355 Search Results for "Grohe, Martin"

Volume

LIPIcs, Volume 297

51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

ICALP 2024, July 8-12, 2024, Tallinn, Estonia

Editors: Karl Bringmann, Martin Grohe, Gabriele Puppis, and Ola Svensson

Document
DOI: 10.4230/LIPIcs.SEA.2026.14
K-Hole Separation in PEO‑Based ILP Treewidth Formulation

Authors: Andrea D'Ascenzo

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

Abstract
In this paper, we introduce a family of valid inequalities for the strongest currently known integer programming formulation of treewidth based on perfect elimination orderings. These inequalities arise from the structure of induced chordless cycles (holes) and strengthen the canonical linear relaxation by enforcing constraints that every feasible chordal completion must satisfy. To handle the exponentially many such inequalities, we develop a dedicated separation routine capable of detecting violated k-hole constraints within a cutting-plane framework. Our computational results show that incorporating these inequalities substantially improves the quality of the lower bounds across a broad range of graph classes, in some cases nearly closing the integrality gap.
Cite as

Andrea D'Ascenzo. K-Hole Separation in PEO‑Based ILP Treewidth Formulation. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dascenzo:LIPIcs.SEA.2026.14,
  author =	{D'Ascenzo, Andrea},
  title =	{{K-Hole Separation in PEO‑Based ILP Treewidth Formulation}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{14:1--14:14},
  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.2026.14},
  URN =		{urn:nbn:de:0030-drops-260186},
  doi =		{10.4230/LIPIcs.SEA.2026.14},
  annote =	{Keywords: Treewidth, Integer Linear Programming, Polyhedral Combinatorics, Chordal Completion, Induced Cycles}
}
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.SWAT.2026.10
Robotic Arm Rotation: Standing up Is Harder Than You Think

Authors: Nicolas Bousquet, Frank Connor, Remy El Sabeh, Louis-Roy Langevin, Amer E. Mouawad, Naomi Nishimura, and Agnes Totschnig

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

Abstract
We study motion-planning problems for planar robotic arms that rotate around fixed centers while avoiding collisions. In the SM-RAMP model, each unit-length arm may rotate at most once; the question is whether all arms can be rotated to the vertical position. We resolve an open problem of Bousquet et al. [Bousquet et al., 2026] by proving that SM-RAMP is NP-complete, even in the horizontal-to-vertical setting. Our hardness proof uses a structural analysis of rotation-propagation chains and introduces a combinatorial abstraction of independent interest, the Lighthouse Propagation problem, which we show is itself NP-complete. We then consider the multi-move variant MM-RAMP, where each arm may rotate multiple times among a fixed set of allowed angles (or orientations). We prove that MM-RAMP is PSPACE-complete even when each arm has only a few allowed angles, in sharp contrast with the single-move case. Finally, we give two fixed-parameter tractable algorithms: for MAX-SM-RAMP parameterized by the number k of arms to be made vertical, and for 2A-MM-RAMP (restricted to horizontal and vertical) parameterized by the number 𝓁 of allowed rotations.
Cite as

Nicolas Bousquet, Frank Connor, Remy El Sabeh, Louis-Roy Langevin, Amer E. Mouawad, Naomi Nishimura, and Agnes Totschnig. Robotic Arm Rotation: Standing up Is Harder Than You Think. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bousquet_et_al:LIPIcs.SWAT.2026.10,
  author =	{Bousquet, Nicolas and Connor, Frank and El Sabeh, Remy and Langevin, Louis-Roy and Mouawad, Amer E. and Nishimura, Naomi and Totschnig, Agnes},
  title =	{{Robotic Arm Rotation: Standing up Is Harder Than You Think}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{10:1--10:17},
  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.2026.10},
  URN =		{urn:nbn:de:0030-drops-260467},
  doi =		{10.4230/LIPIcs.SWAT.2026.10},
  annote =	{Keywords: search, optimization, robotics, robotic arms, parameterized complexity, computational geometry, combinatorial reconfiguration}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.28
The Parameterized Complexity of Coloring Mixed Graphs

Authors: Antonio Lauerbach, Konstanty Junosza-Szaniawski, Marie Diana Sieper, and Alexander Wolff

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

Abstract
A mixed graph contains (undirected) edges as well as (directed) arcs, thus generalizing undirected and directed graphs. A proper coloring c of a mixed graph G assigns a positive integer to each vertex such that c(u)≠c(v) for every edge {u,v} and c(u)<c(v) for every arc (u,v) of G. As in classical coloring, the objective is to minimize the number of colors. Thus, mixed (graph) coloring generalizes classical coloring of undirected graphs and allows for more general applications, such as scheduling with precedence constraints, modeling metabolic pathways, and process management in operating systems; see a survey by Sotskov [Mathematics, 2020]. We initiate the systematic study of the parameterized complexity of mixed coloring. We focus on structural graph parameters that lie between cliquewidth and vertex cover, primarily with respect to the underlying undirected graph. Unlike classical coloring, which is fixed-parameter tractable (FPT) parameterized by treewidth or neighborhood diversity, we show that mixed coloring is W[1]-hard for treewidth and even paraNP-hard for neighborhood diversity. To utilize the directedness of arcs, we introduce and analyze natural generalizations of neighborhood diversity and cliquewidth to mixed graphs, and show that mixed coloring becomes FPT when parameterized by (the generalized) mixed neighborhood diversity. Further, we investigate how these parameters are affected if we add transitive arcs, which do not affect colorings. Finally, we provide tight bounds on the chromatic number of mixed graphs, generalizing known bounds on mixed interval graphs.
Cite as

