71 Search Results for "Munro, Ian"

Document
DOI: 10.4230/LIPIcs.STACS.2026.62
Relative Compressed Reverse Suffix Array

Authors: Muhammed Oguzhan Kulekci, Mano Prakash Parthasarathi, Rahul Shah, and Sharma V. Thankachan

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Suffix trees and suffix arrays are two fundamental data structures in the field of string algorithms. For a string (a.k.a. text or sequence) of length n over an alphabet of size σ, these structures typically require O(nlog n) bits of space. The FM-index provides a compressed representation of the suffix array in ≈ nlog σ bits, allowing for efficient queries on both the suffix array and its inverse array in near logarithmic time. In certain applications, such as approximate pattern matching (i.e., with wildcards, mismatches, edits), there is a need to access the suffix array of a text, as well as the suffix array of text’s reverse. Motivated by this, we explore the possibility of encoding the suffix array of the reversed text in a compact form, assuming the availability of the FM-index for the original text. Our first solution is an O(n)-bit (relative) encoding of the suffix array of the reversed text, with the time for decoding an entry being only O(log^*n) times that of decoding an entry in the text’s suffix array using FM-index. We then demonstrate how to reduce the space to O(n/κ) bits for a parameter κ, while multiplicative factor in time becomes approximately O(κlog^*n+κ³). We can also support inverse suffix array and longest common extension queries on the reversed text. These results are achieved through some careful and non-trivial application of various succinct data structure techniques.
Cite as

Muhammed Oguzhan Kulekci, Mano Prakash Parthasarathi, Rahul Shah, and Sharma V. Thankachan. Relative Compressed Reverse Suffix Array. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 62:1-62:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kulekci_et_al:LIPIcs.STACS.2026.62,
  author =	{Kulekci, Muhammed Oguzhan and Parthasarathi, Mano Prakash and Shah, Rahul and Thankachan, Sharma V.},
  title =	{{Relative Compressed Reverse Suffix Array}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{62:1--62:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.62},
  URN =		{urn:nbn:de:0030-drops-255512},
  doi =		{10.4230/LIPIcs.STACS.2026.62},
  annote =	{Keywords: String Matching, Text Indexing, Data Structures, Suffix Trees}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.31
Delaunay Triangulations with Predictions

Authors: Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set P of n points in the plane and a triangulation G that serves as a "prediction" of the Delaunay triangulation, we would like to use G to compute the correct Delaunay triangulation DT(P) more quickly when G is "close" to DT(P). We obtain a variety of results of this type, under different deterministic and probabilistic settings, including the following: 1) Define D to be the number of edges in G that are not in DT(P). We present a deterministic algorithm to compute DT(P) from G in O(n + Dlog³ n) time, and a randomized algorithm in O(n+Dlog n) expected time, the latter of which is optimal in terms of D. 2) Let R be a random subset of the edges of DT(P), where each edge is chosen independently with probability ρ. Suppose G is any triangulation of P that contains R. We present an algorithm to compute DT(P) from G in O(nlog log n + nlog(1/ρ)) time with high probability. 3) Define d_{vio} to be the maximum number of points of P strictly inside the circumcircle of a triangle in G (the number is 0 if G is equal to DT(P)). We present a deterministic algorithm to compute DT(P) from G in O(nlog^*n + nlog d_{vio}) time. We also obtain results in similar settings for related problems such as 2D Euclidean minimum spanning trees, and hope that our work will open up a fruitful line of future research.
Cite as

Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos. Delaunay Triangulations with Predictions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cabello_et_al:LIPIcs.ITCS.2026.31,
  author =	{Cabello, Sergio and Chan, Timothy M. and Giannopoulos, Panos},
  title =	{{Delaunay Triangulations with Predictions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{31:1--31:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  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.ITCS.2026.31},
  URN =		{urn:nbn:de:0030-drops-253186},
  doi =		{10.4230/LIPIcs.ITCS.2026.31},
  annote =	{Keywords: Delaunay Triangulation, Minimum Spanning Tree, Algorithms with Predictions}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.29
Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings

