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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2026.11

Pinning on Tight Cuts: Improved Algorithm and Bounds for Unsplittable Multicommodity Flows in Outerplanar Graphs

Authors: David Alemán Espinosa and Niklas Schlomberg

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract

The multicommodity flow problem in an undirected capacitated graph G is specified by a set of source-sink pairs with nonnegative demands. A flow is feasible if it routes all demands without exceeding the edge capacities, and it is unsplittable if it routes each demand along a single path. Let α be the smallest value such that the existence of a feasible flow implies the existence of an unsplittable flow that exceeds the edge capacities by at most + α d_max. Schrijver, Seymour, and Winkler showed that α ∈ [1.01, 1.5] if G is a cycle. These bounds were ultimately improved to α ∈ [1.1, 1.3] by Skutella and Däubel. Recently, Alemán Espinosa and Kumar extended this constant upper bound to the broader class of outerplanar graphs, and showed that if G is outerplanar then α ≤ 3.6. We show that α ∈ [4/3,2] if G is outerplanar. We introduce a novel technique that considers the global parameters of the instance, and that may be useful in other (more general) settings where the cut-condition is sufficient, or nearly sufficient, for the existence of a feasible flow.

Cite as

David Alemán Espinosa and Niklas Schlomberg. Pinning on Tight Cuts: Improved Algorithm and Bounds for Unsplittable Multicommodity Flows in Outerplanar Graphs. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alemanespinosa_et_al:LIPIcs.ICALP.2026.11,
  author =	{Alem\'{a}n Espinosa, David and Schlomberg, Niklas},
  title =	{{Pinning on Tight Cuts: Improved Algorithm and Bounds for Unsplittable Multicommodity Flows in Outerplanar Graphs}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{11:1--11:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.11},
  URN =		{urn:nbn:de:0030-drops-264008},
  doi =		{10.4230/LIPIcs.ICALP.2026.11},
  annote =	{Keywords: Unsplittable Flows, Multicommodity Flows, Planar Graphs}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.3

Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization

Authors: Dildar Ali, Ansh Jasrotia, Abishek Salaria, and Suman Banerjee

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

Abstract

How to utilize an allocated budget effectively for branding and promotion of a commercial house is an important problem, particularly when multiple advertising media are available. There exist multiple such media, and among them, two popular ones are billboards and social media advertisements. In this context, the question naturally arises: how should a budget be allocated to maximize total influence? Although there is significant literature on the effective use of budgets in individual advertising media, there are hardly any studies examining budget allocation across multiple advertising media. To bridge this gap, this paper introduces the Budget Splitting Problem in Billboard and Social Network Advertisement. We introduce the notion of interaction effect to capture the additional influence due to triggers from multiple media of advertising. Using this notion, we propose a noble influence function Φ(,) that captures the total influence and shows that this function is non-negative, monotone, and non-bisubmodular. We introduce bi-submodularity ratio (γ) and generalized curvature (α) to measure how close a function is to being bi-submodular and how far a function is from being modular, respectively. We propose the Randomized Greedy and Two-Phase Adaptive Greedy approach, where the influence function is non-bisubmodular and achieves an approximation guarantee of (1/α)(1-e^(-γα)). We conducted several experiments using real-world datasets and observed that the proposed solution approach’s budget splitting leads to a greater influence than existing approaches.

Cite as

Dildar Ali, Ansh Jasrotia, Abishek Salaria, and Suman Banerjee. Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ali_et_al:LIPIcs.SEA.2026.3,
  author =	{Ali, Dildar and Jasrotia, Ansh and Salaria, Abishek and Banerjee, Suman},
  title =	{{Approximation Algorithms for Budget Splitting in Multi-Channel Influence Maximization}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{3:1--3:20},
  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.2026.3},
  URN =		{urn:nbn:de:0030-drops-260070},
  doi =		{10.4230/LIPIcs.SEA.2026.3},
  annote =	{Keywords: Advertisement, Billboard, Social Network, Bi-submodularity, Influence Maximization}
}

Document

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.

Cite as

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.

