi =		{10.4230/LIPIcs.CPM.2025.12},
  annote =	{Keywords: string algorithm, graph algorithm, de Bruijn graph, Eulerian graph}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.16
Net Occurrences in Fibonacci and Thue-Morse Words

Authors: Peaker Guo and Kaisei Kishi

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
A net occurrence of a repeated string in a text is an occurrence with unique left and right extensions, and the net frequency of the string is the number of its net occurrences in the text. Originally introduced for applications in Natural Language Processing, net frequency has recently gained attention for its algorithmic aspects. Guo et al. [CPM 2024] and Ohlebusch et al. [SPIRE 2024] focus on its computation in the offline setting, while Guo et al. [SPIRE 2024], Inenaga [arXiv 2024], and Mieno and Inenaga [CPM 2025] tackle the online counterpart. Mieno and Inenaga also characterize net occurrences in terms of the minimal unique substrings of the text. Additionally, Guo et al. [CPM 2024] initiate the study of net occurrences in Fibonacci words to establish a lower bound on the asymptotic running time of algorithms. Although there has been notable progress in algorithmic developments and some initial combinatorial insights, the combinatorial aspects of net occurrences have yet to be thoroughly examined. In this work, we make two key contributions. First, we confirm the conjecture that each Fibonacci word contains exactly three net occurrences. Second, we show that each Thue-Morse word contains exactly nine net occurrences. To achieve these results, we introduce the notion of overlapping net occurrence cover, which narrows down the candidate net occurrences in any text. Furthermore, we provide a precise characterization of occurrences of Fibonacci and Thue-Morse words of smaller order, offering structural insights that may have independent interest and potential applications in algorithm analysis and combinatorial properties of these words.
Cite as

Peaker Guo and Kaisei Kishi. Net Occurrences in Fibonacci and Thue-Morse Words. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 16:1-16:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{guo_et_al:LIPIcs.CPM.2025.16,
  author =	{Guo, Peaker and Kishi, Kaisei},
  title =	{{Net Occurrences in Fibonacci and Thue-Morse Words}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{16:1--16:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.16},
  URN =		{urn:nbn:de:0030-drops-231107},
  doi =		{10.4230/LIPIcs.CPM.2025.16},
  annote =	{Keywords: Fibonacci words, Thue-Morse words, net occurrence, net frequency, factorization}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.20
Text Indexing for Simple Regular Expressions

Authors: Hideo Bannai, Philip Bille, Inge Li Gørtz, Gad M. Landau, Gonzalo Navarro, Nicola Prezza, Teresa Anna Steiner, and Simon Rumle Tarnow

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
We study the problem of indexing a text T[1..n] ∈ Σⁿ so that, later, given a query regular expression pattern R of size m = |R|, we can report all the occ substrings T[i..j] of T matching R. The problem is known to be hard for arbitrary patterns R, so in this paper, we consider the following two types of patterns. (1) Character-class Kleene-star patterns of the form P₁ D^* P₂, where P₁ and P₂ are strings and D = {c₁, …, c_k} ⊂ Σ is a character-class (shorthand for the regular expression (c₁ | c₂ | ⋯ | c_k)) and (2) String Kleene-star patterns of the form P₁ P^* P₂ where P, P₁ and P₂ are strings. In case (1), we describe an index of O(nlog^{1+ε}n) space (for any constant ε > 0) solving queries in time O(m + log n/log log n + occ) on constant-sized alphabets. We also describe a general solution for any alphabet size. This result is conditioned on the existence of an anchor: a character of P₁P₂ that does not belong to D. We justify this assumption by proving that no efficient indexing solution can exist if an anchor is not present unless the Set Disjointness Conjecture fails. In case (2), we describe an index of size O(n) answering queries in time O(m + (occ+1)log^{ε}n) on any alphabet size.
Cite as

Hideo Bannai, Philip Bille, Inge Li Gørtz, Gad M. Landau, Gonzalo Navarro, Nicola Prezza, Teresa Anna Steiner, and Simon Rumle Tarnow. Text Indexing for Simple Regular Expressions. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bannai_et_al:LIPIcs.CPM.2025.20,
  author =	{Bannai, Hideo and Bille, Philip and G{\o}rtz, Inge Li and Landau, Gad M. and Navarro, Gonzalo and Prezza, Nicola and Steiner, Teresa Anna and Tarnow, Simon Rumle},
  title =	{{Text Indexing for Simple Regular Expressions}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{20:1--20:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.20},
  URN =		{urn:nbn:de:0030-drops-231143},
  doi =		{10.4230/LIPIcs.CPM.2025.20},
  annote =	{Keywords: Text indexing, regular expressions, data structures}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.21
Compressed Dictionary Matching on Run-Length Encoded Strings