Authors: Michael Elberfeld, Frank Kammer, and Johannes Meintrup

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
We call a graph G separable if a balanced separator can be computed for G of size O(n^ε) with ε < 1. Many real-world graphs are separable such as graphs of bounded genus, graphs of constant treewidth, and graphs excluding a fixed minor. In particular, the well-known planar graphs are separable. We present a succinct encoding of separable graphs G such that, after the encoding is computed, any number of depth-first searches (DFS) can be performed from any given start vertex, each in o(n) time and o(n) bits in the word RAM model. After the execution of a DFS, the succinct encoding of G is augmented such that the DFS tree is encoded inside the encoding while maintaining succinctness. Afterward, the encoding provides common DFS-related queries in constant time. These queries include queries such as lowest-common ancestor of two given vertices in the DFS tree or queries that output the lowpoint of a given vertex in the DFS tree. Furthermore, for planar graphs, we show that the succinct encoding can be computed in O(n) bits and expected linear time, and a compact variant can be constructed in O(n) time and bits. For other separable graph classes 𝒢 the runtime and space usage depends on the specific algorithms used to find balanced separators in graphs of 𝒢.
Cite as

Michael Elberfeld, Frank Kammer, and Johannes Meintrup. Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elberfeld_et_al:LIPIcs.ISAAC.2025.29,
  author =	{Elberfeld, Michael and Kammer, Frank and Meintrup, Johannes},
  title =	{{Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.29},
  URN =		{urn:nbn:de:0030-drops-249379},
  doi =		{10.4230/LIPIcs.ISAAC.2025.29},
  annote =	{Keywords: Depth-First Search, Succinct, Space Efficient, Separable Graphs, Planar Graphs, Table Lookup, r-Division}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.TIME.2025.20
Temporal Considerations in DJ Mix Information Retrieval and Generation (Short Paper)

Authors: Alexander Williams, Gregor Meehan, Stefan Lattner, Johan Pauwels, and Mathieu Barthet

Published in: LIPIcs, Volume 355, 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)

Abstract
Music is the art of arranging sounds in time so as to produce a continuous, unified, and evocative composition. Electronic dance music (EDM) is a collection of musical sub-genres produced using computers and electronic instruments and often presented through the medium of DJing, where tracks are curated and mixed sequentially into a continuous stream of music to offer unique listening and dancing experiences over time periods ranging from several minutes to several hours. A DJ’s actions and decisions occur at several levels of temporal granularity, from real-time audio manipulation (e.g. of tempo) for smooth inter-track transitions to long-term planning of track selection and sequencing for mix content and flow. While human DJs can instinctively operate across these different temporal resolutions, replicating this capability in an end-to-end automated DJing system presents significant challenges. In this paper, we analyse existing works in DJ mix information retrieval and generation from this temporal perspective. We first explain the close link between DJing and the temporal notion of musical rhythm, then describe a framework for categorising DJing actions by temporal granularity. Using this framework, we summarise and contrast potential approaches for automating and augmenting sequential DJ decision making, and discuss the unique characteristics of DJ mix track selection as a sequential recommendation task. In doing so, we hope to facilitate the implementation of more robust and complete automated DJing systems in future research.
Cite as