Cite as

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.2026.27

Cycle Basis Algorithms for Reducing Maximum Edge Participation

Authors: Fan Wang and Sandy Irani

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

Abstract

A cycle basis of a graph is a minimal set of cycles from which every cycle in the graph can be generated by symmetric difference. We study the problem of constructing cycle bases of graphs with low maximum edge participation, defined as the maximum number of cycles in the basis that share any single edge. This quantity, though less studied than total weight or length, plays a critical role in quantum fault tolerance, as it directly impacts the overhead of lattice surgery procedures used to implement an almost universal quantum gate set. Building on a recursive algorithm by Freedman and Hastings, we introduce a family of load-aware heuristics that adaptively select vertices and edges to minimize edge participation throughout the cycle basis construction. Our approach improves empirical performance on random regular graphs and on graphs derived from small quantum codes. We further analyze a simplified balls-into-bins process to establish lower bounds on edge participation. While the model differs from the cycle basis algorithm on real graphs, it captures what can be proven for our heuristics without using more complex graph theoretic properties related to the distribution of cycles in the graph. Our analysis suggests that the maximum load of all of our heuristics will be Ω(log² n). Our results indicate that careful cycle basis construction can yield significant practical benefits in the design of fault-tolerant quantum systems. Maximum edge participation has been studied in the graph theory literature under the name basis number, which is the minimum possible maximum edge participation over all cycle bases in a graph.

Cite as

Fan Wang and Sandy Irani. Cycle Basis Algorithms for Reducing Maximum Edge Participation. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{wang_et_al:LIPIcs.SEA.2026.27,
  author =	{Wang, Fan and Irani, Sandy},
  title =	{{Cycle Basis Algorithms for Reducing Maximum Edge Participation}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{27:1--27:20},
  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.2026.27},
  URN =		{urn:nbn:de:0030-drops-260311},
  doi =		{10.4230/LIPIcs.SEA.2026.27},
  annote =	{Keywords: Graph algorithms, Cycle Basis, Quantum fault tolerance}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.20

QuadRank: Engineering a High Throughput Rank

Authors: Ragnar Groot Koerkamp

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

Abstract

Motivation. Given a text, a query rank(q, c) counts the number of occurrences of character c among the first q characters of the text. Space-efficient methods to answer these rank queries form an important building block in many succinct data structures. For example, the FM-index [Ferragina and Manzini, 2000] is a widely used data structure that uses rank queries to locate all occurrences of a pattern in a text. In bioinformatics applications, the goal is usually to process large inputs as fast as possible. Thus, data structures should have high throughput when used with many threads. Contributions. We first survey existing results on rank data structures. For the σ = 2 binary alphabet, we then develop BiRank, which has 3.28% space overhead. BiRank merges the central ideas of two recent papers: (1) we interleave (inline) offsets in each cache line of the underlying bit vector [Laws et al., 2024], reducing cache misses, and (2) these offsets are to the middle of each block so that only half of each needs popcounting [Gottlieb and Reinert, 2025]. In QuadRank (14.4% overhead), we extend these techniques to the σ = 4 (DNA) alphabet. Both data structures typically require only a single cache miss per query, making them highly suitable for high-throughput and memory-bound settings. To enable efficient batch-processing, we support prefetching the cache lines required to answer upcoming queries. Results. BiRank and QuadRank are around 1.5× and 2× faster than similar-overhead methods that do not use interleaving. Prefetching gives an additional 2× speedup, at which point the dual-channel DDR4 RAM bandwidth becomes a hard limit on the total throughput. With prefetching, both methods outperform all other methods apart from SPIDER [Laws et al., 2024] by 2×. When using QuadRank with prefetching in a toy count-only FM-index, QuadFm, this results in a smaller size and up to 4× speedup over Genedex, a state-of-the-art batching FM-index implementation. Conclusion. Optimizing data structures for high throughput, by minimizing cache misses and branch-misses and adding support for prefetching, can result in significant speedups when benchmarks are adjusted accordingly.

Cite as

Ragnar Groot Koerkamp. QuadRank: Engineering a High Throughput Rank. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 20:1-20:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{grootkoerkamp:LIPIcs.SEA.2026.20,
  author =	{Groot Koerkamp, Ragnar},
  title =	{{QuadRank: Engineering a High Throughput Rank}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{20:1--20:23},
  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.2026.20},
  URN =		{urn:nbn:de:0030-drops-260248},
  doi =		{10.4230/LIPIcs.SEA.2026.20},
  annote =	{Keywords: Rank, Succinct Data Structures, Cache Performance, Prefetching}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.17

Sensitivity of Repetitiveness Measures to String Reversal

Authors: Hideo Bannai, Yuto Fujie, Peaker Guo, Shunsuke Inenaga, Yuto Nakashima, Simon J. Puglisi, and Cristian Urbina