Authors: Philip Bille, Inge Li Gørtz, Simon J. Puglisi, and Simon R. Tarnow

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
Given a set of pattern strings 𝒫 = {P₁, P₂,… P_k} and a text string S, the classic dictionary matching problem is to report all occurrences of each pattern in S. We study the dictionary problem in the compressed setting, where the pattern strings and the text string are compressed using run-length encoding, and the goal is to solve the problem without decompression and achieve efficient time and space in the size of the compressed strings. Let m and n be the total length of the patterns 𝒫 and the length of the text string S, respectively, and let ̅m and ̅n be the total number of runs in the run-length encoding of the patterns in 𝒫 and S, respectively. Our main result is an algorithm that achieves O(( ̅m + ̅n)log log m + occ) expected time, and O( ̅m) space, where occ is the total number of occurrences of patterns in S. This is the first non-trivial solution to the problem. Since any solution must read the input, our time bound is optimal within an log log m factor. We introduce several new techniques to achieve our bounds, including a new compressed representation of the classic Aho-Corasick automaton and a new efficient string index that supports fast queries in run-length encoded strings.
Cite as

Philip Bille, Inge Li Gørtz, Simon J. Puglisi, and Simon R. Tarnow. Compressed Dictionary Matching on Run-Length Encoded Strings. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bille_et_al:LIPIcs.CPM.2025.21,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Puglisi, Simon J. and Tarnow, Simon R.},
  title =	{{Compressed Dictionary Matching on Run-Length Encoded Strings}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{21:1--21:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.21},
  URN =		{urn:nbn:de:0030-drops-231158},
  doi =		{10.4230/LIPIcs.CPM.2025.21},
  annote =	{Keywords: Dictionary matching, run-length encoding, compressed pattern matching}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.6
String Problems in the Congested Clique Model

Authors: Shay Golan and Matan Kraus

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
In this paper we present algorithms for several string problems in the Congested Clique model. In the Congested Clique model, n nodes (computers) are used to solve some problem. The input to the problem is distributed among the nodes, and the communication between the nodes is conducted in rounds. In each round, every node is allowed to send an O(log n)-bit message to every other node in the network. We consider three fundamental string problems in the Congested Clique model. First, we present an O(1) rounds algorithm for string sorting that supports strings of arbitrary length. Second, we present an O(1) rounds combinatorial pattern matching algorithm. Finally, we present an O(log log n) rounds algorithm for the computation of the suffix array and the corresponding Longest Common Prefix array of a given string.
Cite as

Shay Golan and Matan Kraus. String Problems in the Congested Clique Model. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{golan_et_al:LIPIcs.CPM.2025.6,
  author =	{Golan, Shay and Kraus, Matan},
  title =	{{String Problems in the Congested Clique Model}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.6},
  URN =		{urn:nbn:de:0030-drops-231003},
  doi =		{10.4230/LIPIcs.CPM.2025.6},
  annote =	{Keywords: String Sorting, Pattern Matching, Suffix Array, Congested Clique, Sorting}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.5
Covers in Optimal Space

Authors: Itai Boneh and Shay Golan

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
A cover of a string S is a string C such that every index of S is contained in some occurrence of C. First introduced by Apostolico and Ehrenfeucht [TCS'93] over 30 years ago, covers have since received significant attention in the string algorithms community. In this work, we present a space-efficient algorithm for computing a compact representation of all covers of a given string. Our algorithm requires only O(log n) additional memory while accessing the input string of length n in a read-only manner. Moreover, it runs in O(n) time, matching the best-known time complexity for this problem while achieving an exponential improvement in space usage.
Cite as

Itai Boneh and Shay Golan. Covers in Optimal Space. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{boneh_et_al:LIPIcs.CPM.2025.5,
  author =	{Boneh, Itai and Golan, Shay},
  title =	{{Covers in Optimal Space}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{5:1--5:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.5},
  URN =		{urn:nbn:de:0030-drops-230993},
  doi =		{10.4230/LIPIcs.CPM.2025.5},
  annote =	{Keywords: Cover, Read-only random access, small space}
}
Document
DOI: 10.4230/LIPIcs.CPM.2024.25
Walking on Words

Authors: Ian Pratt-Hartmann

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract
Any function f with domain {1, … , m} and co-domain {1, … , n} induces a natural map from words of length n to those of length m: the ith letter of the output word (1 ≤ i ≤ m) is given by the f(i)th letter of the input word. We study this map in the case where f is a surjection satisfying the condition |f(i+1)-f(i)| ≤ 1 for 1 ≤ i < m. Intuitively, we think of f as describing a "walk" on a word u, visiting every position, and yielding a word w as the sequence of letters encountered en route. If such an f exists, we say that u generates w. Call a word primitive if it is not generated by any word shorter than itself. We show that every word has, up to reversal, a unique primitive generator. Observing that, if a word contains a non-trivial palindrome, it can generate the same word via essentially different walks, we obtain conditions under which, for a chosen pair of walks f and g, those walks yield the same word when applied to a given primitive word. Although the original impulse for studying primitive generators comes from their application to decision procedures in logic, we end, by way of further motivation, with an analysis of the primitive generators for certain word sequences defined via morphisms.
Cite as