Alexander Williams, Gregor Meehan, Stefan Lattner, Johan Pauwels, and Mathieu Barthet. Temporal Considerations in DJ Mix Information Retrieval and Generation (Short Paper). In 32nd International Symposium on Temporal Representation and Reasoning (TIME 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 355, pp. 20:1-20:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{williams_et_al:LIPIcs.TIME.2025.20,
  author =	{Williams, Alexander and Meehan, Gregor and Lattner, Stefan and Pauwels, Johan and Barthet, Mathieu},
  title =	{{Temporal Considerations in DJ Mix Information Retrieval and Generation}},
  booktitle =	{32nd International Symposium on Temporal Representation and Reasoning (TIME 2025)},
  pages =	{20:1--20:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-401-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{355},
  editor =	{Vidal, Thierry and Wa{\l}\k{e}ga, Przemys{\l}aw Andrzej},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2025.20},
  URN =		{urn:nbn:de:0030-drops-244662},
  doi =		{10.4230/LIPIcs.TIME.2025.20},
  annote =	{Keywords: Music Information Retrieval, Computational Creativity, Recommender Systems, Electronic Dance Music, DJ}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.94
Faster Algorithm for Bounded Tree Edit Distance in the Low-Distance Regime

Authors: Tomasz Kociumaka and Ali Shahali

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

Abstract
The tree edit distance is a natural dissimilarity measure between rooted ordered trees whose nodes are labeled over an alphabet Σ. It is defined as the minimum number of node edits - insertions, deletions, and relabelings - required to transform one tree into the other. The weighted variant assigns costs ≥ 1 to edits (based on node labels), minimizing total cost rather than edit count. The unweighted tree edit distance between two trees of total size n can be computed in 𝒪(n^{2.6857}) time; in contrast, determining the weighted tree edit distance is fine-grained equivalent to the All-Pairs Shortest Paths (APSP) problem and requires n³/2^Ω(√{log n}) time [Nogler, Polak, Saha, Vassilevska Williams, Xu, Ye; STOC'25]. These impractical super-quadratic times for large, similar trees motivate the bounded version, parameterizing runtime by the distance k to enable faster algorithms for k ≪ n. Prior algorithms for bounded unweighted edit distance achieve 𝒪(nk²log n) [Akmal & Jin; ICALP’21] and 𝒪(n + k⁷log k) [Das, Gilbert, Hajiaghayi, Kociumaka, Saha; STOC'23]. For weighted, only 𝒪(n + k^{15}) is known [Das, Gilbert, Hajiaghayi, Kociumaka, Saha; STOC'23]. We present an 𝒪(n + k⁶ log k)-time algorithm for bounded tree edit distance in both weighted/unweighted settings. First, we devise a simpler weighted 𝒪(nk² log n)-time algorithm. Next, we exploit periodic structures in input trees via an optimized universal kernel: modifying prior 𝒪(n)-time 𝒪(k⁵)-size kernels to generate such structured instances, enabling efficient analysis.
Cite as

Tomasz Kociumaka and Ali Shahali. Faster Algorithm for Bounded Tree Edit Distance in the Low-Distance Regime. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 94:1-94:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kociumaka_et_al:LIPIcs.ESA.2025.94,
  author =	{Kociumaka, Tomasz and Shahali, Ali},
  title =	{{Faster Algorithm for Bounded Tree Edit Distance in the Low-Distance Regime}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{94:1--94:16},
  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.2025.94},
  URN =		{urn:nbn:de:0030-drops-245634},
  doi =		{10.4230/LIPIcs.ESA.2025.94},
  annote =	{Keywords: tree edit distance, edit distance, kernelization, dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.5
External-Memory Priority Queues with Optimal Insertions

Authors: Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning

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

Abstract
We present an external-memory priority queue structure supporting Insert and DeleteMin with amortized 𝒪(1) and 𝒪(lg N) comparisons, respectively, and amortized 𝒪(1/B) and 𝒪(1/B log_{M/B} N/B) I/Os, respectively. Here, M is the size of the internal memory, B is the block size of I/Os between internal and external memory, and N is the number of elements in the priority queue just before an operation is performed. Previous external-memory priority queues required amortized 𝒪(lg N) comparisons and 𝒪(1/B log_{M/B} N/B) I/Os for both Insert and DeleteMin. The construction requires the minimal assumption M ≥ 2B.
Cite as

Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning. External-Memory Priority Queues with Optimal Insertions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brodal_et_al:LIPIcs.ESA.2025.5,
  author =	{Brodal, Gerth St{\o}lting and Goodrich, Michael T. and Iacono, John and Lo, Jared and Meyer, Ulrich and Pagan, Victor and Sitchinava, Nodari and Svenning, Rolf},
  title =	{{External-Memory Priority Queues with Optimal Insertions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{5:1--5:14},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-244734},
  doi =		{10.4230/LIPIcs.ESA.2025.5},
  annote =	{Keywords: priority queues, external memory, cache aware, amortized complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.25
Instance-Optimal Imprecise Convex Hull

Authors: Sarita de Berg, Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann, and Sampson Wong

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

Abstract
Imprecise measurements of a point set P = (p₁, …, p_n) can be modelled by a family of regions F = (R₁, …, R_n), where each imprecise region R_i ∈ F contains a unique point p_i ∈ P. A retrieval models an accurate measurement by replacing an imprecise region R_i with its corresponding point p_i. We construct the convex hull of an imprecise point set in the plane, by determining the cyclic ordering of the convex hull vertices of P as efficiently as possible. Efficiency is interpreted in two ways: (i) minimising the number of retrievals, and (ii) the computation time to determine the set of regions that must be retrieved. Previous works focused on only one of these two aspects: either minimising retrievals or optimising algorithmic runtime. Our contribution is the first to simultaneously achieve both. Let r(F, P) denote the minimal number of retrievals required by any algorithm to determine the convex hull of P for a given instance (F, P). For a family F of n constant-complexity polygons, our main result is a reconstruction algorithm that performs Θ(r(F, P)) retrievals in O(r(F, P) log³ n) time. Compared to previous approaches that achieve optimal retrieval counts, we improve the runtime per retrieval from polynomial to polylogarithmic. We extend the generality of previous results to simple k-gons, to pairwise disjoint disks with radii in [1,k], and to unit disks where at most k disks overlap in a single point. Our runtime scales linearly with k.
Cite as

Sarita de Berg, Ivor van der Hoog, Eva Rotenberg, Daniel Rutschmann, and Sampson Wong. Instance-Optimal Imprecise Convex Hull. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{deberg_et_al:LIPIcs.ESA.2025.25,
  author =	{de Berg, Sarita and van der Hoog, Ivor and Rotenberg, Eva and Rutschmann, Daniel and Wong, Sampson},
  title =	{{Instance-Optimal Imprecise Convex Hull}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{25:1--25:15},
  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.2025.25},
  URN =		{urn:nbn:de:0030-drops-244932},
  doi =		{10.4230/LIPIcs.ESA.2025.25},
  annote =	{Keywords: convex hull, imprecise geometry preprocessing model, partial information}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.71
Simpler Universally Optimal Dijkstra

Authors: Ivor van der Hoog, Eva Rotenberg, and Daniel Rutschmann

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

Abstract
Let G be a weighted (directed) graph with n vertices and m edges. Given a source vertex s, Dijkstra’s algorithm computes the shortest path lengths from s to all other vertices in O(m + n log n) time. This bound is known to be worst-case optimal via a reduction to sorting. Theoretical computer science has developed numerous fine-grained frameworks for analyzing algorithmic performance beyond standard worst-case analysis, such as instance optimality and output sensitivity. Haeupler, Hladík, Rozhoň, Tarjan, and Tětek [FOCS '24] consider the notion of universal optimality, a refined complexity measure that accounts for both the graph topology and the edge weights. For a fixed graph topology, the universal running time of a weighted graph algorithm is defined as its worst-case running time over all possible edge weightings of G. An algorithm is universally optimal if no other algorithm achieves a better asymptotic universal running time on any particular graph topology. Haeupler, Hladík, Rozhoň, Tarjan, and Tětek show that Dijkstra’s algorithm can be made universally optimal by replacing the heap with a custom data structure. Their approach builds on Iacono’s [SWAT '00] working-set bound ϕ(x). This is a technical definition that, intuitively, for a heap element x, counts the maximum number of simultaneously-present elements y that were pushed onto the heap whilst x was in the heap. They design a new heap data structure that can pop an element x in O(1 + log ϕ(x)) time. They show that Dijkstra’s algorithm with their heap data structure is universally optimal. In this work, we revisit their result. We use a simpler heap property that we will call timestamp optimality, where the cost of popping an element x is logarithmic in the number of elements inserted between pushing and popping x. We show that timestamp optimal heaps are not only easier to define but also easier to implement. Using these time stamps, we provide a significantly simpler proof that Dijkstra’s algorithm, with the right kind of heap, is universally optimal.
Cite as