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

Abstract

We study the impact that string reversal can have on several repetitiveness measures. First, we exhibit an infinite family of strings where the number, r, of runs in the run-length encoding of the Burrows-Wheeler transform (BWT) can increase additively by Θ(n) when reversing the string. This substantially improves the known Ω(log n) lower-bound for the additive sensitivity of r and it is asymptotically tight. We generalize our result to other variants of the BWT, including the variant with an appended end-of-string symbol and the bijective BWT. We show that an analogous result holds for the size z of the Lempel-Ziv 77 (LZ) parsing of the text, and also for some of its variants, including the non-overlapping LZ parsing, and the LZ-end parsing. Moreover, we describe a family of strings for which the ratio z(w^R)/z(w) approaches 3 from below as |w| → ∞. We also show an asymptotically tight lower-bound of Θ(n) for the additive sensitivity of the size v of the smallest lexicographic parsing to string reversal. Finally, we show that the multiplicative sensitivity of v to reversing the string is Θ(log n), and this lower-bound is also tight. Overall, our results expose the limitations of repetitiveness measures that are widely used in practice, against string reversal - a simple and natural data transformation.

Cite as

Hideo Bannai, Yuto Fujie, Peaker Guo, Shunsuke Inenaga, Yuto Nakashima, Simon J. Puglisi, and Cristian Urbina. Sensitivity of Repetitiveness Measures to String Reversal. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bannai_et_al:LIPIcs.CPM.2026.17,
  author =	{Bannai, Hideo and Fujie, Yuto and Guo, Peaker and Inenaga, Shunsuke and Nakashima, Yuto and Puglisi, Simon J. and Urbina, Cristian},
  title =	{{Sensitivity of Repetitiveness Measures to String Reversal}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{17:1--17:18},
  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.2026.17},
  URN =		{urn:nbn:de:0030-drops-259434},
  doi =		{10.4230/LIPIcs.CPM.2026.17},
  annote =	{Keywords: String reversal, Repetitiveness measures, Burrows-Wheeler transform, Lempel-Ziv parsing, Lexicographic parsings}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.29

The TAG Array of a Multiple Sequence Alignment

Authors: Jannik Olbrich and Enno Ohlebusch

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

Abstract

Modern genomic analyses increasingly rely on pangenomes, that is, representations of the genome of entire populations. The simplest representation of a pangenome is a set of individual genome sequences. Compared to e.g. sequence graphs, this has the advantage that efficient exact search via indexes based on the Burrows-Wheeler Transform (BWT) is possible, that no chimeric sequences are created, and that the results are not influenced by heuristics. However, such an index may report a match in thousands of positions even if these all correspond to the same locus, making downstream analysis unnecessarily more expensive. For sufficiently similar sequences (e.g. human chromosomes), a multiple sequence alignment (MSA) can be computed. Since an MSA tends to group similar strings in the same columns, it is likely that a string occurring thousands of times in the pangenome can be described by very few columns in the MSA. We describe a method to tag entries in the BWT with the corresponding column in the MSA and develop an index that can map matches in the BWT to columns in the MSA in time proportional to the output. As a by-product, we can project a match to a designated reference genome, a capability that current pangenome aligners lack.

Cite as

Jannik Olbrich and Enno Ohlebusch. The TAG Array of a Multiple Sequence Alignment. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{olbrich_et_al:LIPIcs.CPM.2026.29,
  author =	{Olbrich, Jannik and Ohlebusch, Enno},
  title =	{{The TAG Array of a Multiple Sequence Alignment}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{29:1--29:14},
  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.2026.29},
  URN =		{urn:nbn:de:0030-drops-259555},
  doi =		{10.4230/LIPIcs.CPM.2026.29},
  annote =	{Keywords: Burrows-Wheeler Transform, pattern matching, index data structure, pangenomics}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.18

On Fréchet Traveling Salesmen Problems

Authors: Omrit Filtser, Tzalik Maimon, and Michal Moiseev

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

Abstract

The Fréchet distance is a well-studied distance measure between two curves. In this work, we demonstrate that the merit of Fréchet distance extends beyond evaluating similarity, and introduce a new setting in which it proves useful. Consider a situation where two agents are required to visit a given set of sites, while staying close to each other throughout their traversal. In this paper, we study problems where the goal is to construct two curves whose vertices are from a given set of points, under the constraint that the Fréchet distance between the curves is kept as small as possible. This problem can be viewed as a variant of the Traveling Salesman Problem (TSP), and thus may be of interest in routing, network planning and more. We present a near-linear algorithm for this problem under the discrete Fréchet distance, and explore several variants of the problem, including minimizing the lengths of the curves and balancing the number of sites assigned to each agent. Lastly, we prove that the problem is NP-hard under the continuous Fréchet Distance.