Ian Pratt-Hartmann. Walking on Words. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{pratthartmann:LIPIcs.CPM.2024.25,
  author =	{Pratt-Hartmann, Ian},
  title =	{{Walking on Words}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke 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.CPM.2024.25},
  URN =		{urn:nbn:de:0030-drops-201352},
  doi =		{10.4230/LIPIcs.CPM.2024.25},
  annote =	{Keywords: word combinatorics, palindrome, Rauzy morphism}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.22
Generating Verified LLVM from Isabelle/HOL

Authors: Peter Lammich

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
We present a framework to generate verified LLVM programs from Isabelle/HOL. It is based on a code generator that generates LLVM text from a simplified fragment of LLVM, shallowly embedded into Isabelle/HOL. On top, we have developed a separation logic, a verification condition generator, and an LLVM backend to the Isabelle Refinement Framework. As case studies, we have produced verified LLVM implementations of binary search and the Knuth-Morris-Pratt string search algorithm. These are one order of magnitude faster than the Standard-ML implementations produced with the original Refinement Framework, and on par with unverified C implementations. Adoption of the original correctness proofs to the new LLVM backend was straightforward. The trusted code base of our approach is the shallow embedding of the LLVM fragment and the code generator, which is a pretty printer combined with some straightforward compilation steps.
Cite as

Peter Lammich. Generating Verified LLVM from Isabelle/HOL. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{lammich:LIPIcs.ITP.2019.22,
  author =	{Lammich, Peter},
  title =	{{Generating Verified LLVM from Isabelle/HOL}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.22},
  URN =		{urn:nbn:de:0030-drops-110777},
  doi =		{10.4230/LIPIcs.ITP.2019.22},
  annote =	{Keywords: Isabelle/HOL, LLVM, Separation Logic, Verification Condition Generator, Code Generation}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2016.30
Time-Space Trade-offs for Triangulating a Simple Polygon

Authors: Boris Aronov, Matias Korman, Simon Pratt, André van Renssen, and Marcel Roeloffzen

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Abstract
An s-workspace algorithm is an algorithm that has read-only access to the values of the input, write-only access to the output, and only uses O(s) additional words of space. We give a randomized s-workspace algorithm for triangulating a simple polygon P of n vertices, for any s up to n. The algorithm runs in O(n^2/s+n(log s)log^5(n/s)) expected time using O(s) variables, for any s up to n. In particular, the algorithm runs in O(n^2/s) expected time for most values of s.
Cite as

Boris Aronov, Matias Korman, Simon Pratt, André van Renssen, and Marcel Roeloffzen. Time-Space Trade-offs for Triangulating a Simple Polygon. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 30:1-30:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{aronov_et_al:LIPIcs.SWAT.2016.30,
  author =	{Aronov, Boris and Korman, Matias and Pratt, Simon and van Renssen, André and Roeloffzen, Marcel},
  title =	{{Time-Space Trade-offs for Triangulating a Simple Polygon}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{30:1--30:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.30},
  URN =		{urn:nbn:de:0030-drops-60522},
  doi =		{10.4230/LIPIcs.SWAT.2016.30},
  annote =	{Keywords: simple polygon, triangulation, shortest path, time-space trade-off}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2016.28
Two Approaches to Building Time-Windowed Geometric Data Structures

Authors: Timothy M. Chan and Simon Pratt

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

Abstract
Given a set of geometric objects each associated with a time value, we wish to determine whether a given property is true for a subset of those objects whose time values fall within a query time window. We call such problems time-windowed decision problems, and they have been the subject of much recent attention, for instance studied by Bokal, Cabello, and Eppstein [SoCG 2015]. In this paper, we present new approaches to this class of problems that are conceptually simpler than Bokal et al.'s, and also lead to faster algorithms. For instance, we present algorithms for preprocessing for the time-windowed 2D diameter decision problem in O(n log n) time and the time-windowed 2D convex hull area decision problem in O(n alpha(n) log n) time (where alpha is the inverse Ackermann function), improving Bokal et al.'s O(n log^2 n) and O(n log n loglog n) solutions respectively. Our first approach is to reduce time-windowed decision problems to a generalized range successor problem, which we solve using a novel way to search range trees. Our other approach is to use dynamic data structures directly, taking advantage of a new observation that the total number of combinatorial changes to a planar convex hull is near linear for any FIFO update sequence, in which deletions occur in the same order as insertions. We also apply these approaches to obtain the first O(n polylog n) algorithms for the time-windowed 3D diameter decision and 2D orthogonal segment intersection detection problems.
Cite as

Timothy M. Chan and Simon Pratt. Two Approaches to Building Time-Windowed Geometric Data Structures. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chan_et_al:LIPIcs.SoCG.2016.28,
  author =	{Chan, Timothy M. and Pratt, Simon},
  title =	{{Two Approaches to Building Time-Windowed Geometric Data Structures}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.28},
  URN =		{urn:nbn:de:0030-drops-59201},
  doi =		{10.4230/LIPIcs.SoCG.2016.28},
  annote =	{Keywords: time window, geometric data structures, range searching, dynamic convex hull}
}
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