Ivor van der Hoog, Eva Rotenberg, and Daniel Rutschmann. Simpler Universally Optimal Dijkstra. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 71:1-71:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanderhoog_et_al:LIPIcs.ESA.2025.71,
  author =	{van der Hoog, Ivor and Rotenberg, Eva and Rutschmann, Daniel},
  title =	{{Simpler Universally Optimal Dijkstra}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{71:1--71:9},
  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.2025.71},
  URN =		{urn:nbn:de:0030-drops-245390},
  doi =		{10.4230/LIPIcs.ESA.2025.71},
  annote =	{Keywords: Graph algorithms, instance optimality, Fibonnacci heaps, simplification}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.76
A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs

Authors: Mateusz Basiak, Marcin Bienkowski, Martin Böhm, Marek Chrobak, Łukasz Jeż, Jiří Sgall, and Agnieszka Tatarczuk

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

Abstract
We consider the List Update problem where the cost of each swap is assumed to be 1. This is in contrast to the "standard" model, in which an algorithm is allowed to swap the requested item with previous items for free. We construct an online algorithm Full-Or-Partial-Move (FPM), whose competitive ratio is at most 3.3904, improving over the previous best known bound of 4.
Cite as

Mateusz Basiak, Marcin Bienkowski, Martin Böhm, Marek Chrobak, Łukasz Jeż, Jiří Sgall, and Agnieszka Tatarczuk. A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 76:1-76:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{basiak_et_al:LIPIcs.ESA.2025.76,
  author =	{Basiak, Mateusz and Bienkowski, Marcin and B\"{o}hm, Martin and Chrobak, Marek and Je\.{z}, {\L}ukasz and Sgall, Ji\v{r}{\'\i} and Tatarczuk, Agnieszka},
  title =	{{A 3.3904-Competitive Online Algorithm for List Update with Uniform Costs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{76:1--76:15},
  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.2025.76},
  URN =		{urn:nbn:de:0030-drops-245442},
  doi =		{10.4230/LIPIcs.ESA.2025.76},
  annote =	{Keywords: List update, work functions, amortized analysis, online algorithms, competitive analysis}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.72
Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions

Authors: Noam Horowicz and Tsvi Kopelowitz

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

Abstract
In the snippets problem, the goal is to preprocess a text T so that given two pattern queries, P₁ and P₂, one can quickly locate the occurrences of the two patterns in T that are closest to each other, or report the distance between these occurrences. Kopelowitz and Krauthgamer [CPM2016] showed upper bound tradeoffs and conditional lower bounds tradeoffs for the snippets problem, by utilizing connections between the snippets problem and the problem of constructing a color distance oracle (CDO), which is a data structure that preprocess a set of points with associated colors so that given two colors c and c' one can quickly find the (distance between the) closest pair of points where one has color c and the other has color c'. However, the existing upper bound and lower bound curves are not tight. Inspired by recent advances by Kopelowitz and Vassilevska-Williams [ICALP2020] regarding tradeoff curves for Set-disjointness data structures, in this paper we introduce new conditionally optimal algorithms for a (1+ε) approximation version of the snippets problem and a (1+ε) approximation version of the CDO problem, by applying fast matrix multiplication. For example, for CDO on n points in an array, if the preprocessing time is Õ(n^a) and the query time is Õ(n^b) then, assuming that ω = 2 (where ω is the exponent of n in the runtime of the fastest matrix multiplication algorithm on two squared matrices of size n× n), we show that approximate CDO can be solved with the following tradeoff a + 2b = 2 (if 0 ≤ b ≤ 1/3) 2a + b = 3 (if 1/3 ≤ b ≤ 1). Moreover, we prove that for exact CDO on points in an array, the algorithm of Kopelowitz and Krauthgamer [CPM2016], which obtains a tradeoff of a+b = 2, is essentially optimal assuming that the strong all-pairs shortest paths hypothesis holds for randomized algorithms. Thus, we demonstrate that the exact version of CDO is strictly harder than the approximate version. Moreover, this separation carries over to the snippets problem.
Cite as

