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DOI: 10.4230/LIPIcs.SEA.2026.8

General Multiplicative Spanners in Practice

Authors: Fritz Bökler, Markus Chimani, and Henning Jasper

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

Given an undirected graph G with edge weights and lengths, a minimum α-spanner is a least-weight subgraph H ⊆ G that preserves distances w.r.t. the lengths between all node pairs up to a factor of α. Literature often takes the simplifying assumption of a single (coupled) edge function for weights and lengths. For such instances, several exact and non-exact algorithms are known and have been thoroughly evaluated in practice. However, many practical instances have decoupled form, as their weights and lengths are generally independent. Due to the increased complexity, only few (and even fewer practical) algorithms are able to guarantee low-weight solutions. This prompts practitioners to force their naturally decoupled instances into a coupled format, forsaking any quality guarantee. We implement several exact, approximative and heuristic algorithms for decoupled α-spanners, and use algorithm engineering to speed them up in practice. Our hypothesis-driven experiments evaluate their performance w.r.t. solution quality and speed. Generally, many practical instances can indeed be solved exactly within reasonable time, while LP-based approximation algorithms are not worthwhile. We find that standard greedy algorithms often yield acceptable results, but there are also practical instances for which they yield arbitrarily poor solutions. Here, augmented greedy variations offer a good compromise between solution quality and speed.

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Fritz Bökler, Markus Chimani, and Henning Jasper. General Multiplicative Spanners in Practice. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bokler_et_al:LIPIcs.SEA.2026.8,
  author =	{B\"{o}kler, Fritz and Chimani, Markus and Jasper, Henning},
  title =	{{General Multiplicative Spanners in Practice}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{8:1--8:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.8},
  URN =		{urn:nbn:de:0030-drops-260120},
  doi =		{10.4230/LIPIcs.SEA.2026.8},
  annote =	{Keywords: Graph spanners, ILP, experimental study, algorithm engineering}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.15

Computational Generation of Substrate-Specific Molecular Cages

Authors: Noé Demange, Yann Strozecki, and Sandrine Vial

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

In this paper, we propose a method to build molecular cages designed to capture a specific substrate. We model a cage as a graph of atoms with coordinates in space, and several constraints on their edges (degree, length and angle). We use a simple method to place binding patterns which are able to interact with certain parts of the substrate. We then propose an algorithm which considers all possible ways of connecting these binding patterns and try to construct the smallest possible molecular paths realizing these connections. We investigate many variants of our method in order to obtain the most efficient algorithm, able to build cages of more than a hundred atoms.

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Noé Demange, Yann Strozecki, and Sandrine Vial. Computational Generation of Substrate-Specific Molecular Cages. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 15:1-15:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{demange_et_al:LIPIcs.SEA.2026.15,
  author =	{Demange, No\'{e} and Strozecki, Yann and Vial, Sandrine},
  title =	{{Computational Generation of Substrate-Specific Molecular Cages}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{15:1--15:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.15},
  URN =		{urn:nbn:de:0030-drops-260191},
  doi =		{10.4230/LIPIcs.SEA.2026.15},
  annote =	{Keywords: Enumeration, Molecular Cage, Cheminformatics, Geometric Algorithms, Experimental Algorithms}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.24

ZOR Filters: Fast and Smaller Than Fuse Filters

Authors: Antoine Limasset

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

Probabilistic membership filters support fast approximate membership queries with controlled false-positive probability ε and are widely used across storage, analytics, networking, and bioinformatics [Chang et al., 2008; Niv Dayan et al., 2018; Broder and Mitzenmacher, 2004; Harris and Medvedev, 2020; Marchet and Limasset, 2023; Chikhi et al., 2025; Hernandez-Courbevoie et al., 2025]. In the static setting, low-overhead methods such as XOR, Fuse, and BuRR have been proposed [Graf and Lemire, 2020; Graf and Lemire, 2022; Dillinger et al., 2022; Ulrich and Renard, 2023]. Among these, Fuse filters are known for near-optimal query throughput. For XOR/Fuse-style peeling constructions, however, build success is only high probability, which complicates deterministic builds. We introduce ZOR filters, a deterministic continuation of XOR/Fuse-style constructions that guarantees termination while preserving the same XOR-based query mechanism. ZOR replaces restart-on-failure with deterministic peeling that abandons a small fraction of keys, and restores false-positive-only semantics by storing the remainder in a compact auxiliary structure. In our experiments, the abandoned fraction drops below 1% for moderate arity (e.g., N ≥ 5), so the auxiliary handles a negligible fraction of keys. As a result, ZOR filters can be substantially more memory-efficient than Fuse filters, with overhead below 1%, while not yet matching the near-optimal overhead of BuRR (below 0.1%). In query performance, ZOR-pure is close to Fuse and faster than BuRR on positive queries, while the complete interleaved variant trades additional negative-query latency for deterministic continuation. Relative to optimised Fuse/BuRR implementations [Graf and Lemire, 2022; Dillinger et al., 2022], the current ZOR prototype remains slower in construction because deterministic peeling requires explicit incidence handling; reducing this construction gap is an important direction for future work.