Cite as

Omrit Filtser, Tzalik Maimon, and Michal Moiseev. On Fréchet Traveling Salesmen Problems. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{filtser_et_al:LIPIcs.SWAT.2026.18,
  author =	{Filtser, Omrit and Maimon, Tzalik and Moiseev, Michal},
  title =	{{On Fr\'{e}chet Traveling Salesmen Problems}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{18:1--18:17},
  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.2026.18},
  URN =		{urn:nbn:de:0030-drops-260545},
  doi =		{10.4230/LIPIcs.SWAT.2026.18},
  annote =	{Keywords: Fr\'{e}chet distance, traveling salesman problem}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.34

LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access

Authors: Hiroki Shibata, Yuto Nakashima, Yutaro Yamaguchi, and Shunsuke Inenaga

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

Abstract

An LZ-like factorization of a string divides it into factors, each being either a single character or a copy of a preceding substring. While grammar-based compression schemes support efficient random access with space linear in the compressed size, no comparable guarantees are known for general LZ-like factorizations. This limitation motivated restricted variants such as LZ-End [Kreft and Navarro, 2013] and height-bounded LZ (LZHB) [Bannai et al., 2024], which trade off some compression efficiency for faster access. In this paper, we introduce LZ-Begin-End (LZBE), a new LZ-like variant in which every copy factor must refer to a contiguous sequence of preceding factors. This structural restriction ensures that any context-free grammar can be transformed into an LZBE factorization of the same size. We further study the greedy LZBE factorization, which selects each copy factor to be as long as possible while processing the input from left to right, and show that it can be computed in linear time. Moreover, we exhibit a family of strings for which the greedy LZBE factorization is asymptotically smaller than the smallest grammar. These results demonstrate that the LZBE scheme is strictly more expressive than grammar-based compression in the worst case. To support fast queries, we propose a data structure for LZBE-compressed strings that permits O(log n)-time random access within space linear in the compressed size, where n is the length of the input string.

Cite as

Hiroki Shibata, Yuto Nakashima, Yutaro Yamaguchi, and Shunsuke Inenaga. LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{shibata_et_al:LIPIcs.CPM.2026.34,
  author =	{Shibata, Hiroki and Nakashima, Yuto and Yamaguchi, Yutaro and Inenaga, Shunsuke},
  title =	{{LZBE: An LZ-Style Compressor Supporting O(log n)-Time Random Access}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{34:1--34:18},
  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.2026.34},
  URN =		{urn:nbn:de:0030-drops-259609},
  doi =		{10.4230/LIPIcs.CPM.2026.34},
  annote =	{Keywords: data compression, Lempel-Ziv parsing, string algorithms, random access}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.29

Bichromatic Classifications of Points Using Strips

Authors: Jaegun Lee, Chaeyoon Chung, and Hee-Kap Ahn

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

Abstract

Given a set of n points in the plane, each colored either blue or red, we study the problem of finding a strip that separates the blue points from the red points. Specifically, we consider the following two variants: (1) locating a strip that contains no red points while maximizing the number of blue points within the strip, and (2) locating a strip that contains all blue points while minimizing the number of red points within the strip. For variant (1), we present an O(n²)-time algorithm, improving upon the previously best O(n²log n)-time result. We also show that this running time is optimal under the standard 3SUM conjecture. We also give an output-sensitive algorithm with running time O(k_{opt} n log n) that returns a strip, where k_{opt} is the number of blue points not contained within the strip in an optimal solution. We extend our results to the case of up to t parallel strips, obtaining an O(n²log n)-time algorithm. For variant (2), an optimal Θ(nlog n)-time algorithm is known for t = 1. We show 3SUM-hardness for t = 2 and give an O(n²)-time algorithm. For any t ≥ 3, we present an O(n²log n)-time algorithm.