Noam Horowicz and Tsvi Kopelowitz. Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 72:1-72:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{horowicz_et_al:LIPIcs.ESA.2025.72,
  author =	{Horowicz, Noam and Kopelowitz, Tsvi},
  title =	{{Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{72:1--72:17},
  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.2025.72},
  URN =		{urn:nbn:de:0030-drops-245403},
  doi =		{10.4230/LIPIcs.ESA.2025.72},
  annote =	{Keywords: data structures, fast matrix multiplication, fine-grained complexity, pattern matching, distance oracles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.60
Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars

Authors: Jannik Olbrich

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

Abstract
The Burrows-Wheeler Transform (BWT) serves as the basis for many important sequence indexes. On very large datasets (e.g. genomic databases), classical BWT construction algorithms are often infeasible because they usually need to have the entire dataset in main memory. Fortunately, such large datasets are often highly repetitive. It can thus be beneficial to compute the BWT from a compressed representation. We propose an algorithm for computing the BWT via the Lyndon straight-line program, a grammar based on the standard factorization of Lyndon words. Our algorithm can also be used to compute the extended BWT (eBWT) of a multiset of sequences. We empirically evaluate our implementation and find that we can compute the BWT and eBWT of very large datasets faster and/or with less memory than competing methods.
Cite as

Jannik Olbrich. Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 60:1-60:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{olbrich:LIPIcs.ESA.2025.60,
  author =	{Olbrich, Jannik},
  title =	{{Fast and Memory-Efficient BWT Construction of Repetitive Texts Using Lyndon Grammars}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{60:1--60:19},
  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.2025.60},
  URN =		{urn:nbn:de:0030-drops-245286},
  doi =		{10.4230/LIPIcs.ESA.2025.60},
  annote =	{Keywords: Burrows-Wheeler Transform, Grammar compression}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.104
Optimal Antimatroid Sorting

Authors: Benjamin Aram Berendsohn

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

Abstract
The classical comparison-based sorting problem asks us to find the underlying total ordering of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a set T of possible total orderings is given, usually in some compressed form. Recently, an algorithm called topological heapsort with optimal running time was found for case where T is the set of topological orderings of a given directed acyclic graph, or, equivalently, T is the set of linear extensions of a partial ordering [Haeupler et al. 2024]. We show that a simple generalization of topological heapsort is applicable to a much broader class of restricted sorting problems, where T corresponds to a given antimatroid. As a consequence, we obtain optimal algorithms for the following restricted sorting problems, where the allowed total orders are … - … restricted by a given set of monotone precedence formulas; - … the perfect elimination orders of a given chordal graph; or - … the possible vertex search orders of a given connected rooted graph.
Cite as

Benjamin Aram Berendsohn. Optimal Antimatroid Sorting. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 104:1-104:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berendsohn:LIPIcs.ESA.2025.104,
  author =	{Berendsohn, Benjamin Aram},
  title =	{{Optimal Antimatroid Sorting}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{104:1--104:14},
  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.2025.104},
  URN =		{urn:nbn:de:0030-drops-245735},
  doi =		{10.4230/LIPIcs.ESA.2025.104},
  annote =	{Keywords: sorting, working-set heap, greedy, antimatroid}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.39
Going Beyond Surfaces in Diameter Approximation