Cite as

Antoine Limasset. ZOR Filters: Fast and Smaller Than Fuse Filters. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{limasset:LIPIcs.SEA.2026.24,
  author =	{Limasset, Antoine},
  title =	{{ZOR Filters: Fast and Smaller Than Fuse Filters}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.24},
  URN =		{urn:nbn:de:0030-drops-260281},
  doi =		{10.4230/LIPIcs.SEA.2026.24},
  annote =	{Keywords: Data structure, Approximate Set Membership, Static filter}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.26

Engineering Algorithms for Dynamic Greedy Set Cover

Authors: Amitai Uzrad

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

In the dynamic set cover problem, the input is a dynamic universe of elements and a fixed collection of sets. As elements are inserted or deleted, the goal is to efficiently maintain an approximate minimum set cover. While the past decade has seen significant theoretical breakthroughs for this problem, a notable gap remains between theoretical design and practical performance, as no comprehensive experimental study currently exists to validate these results. In this paper, we bridge this gap by implementing and evaluating four greedy-based dynamic algorithms across a diverse range of real-world instances. We derive our implementations from state-of-the-art frameworks - such as [GKKP(STOC'17); SU(STOC'23); SUZ(FOCS'24)] - which we simplify by identifying and modifying intricate subroutines that optimize asymptotic bounds but hinder practical performance. We evaluate these algorithms based on solution quality (set cover size) and efficiency, which comprises update time - the time required to update the solution following each insertion/deletion - and recourse - the number of changes made to the solution per update. Each algorithm uses a parameter β to balance quality against efficiency; we investigate the influence of this tradeoff parameter on each algorithm and then perform a comparative analysis to evaluate the algorithms against each other. Our results provide the first practical insights into which algorithmic strategies provide the most value in realistic scenarios.

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Amitai Uzrad. Engineering Algorithms for Dynamic Greedy Set Cover. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{uzrad:LIPIcs.SEA.2026.26,
  author =	{Uzrad, Amitai},
  title =	{{Engineering Algorithms for Dynamic Greedy Set Cover}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.26},
  URN =		{urn:nbn:de:0030-drops-260308},
  doi =		{10.4230/LIPIcs.SEA.2026.26},
  annote =	{Keywords: Dynamic graphs, set cover, recourse}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.28

The Dual-Path Fixing Strategy and Its Application to the Set-Covering Problem

Authors: Paulo Michel F. Yamagishi, Marcia Fampa, and Jon Lee

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

We introduce the dual-path fixing strategy to exploit dual algorithms for solving relaxations of mixed-integer nonlinear-optimization problems. Such dual algorithms are naturally applied in the context of branch-and-bound, and eventual impact on the success of branch-and-bound is our strong motivation. Our fixing strategy aims to be more powerful than the common strategy of fixing variables based on a single dual-feasible solution (e.g., standard reduced-cost fixing for mixed-integer linear optimization), but to be much faster than "strong fixing", essentially requiring no more time than that of the dual algorithm that we exploit. We have successfully tested our ideas on mixed-integer linear-optimization set-covering instances from the literature, in the context of the dual-simplex method applied to the continuous relaxations.

Cite as

Paulo Michel F. Yamagishi, Marcia Fampa, and Jon Lee. The Dual-Path Fixing Strategy and Its Application to the Set-Covering Problem. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{yamagishi_et_al:LIPIcs.SEA.2026.28,
  author =	{Yamagishi, Paulo Michel F. and Fampa, Marcia and Lee, Jon},
  title =	{{The Dual-Path Fixing Strategy and Its Application to the Set-Covering Problem}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.28},
  URN =		{urn:nbn:de:0030-drops-260329},
  doi =		{10.4230/LIPIcs.SEA.2026.28},
  annote =	{Keywords: integer programming, mixed-integer programming, variable fixing, reduced-cost fixing, strong fixing, dual-path fixing, set cover}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.19