Cite as

Jaegun Lee, Chaeyoon Chung, and Hee-Kap Ahn. Bichromatic Classifications of Points Using Strips. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lee_et_al:LIPIcs.SWAT.2026.29,
  author =	{Lee, Jaegun and Chung, Chaeyoon and Ahn, Hee-Kap},
  title =	{{Bichromatic Classifications of Points Using Strips}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{29:1--29:17},
  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.2026.29},
  URN =		{urn:nbn:de:0030-drops-260659},
  doi =		{10.4230/LIPIcs.SWAT.2026.29},
  annote =	{Keywords: Bichromatic Classification, Separation, Strip, Duality}
}

Document

DOI: 10.4230/LIPIcs.SWAT.2026.31

Improved and Parameterized Algorithms for Online Multi-Level Aggregation

Authors: Young-San Lin and Alex Turoczy

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

Abstract

We study the online multi-level aggregation problem with deadlines (MLAP-D) introduced by Bienkowski, Böhm, Byrka, Chrobak, Dürr, Folwarczný, Jeż, Sgall, Thang, and Veselý (ESA 2016, OR 2020). In this problem, requests arrive over time at the vertices of a given vertex-weighted tree, and each request has a deadline that it must be served by. The cost of serving a request equals the cost of a path from the root to the vertex where the request resides. Instead of serving each request individually, requests can be aggregated and served by transmitting a subtree from the root that spans the vertices on which the requests reside, to potentially be more cost-effective. The aggregated cost is the weight of the transmission subtree. The goal of MLAP-D is to find an aggregation solution that minimizes the total cost while serving all requests. MLAP-D generalizes some well-studied problems including the TCP acknowledgment problem and the joint replenishment problem, and arises in natural scenarios such as multi-casting, sensor networks, and supply chain management. We present improved and parameterized algorithms for MLAP-D. Our result is twofold. First, we present an e(D+1)-competitive algorithm where D is the depth of the tree. Second, we present an e(4H+2)-competitive algorithm where H is the caterpillar dimension of the tree. Here, H ≤ D and H ≤ log₂ |V| where |V| is the number of vertices in the given tree. The caterpillar dimension remains constant for rich but simple classes of trees, such as line graphs (H = 1), caterpillar graphs (H = 2), and lobster graphs (H = 3). To the best of our knowledge, this is the first online algorithm parameterized on a measure better than depth. The state-of-the-art online algorithms are 6(D+1)-competitive by Buchbinder, Feldman, Naor, and Talmon (SODA 2017) and O(log |V|)-competitive by Azar and Touitou (FOCS 2020). Our framework outperforms the state-of-the-art ratios when H = o(min{D,log₂ |V|}). Our memory-based algorithms extend transmission subtrees with a cost comparable to transmission subtrees used to serve previous requests. Our simple framework directly applies to trees with any structure and differs from the previous frameworks that reduce the problem to trees with specific structures.

Cite as

Young-San Lin and Alex Turoczy. Improved and Parameterized Algorithms for Online Multi-Level Aggregation. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lin_et_al:LIPIcs.SWAT.2026.31,
  author =	{Lin, Young-San and Turoczy, Alex},
  title =	{{Improved and Parameterized Algorithms for Online Multi-Level Aggregation}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{31:1--31:17},
  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.2026.31},
  URN =		{urn:nbn:de:0030-drops-260673},
  doi =		{10.4230/LIPIcs.SWAT.2026.31},
  annote =	{Keywords: Online Algorithms, Approximation Algorithms, Graph Problems}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.7

When to Ask a Question: Understanding Communication Strategies in Generative AI Tools

Authors: Charlotte Park, Kate Donahue, and Manish Raghavan

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract

Generative AI models differ from traditional machine learning tools in that they allow users to provide as much or as little information as they choose in their inputs. This flexibility often leads users to omit certain details, relying on the models to infer and fill in under-specified information based on distributional knowledge of user preferences. Such inferences may privilege majority viewpoints and disadvantage users with atypical preferences, raising concerns about fairness. Unlike more traditional recommender systems, LLMs can explicitly solicit more information from users through natural language. However, while directly eliciting user preferences could increase personalization and mitigate inequality, excessive querying places a burden on users who value efficiency. We develop a stylized model of user-LLM interaction and develop an objective that captures tradeoff between user burden and preference representation. Building on the observation that individual preferences are often correlated, we analyze how AI systems should balance inference and elicitation, characterizing the optimal amount of information to solicit before content generation. Ultimately, we show that information elicitation can mitigate the systematic biases of preference inference, enabling the design of generative tools that better incorporate diverse user perspectives while maintaining efficiency. We complement this theoretical analysis with an empirical evaluation illustrating the model’s predictions and exploring their practical implications.