Authors: Michał Włodarczyk

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

Abstract
Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge weights, there are known (1+ε)-approximation algorithms with running time poly(1/ε, log n)⋅ n. However, these algorithms rely on shortest path separators and this technique falls short to yield efficient algorithms beyond graphs of bounded genus. In this work we depart from embedding-based arguments and obtain diameter approximations relying on VC set systems and the local treewidth property. We present two orthogonal extensions of the planar case by giving (1+ε)-approximation algorithms with the following running times: - 𝒪_h((1/ε)^𝒪(h) ⋅ nlog² n)-time algorithm for graphs excluding an apex graph of size h as a minor, - 𝒪_d((1/ε)^𝒪(d) ⋅ nlog² n)-time algorithm for the class of d-apex graphs. As a stepping stone, we obtain efficient (1+ε)-approximate distance oracles for graphs excluding an apex graph of size h as a minor. Our oracle has preprocessing time 𝒪_h((1/ε)⁸⋅ nlog nlog W) and query time 𝒪_h((1/ε)²⋅log n log W), where W is the metric stretch. Such oracles have been so far only known for bounded genus graphs. All our algorithms are deterministic.
Cite as

Michał Włodarczyk. Going Beyond Surfaces in Diameter Approximation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.ESA.2025.39,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Going Beyond Surfaces in Diameter Approximation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{39:1--39:19},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-245076},
  doi =		{10.4230/LIPIcs.ESA.2025.39},
  annote =	{Keywords: diameter, approximation, distance oracles, graph minors, treewidth}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.35
Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage

Authors: Meng He and Kaiyu Wu

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We improve the recent succinct data structure result of Balakrishnan et al. for chordal graphs with bounded vertex leafage (SWAT 2024). A chordal graph is a widely studied graph class which can be characterized as the intersection graph of subtrees of a host tree, denoted as a tree representation of the chordal graph. The vertex leafage and leafage parameters of a chordal graph deal with the existence of a tree representation with a bounded number of leaves in either the subtrees representing the vertices or the host tree itself. We simplify the lower bound proof of Balakrishnan et al. which applied to only chordal graphs with bounded vertex leafage, and extend it to a lower bound proof for chordal graphs with bounded leafage as well. For both classes of graphs, the information-theoretic lower bound we (re-)obtain for k = o(n) is (k-1)nlog n - knlog k - o(knlog n) bits, where the leafage or vertex leafage of the graph is at most k = o(n). We further extend the range of the parameter k to Θ(n) as well. Then we give a succinct data structure using (k-1)nlog (n/k) + o(knlog n) bits to answer adjacent queries, which test the adjacency between pairs of vertices, in O((log k)/(log log n) + 1) time compared to the O(klog n) time of the data structure of Balakrishnan et al. For the neighborhood query which lists the neighbours of a given vertex, our query time is O((log n)/(log log n)) per neighbour compared to O(k²log n) per neighbour. We also extend the data structure ideas to obtain a succinct data structure for chordal graphs with bounded leafage k, answering an open question of Balakrishnan et al. Our succinct data structure, which uses (k-1)nlog (n/k) + o(knlog n) bits, has query time O(1) for the adjacent query and O(1) per neighbour for the neighborhood query. Using slightly more space (an additional (1+ε)nlog n bits for any ε > 0) allows distance queries, which compute the number of edges in the shortest path between two given vertices, to be answered in O(1) time as well.
Cite as

Meng He and Kaiyu Wu. Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{he_et_al:LIPIcs.WADS.2025.35,
  author =	{He, Meng and Wu, Kaiyu},
  title =	{{Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{35:1--35:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.35},
  URN =		{urn:nbn:de:0030-drops-242660},
  doi =		{10.4230/LIPIcs.WADS.2025.35},
  annote =	{Keywords: Chordal Graph, Leafage, Vertex Leafage, Succinct Data Structure}
}
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}
}
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