Breaking 2-Cores for Invertible Bloom Lookup Tables by Structure Prediction

Authors: Vojtěch Gaďurek and Pavel Veselý

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract

Invertible Bloom Lookup Tables (IBLTs) provide a highly space-efficient way to reconstruct small sets resulting from a large number of insertions and deletions of elements, such as in streaming or distributed computation of the symmetric difference of similar sets. The set recovery process succeeds if the IBLT size is at least 1.22 times the size of the encoded set; otherwise, a 2-core occurs with high probability in the corresponding random hypergraph. However, the sets in practice often exhibit structure that allows for performance beyond worst-case bounds. Here, we demonstrate that structured sets - such as the k-mers in the symmetric difference of two closely related genomes - can be recovered with an IBLT of significantly smaller size. We achieve this by employing structure-aware predictors to break the 2-core whenever the recovery process gets stuck. Importantly, this approach modifies only the decoding procedure, leaving the IBLT data structure unchanged. We prove that even a weak matching-based predictor enables the recovery of 27% more elements than the nominal IBLT size. Equipped with simple predictors for k-mers of genomic datasets, we demonstrate that recovering a symmetric difference with high probability can be done with an IBLT of size only 66% of the encoded set size for k = 31, improving the space efficiency by almost a factor of two. Moreover, we design an improved method for k-mers with large k that combines subsampling with nearly perfect prediction via fingerprinting and achieves a scaling property, requiring only O(M log M) bits for recovering M k-mers, instead of Θ(k⋅M) bits of the standard IBLT. Overall, our results highlight the possibility of significant space-efficiency improvements for IBLTs on datasets with predictable structure.

Cite as

Vojtěch Gaďurek and Pavel Veselý. Breaking 2-Cores for Invertible Bloom Lookup Tables by Structure Prediction. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gadurek_et_al:LIPIcs.SEA.2026.19,
  author =	{Ga\v{d}urek, Vojt\v{e}ch and Vesel\'{y}, Pavel},
  title =	{{Breaking 2-Cores for Invertible Bloom Lookup Tables by Structure Prediction}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{19:1--19:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.19},
  URN =		{urn:nbn:de:0030-drops-260237},
  doi =		{10.4230/LIPIcs.SEA.2026.19},
  annote =	{Keywords: Invertible Bloom Lookup Table, symmetric difference, k-mer sets}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.2

Near-Real-Time Solutions for Online String Problems

Authors: Dominik Köppl and Gregory Kucherov

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract

Based on the Breslauer-Italiano online suffix tree construction algorithm (2013) with double logarithmic worst-case guarantees on the update time per letter, we develop near-real-time algorithms for several classical problems on strings, including the computation of the longest repeating suffix array, the (reversed) Lempel-Ziv 77 factorization, and the maintenance of minimal unique substrings, all in an online manner. Our solutions improve over the best known running times for these problems in terms of the worst-case time per letter, for which we achieve a poly-log-logarithmic time complexity, within a linear space. Best known results for these problems require a poly-logarithmic time complexity per letter or only provide amortized complexity bounds. As a result of independent interest, we give conversions between the longest previous factor array and the longest repeating suffix array in space and time bounds based on their irreducible representations, which can have sizes sublinear in the length of the input string.

Cite as

Dominik Köppl and Gregory Kucherov. Near-Real-Time Solutions for Online String Problems. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2026.2,
  author =	{K\"{o}ppl, Dominik and Kucherov, Gregory},
  title =	{{Near-Real-Time Solutions for Online String Problems}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.2},
  URN =		{urn:nbn:de:0030-drops-259287},
  doi =		{10.4230/LIPIcs.CPM.2026.2},
  annote =	{Keywords: online algorithms, string algorithms, suffix tree, real-time computation, Lempel-Ziv factorization, minimal unique substrings}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.3