Cite as

Charlotte Park, Kate Donahue, and Manish Raghavan. When to Ask a Question: Understanding Communication Strategies in Generative AI Tools. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 7:1-7:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{park_et_al:LIPIcs.FORC.2026.7,
  author =	{Park, Charlotte and Donahue, Kate and Raghavan, Manish},
  title =	{{When to Ask a Question: Understanding Communication Strategies in Generative AI Tools}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{7:1--7:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.7},
  URN =		{urn:nbn:de:0030-drops-259782},
  doi =		{10.4230/LIPIcs.FORC.2026.7},
  annote =	{Keywords: human-AI interaction, user modeling, personalization}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.12

Tradeoffs in Privacy, Welfare, and Fairness for Facility Location

Authors: Sara Fish, Yannai A. Gonczarowski, Jason Z. Tang, and Salil Vadhan

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract

The differentially private (DP) facility location problem seeks to determine a socially optimal placement for a public facility while ensuring that each participating agent’s location remains private. In order to privatize its input data, a DP mechanism must inject noise into its output distribution, producing a placement that will have lower expected social welfare than the optimal spot for the facility. The privacy-induced welfare loss can be viewed as the "cost of privacy," illustrating a tradeoff between social welfare and privacy that has been the focus of prior work. Yet, the imposition of privacy also induces a third consideration that has not been similarly studied: fairness in how the "cost of privacy" is distributed across individuals. For instance, a mechanism may satisfy differential privacy with minimal social welfare loss, yet still be undesirable if that loss falls entirely on one individual. In this paper, we quantify this new notion of unfairness and design mechanisms for facility location that attempt to simultaneously optimize across these three objectives of privacy, social welfare, and fairness. Under this setup, we first derive an impossibility result, showing that privacy and fairness cannot be simultaneously guaranteed over all possible datasets that could represent the locations of individuals in a population. We then consider a relaxation of the original problem that still requires worst-case differential privacy, but only seeks fairness and appealing social welfare over smaller, more "realistic-looking" families of datasets. For this relaxation, we construct a DP mechanism and demonstrate that it is simultaneously optimal (or, for a harder family of datasets, near-optimal up to small factors) on fairness and social welfare. This suggests that while there is a tradeoff between privacy and each of social welfare and fairness, there is no additional tradeoff when we consider all three objectives simultaneously, provided that the population data is sufficiently natural.

Cite as

Sara Fish, Yannai A. Gonczarowski, Jason Z. Tang, and Salil Vadhan. Tradeoffs in Privacy, Welfare, and Fairness for Facility Location. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fish_et_al:LIPIcs.FORC.2026.12,
  author =	{Fish, Sara and Gonczarowski, Yannai A. and Tang, Jason Z. and Vadhan, Salil},
  title =	{{Tradeoffs in Privacy, Welfare, and Fairness for Facility Location}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.12},
  URN =		{urn:nbn:de:0030-drops-259858},
  doi =		{10.4230/LIPIcs.FORC.2026.12},
  annote =	{Keywords: differential privacy, facility location, fairness, mechanism design}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.20

Privacy, Prediction, and Allocation

Authors: Ben Jacobsen and Nitin Kohli

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract

Algorithmic predictions are increasingly used to inform the allocation of scarce resources. The promise of these methods is that, through machine learning, they can better identify the people who would benefit most from interventions. Recently, however, several works have called this assumption into question by demonstrating the existence of settings where simple, unit-level allocation strategies can meet or even exceed the performance of those based on individual-level targeting. Separately, other works have objected to individual-level targeting on privacy grounds, leading to an unusual situation where a single solution, unit-level targeting, is recommended for reasons of both privacy and utility. Motivated by the desire to fully understand the interplay of privacy and targeting levels, we initiate the study of aid allocation systems that satisfy differential privacy, synthesizing existing works on private optimization with the economic models of aid allocation used in the non-private literature. To this end, we investigate private variants of both individual and unit-level allocation strategies in both stochastic and distribution-free settings under a range of constraints on data availability. Through this analysis, we provide clean, interpretable bounds characterizing the tradeoffs between privacy, efficiency, and targeting precision in allocation.

Cite as

Ben Jacobsen and Nitin Kohli. Privacy, Prediction, and Allocation. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 20:1-20:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{jacobsen_et_al:LIPIcs.FORC.2026.20,
  author =	{Jacobsen, Ben and Kohli, Nitin},
  title =	{{Privacy, Prediction, and Allocation}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{20:1--20:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.20},
  URN =		{urn:nbn:de:0030-drops-259935},
  doi =		{10.4230/LIPIcs.FORC.2026.20},
  annote =	{Keywords: Differential privacy, fair allocation, limits of prediction}
}

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