Computing k-mers in Graphs

Authors: Jarno N. Alanko and Máximo Pérez-López

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract

We initiate the study of computational problems on k-mers (strings of length k) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct k-mers found on the walks of a graph. We establish that this is #P-hard, even on connected deterministic DAGs. However, in the class of deterministic Wheeler graphs (Gagie, Manzini, and Sirén, TCS 2017), we show that distinct k-mers of such a graph W = (V, E) can be counted using O(|W|k) or O(n⁴ log k) arithmetic operations, where n = |V|, m = |E| and |W| = n+m. The latter result uses a new generalization of the technique of prefix doubling to Wheeler graphs. To generalize our results beyond Wheeler graphs, we discuss ways to transform a graph into a Wheeler graph in a manner that preserves the k-mers. As an application of our k-mer counting algorithms, we construct a representation of the de Bruijn graph of the k-mers that occupies O(n_k + |W|k log(max_{1 ≤ 𝓁 ≤ k} n_𝓁) + σlog m) bits of space, where n_𝓁 is the number of distinct 𝓁-mers in the Wheeler graph, and σ is the size of the alphabet. We show how to construct it in the same time complexity. Given that the Wheeler graph can be exponentially smaller than the de Bruijn graph, for large k this provides a theoretical improvement over previous de Bruijn graph construction methods from graphs, which must spend Ω(k) time per k-mer in the graph.

Cite as

Jarno N. Alanko and Máximo Pérez-López. Computing k-mers in Graphs. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 3:1-3:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alanko_et_al:LIPIcs.CPM.2026.3,
  author =	{Alanko, Jarno N. and P\'{e}rez-L\'{o}pez, M\'{a}ximo},
  title =	{{Computing k-mers in Graphs}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.3},
  URN =		{urn:nbn:de:0030-drops-259294},
  doi =		{10.4230/LIPIcs.CPM.2026.3},
  annote =	{Keywords: Wheeler graph, Wheeler language, de Bruijn graph, graph, k-mer, q-gram, DFA, #P-hard}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.40

Maximum Independent Sets in Disk Graphs with Disks in Convex Position

Authors: Anastasiia Tkachenko and Haitao Wang

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

For a set 𝒟 of disks in the plane, its disk graph G(𝒟) is the graph with vertex set 𝒟, where two vertices are adjacent if and only if the corresponding disks intersect. Given a set 𝒟 of n weighted disks, computing a maximum independent set of G(𝒟) is NP-hard. In this paper, we present an O(n³log n)-time algorithm for this problem in a special setting in which the disks are in convex position, meaning that every disk appears on the convex hull of 𝒟. This setting has been studied previously for disks of equal radius, for which an O(n^{37/11})-time algorithm was known. Our algorithm also works in the weighted case where disks have weights and the goal is to compute a maximum-weight independent set. As an application of our result, we obtain an O(n³log² n)-time algorithm for the dispersion problem on a set of n disks in convex position: given an integer k, compute a subset of k disks that maximizes the minimum pairwise distance among all disks in the subset.

Cite as

Anastasiia Tkachenko and Haitao Wang. Maximum Independent Sets in Disk Graphs with Disks in Convex Position. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 40:1-40:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{tkachenko_et_al:LIPIcs.SWAT.2026.40,
  author =	{Tkachenko, Anastasiia and Wang, Haitao},
  title =	{{Maximum Independent Sets in Disk Graphs with Disks in Convex Position}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{40:1--40:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.40},
  URN =		{urn:nbn:de:0030-drops-260766},
  doi =		{10.4230/LIPIcs.SWAT.2026.40},
  annote =	{Keywords: disk graphs, independent sets, convex position, dispersion}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.14

Hardness Results on Characteristics for Elastic-Degenerate Strings

Authors: Dominik Köppl and Jannik Olbrich

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract

Generalizations of plain strings have been proposed as a compact way to represent a collection of nearly identical sequences or to express uncertainty at specific text positions by enumerating all possibilities. While a plain string stores a character at each of its positions, generalizations consider a set of characters (indeterminate strings), a set of strings of equal length (generalized degenerate strings, or shortly GD strings), or a set of strings of arbitrary lengths (elastic-degenerate strings, or shortly ED strings). These generalizations are of importance to compactly represent such type of data, and find applications in bioinformatics for representing and maintaining a set of genetic sequences of the same taxonomy or a multiple sequence alignment. To be of use, attention has been drawn to answering various query types such as pattern matching or measuring similarity of ED strings by generalizing techniques known to plain strings. However, for some types of queries, it has been shown that a generalization of a polynomial-time solvable query on classic strings becomes NP-hard on ED strings, e.g. [Russo et al., 2022]. In that light, we wonder about other types of queries that are of particular interest to bioinformatics: unique substrings, absent words, anti-powers, longest previous factors, and Lempel-Ziv-like compression schemes. While we obtain a polynomial time algorithm for a variation of longest previous factors, we show that all other problems are NP-hard to compute, some of them even under the restriction that the input can be modeled as an indeterminate or GD string.

Cite as

Dominik Köppl and Jannik Olbrich. Hardness Results on Characteristics for Elastic-Degenerate Strings. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 14:1-14:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{koppl_et_al:LIPIcs.CPM.2026.14,
  author =	{K\"{o}ppl, Dominik and Olbrich, Jannik},
  title =	{{Hardness Results on Characteristics for Elastic-Degenerate Strings}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{14:1--14:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.14},
  URN =		{urn:nbn:de:0030-drops-259409},
  doi =		{10.4230/LIPIcs.CPM.2026.14},
  annote =	{Keywords: Elastic-degenerate strings, NP-hardness, longest common factor, minimal unique substring, minimal absent word, anti-power, longest previous factor}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.9

QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes

Authors: Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

We present a quasipolynomial-time approximation scheme (QPTAS) for the Maximum Independent Set (MWIS) in graphs with a bounded number of pairwise vertex-disjoint and non-adjacent long induced cycles. More formally, for every fixed s and t, we show a QPTAS for MWIS in graphs that exclude sC_t as an induced minor. Combining this with known results, we obtain a QPTAS for the problem of finding a largest induced subgraph of bounded treewidth with given hereditary property definable in Counting Monadic Second Order Logic, in the same classes of graphs. This is a step towards a conjecture of Gartland and Lokshtanov which asserts that for any planar graph H, graphs that exclude H as an induced minor admit a polynomial-time algorithm for the latter problem. This conjecture is notoriously open and even its weaker variants are confirmed only for very restricted graphs H.

Cite as

Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski. QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bonnet_et_al:LIPIcs.SWAT.2026.9,
  author =	{Bonnet, \'{E}douard and Czy\.{z}ewska, Jadwiga and Masa\v{r}{\'\i}k, Tom\'{a}\v{s} and Pilipczuk, Marcin and Rz\k{a}\.{z}ewski, Pawe{\l}},
  title =	{{QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.9},
  URN =		{urn:nbn:de:0030-drops-260454},
  doi =		{10.4230/LIPIcs.SWAT.2026.9},
  annote =	{Keywords: independent set, long holes, QPTAS, induced subgraphs}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.22

Search-Space Reduction for Boolean MinCSPs via Essential Constraints

Authors: Bart M. P. Jansen and Ruben F. A. Verhaegh

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

For a fixed set ℱ of Boolean constraint types, a MinCSP(ℱ)-instance consists of a formula F that applies m constraints from ℱ to a set of n Boolean variables. The goal is to remove a minimum subset of constraint applications from F to make the remaining formula satisfiable. Previous work characterized how the choice of ℱ affects its polynomial-time solvability and approximability. We extend a recently introduced preprocessing framework for graph problems to the problem above. Rephrased in the context of CSPs, this framework defines a constraint application from a given formula F as c-essential if it is contained in all c-approximate solutions to F. Being able to efficiently detect these essential parts of a solution reduces the search space of any follow-up FPT algorithms parameterized by the solution size and yields an immediate asymptotic improvement to the runtime of such algorithms. In this work, we present a dichotomy theorem that distinguishes constraint sets ℱ for which c_ℱ-essential constraint applications can be detected efficiently for some c_{ℱ} ∈ 𝒪(1), from those for which this task is intractable under established complexity-theoretic conjectures. Our results show that for any set ℱ of bijunctive constraints, there is a polynomial-time algorithm that detects 𝒪(1)-essential constraint applications. This contrasts the fact that constant-factor approximating a bijunctive MinCSP(ℱ)-problem is intractable under the Unique Games Conjecture.

Cite as

Bart M. P. Jansen and Ruben F. A. Verhaegh. Search-Space Reduction for Boolean MinCSPs via Essential Constraints. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{jansen_et_al:LIPIcs.SWAT.2026.22,
  author =	{Jansen, Bart M. P. and Verhaegh, Ruben F. A.},
  title =	{{Search-Space Reduction for Boolean MinCSPs via Essential Constraints}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.22},
  URN =		{urn:nbn:de:0030-drops-260586},
  doi =		{10.4230/LIPIcs.SWAT.2026.22},
  annote =	{Keywords: fixed-parameter tractability, constraint satisfaction problems}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.20

Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs

Authors: Jie Gao, Paweł Gawrychowski, Panos Giannopoulos, Wolfgang Mulzer, Satyam Singh, Frank Staals, and Meirav Zehavi

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

A disk graph is the intersection graph of (closed) disks in the plane. We consider the classic problem of finding a maximum clique in a disk graph. For general disk graphs, the complexity of this problem is still open, but for unit disk graphs, it is well known to be in P. The currently fastest algorithm runs in time O(n^{7/3+ o(1)}), where n denotes the number of disks [Jared Espenant et al., 2023; J. Mark Keil and Debajyoti Mondal, 2025]. Moreover, for the case of disk graphs with t distinct radii, the problem has also recently been shown to be in XP. More specifically, it is solvable in time O^*(n^{2t}) [J. Mark Keil and Debajyoti Mondal, 2025]. In this paper, we present algorithms with improved running times by allowing for approximate solutions and by using randomization: [(i)] 1) for unit disk graphs, we give an algorithm that, with constant success probability, computes a (1-ε)-approximate maximum clique in expected time Õ(n/ε²); and 2) for disk graphs with t distinct radii, we give a parameterized approximation scheme that, with a constant success probability, computes a (1-ε)-approximate maximum clique in expected time Õ(f(t)⋅ (1/ε)^{O(t)} ⋅ n), for some (exponential) function f(t).

Cite as

Jie Gao, Paweł Gawrychowski, Panos Giannopoulos, Wolfgang Mulzer, Satyam Singh, Frank Staals, and Meirav Zehavi. Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gao_et_al:LIPIcs.SWAT.2026.20,
  author =	{Gao, Jie and Gawrychowski, Pawe{\l} and Giannopoulos, Panos and Mulzer, Wolfgang and Singh, Satyam and Staals, Frank and Zehavi, Meirav},
  title =	{{Near-Linear and Parameterized Approximations for Maximum Cliques in Disk Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.20},
  URN =		{urn:nbn:de:0030-drops-260563},
  doi =		{10.4230/LIPIcs.SWAT.2026.20},
  annote =	{Keywords: Maximum Clique, Disk Graphs, Unit Disk Graphs, FPT Approximation}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.24

Cutwidth Versus BFS-Width with Applications to Graph Reconstruction from Distance Queries

Authors: Chirag Kaudan and Amir Nayyeri

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

Eppstein, Goodrich, and Liu [ESA 2025] introduced a new graph parameter, called BFS-width, and gave polylogarithmic bounds on it for bounded bandwidth graphs. Their bounds naturally imply several applications, e.g. in graph reconstruction via shortest path distance queries, graph drawing, and matrix reordering. We study this parameter for a broader class of graphs, namely bounded cutwidth graphs. We prove a sublinear upper bound on the BFS-width of bounded cutwidth graphs and show that our bounds are asymptotically tight. Our upper bound implies the first deterministic algorithm for reconstructing a bounded cutwidth graph with a subquadratic number of shortest path distance queries.

Cite as

Chirag Kaudan and Amir Nayyeri. Cutwidth Versus BFS-Width with Applications to Graph Reconstruction from Distance Queries. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kaudan_et_al:LIPIcs.SWAT.2026.24,
  author =	{Kaudan, Chirag and Nayyeri, Amir},
  title =	{{Cutwidth Versus BFS-Width with Applications to Graph Reconstruction from Distance Queries}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{24:1--24:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.24},
  URN =		{urn:nbn:de:0030-drops-260600},
  doi =		{10.4230/LIPIcs.SWAT.2026.24},
  annote =	{Keywords: Graph algorithms, graph theory, cutwidth, pathwidth, BFS-width}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.36

Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates

Authors: Seongbin Park and Eunjin Oh

Published in: LIPIcs, Volume 370, 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)

Abstract

In this paper, we study the many-to-many matching problem on planar point sets with integer coordinates: Given two disjoint sets R,B ⊂ [Δ]² with |R|+|B| = n, the goal is to select a set of edges between R and B so that every point is incident to at least one edge and the total Euclidean length is minimized. In the general case that R and B are point sets in the plane, the best-known algorithm for the many-to-many matching problem takes Õ(n²) time. We present an exact Õ(n^{1.5} log Δ) time algorithm for point sets in [Δ]². To the best of our knowledge, this is the first subquadratic exact algorithm for planar many-to-many matching under bounded integer coordinates.

Cite as

Seongbin Park and Eunjin Oh. Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{park_et_al:LIPIcs.SWAT.2026.36,
  author =	{Park, Seongbin and Oh, Eunjin},
  title =	{{Exact Subquadratic Algorithm for Many-To-Many Matching on Planar Point Sets with Integer Coordinates}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.36},
  URN =		{urn:nbn:de:0030-drops-260728},
  doi =		{10.4230/LIPIcs.SWAT.2026.36},
  annote =	{Keywords: Edge cover, many-to-many matching, similarity, geometric matching}
}

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