Antonio Lauerbach, Konstanty Junosza-Szaniawski, Marie Diana Sieper, and Alexander Wolff. The Parameterized Complexity of Coloring Mixed Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lauerbach_et_al:LIPIcs.SWAT.2026.28,
  author =	{Lauerbach, Antonio and Junosza-Szaniawski, Konstanty and Sieper, Marie Diana and Wolff, Alexander},
  title =	{{The Parameterized Complexity of Coloring Mixed Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{28:1--28:18},
  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.2026.28},
  URN =		{urn:nbn:de:0030-drops-260644},
  doi =		{10.4230/LIPIcs.SWAT.2026.28},
  annote =	{Keywords: Mixed Graphs, Coloring, Parameterized Complexity, Structural Graph Parameters}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.35
Path-Reporting Distance Oracles for Vertex-Labeled Graphs

Authors: Ofer Neiman and Alon Spector

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

Abstract
Let G = (V,E) be a weighted undirected graph, with n vertices. A distance oracle is a data structure that can quickly answer distance queries, with some stretch factor. A seminal work of [Thorup and Zwick, 2005], given an integer k ≥ 1, provides such an oracle with stretch 2k-1, query time O(k), and size O(k⋅ n^{1+1/k}). Furthermore, this oracle can also report a path in G corresponding to the returned distance. In this paper we focus on vertex-labeled graphs, in which each vertex is given a label from a set L of size 𝓁. A vertex-label distance oracle answers queries of the form (v,λ), where v ∈ V and λ ∈ L, by reporting (an approximation to) the distance from v to the closest vertex of label λ. Following [Danny Hermelin et al., 2011], it was shown in [Chechik, 2012] that for any integer k > 1, there exists a vertex-label distance oracle with stretch 4k-5, query time O(k), and size O(k⋅ n⋅ 𝓁^{1/k}). This state-of-the-art result suffers from two main drawbacks: The stretch is roughly a factor of 2 larger than in [Thorup and Zwick, 2005], and it is not path-reporting. We address these concerns in this work, and provide the following results. - First, we devise a path-reporting vertex-label distance oracle, at the cost of a slight increase in stretch and size. For any constant 0 < ε < 1, our oracle has stretch (4k-5)⋅(1+ε), query time O(k), and size O(n^{1+o(1)}⋅ 𝓁^{1/k}). - Second, we show how to improve the stretch to the optimal 2k-1, at the cost of mildly increasing the query time. Specifically, we devise a vertex-label distance oracle with stretch 2k-1, query time O(𝓁^{1/k}⋅log n), and size O(k⋅ n⋅ 𝓁^{1/k}).
Cite as

Ofer Neiman and Alon Spector. Path-Reporting Distance Oracles for Vertex-Labeled Graphs. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{neiman_et_al:LIPIcs.SWAT.2026.35,
  author =	{Neiman, Ofer and Spector, Alon},
  title =	{{Path-Reporting Distance Oracles for Vertex-Labeled Graphs}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{35:1--35:16},
  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.2026.35},
  URN =		{urn:nbn:de:0030-drops-260719},
  doi =		{10.4230/LIPIcs.SWAT.2026.35},
  annote =	{Keywords: Graph Algorithms, Shortest Paths, Distance Oracles}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.24
Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support

Authors: Reilly Browne and Hsien-Chih Chang

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Given an unweighted graph G, the minimum r-dominating set problem asks for a subset of vertices S of the smallest cardinality, such that every vertex in G is within radius r to some vertex in S. While the r-dominating set problem on planar graph admits PTAS from Baker’s shifting/layering technique when r is a constant, the problem becomes significantly harder when r can depend on n. In fact, under Exponential-Time Hypothesis, Fox-Epstein ηl [SODA 2019] observed that no efficient PTAS can exist for the unbounded r-dominating set problem on planar graphs. One may consider even harder weighted-variant known as the vertex-weighted metric r-dominating set, where edges are associated with lengths, and every vertex is associated with a positive-valued weight, and the goal is to compute an r-dominating set with minimum total weight. As a result, people resorted to bicriteria algorithms by allowing the returned solution to use radius-(1+ε)r balls instead, in addition to the total weight being a 1+ε approximation to the optimal value. We establish the first single-criteria polynomial-time O(1)-approximation algorithm for the vertex-weighted metric r-dominating set problem on planar graphs when r is part of the input, and can be arbitrarily large compared to n. Our new (single-criteria) O(1)-approximation algorithm uses the quasi-uniformity sampling technique of Chan et al. [SODA 2012] by bounding the shallow cell complexity of the (unbounded) radius-r ball system to be linear in n. To this end we have two technical innovations: 1) The discrete ball system on planar graphs are neither pseudodisks nor have well-defined boundaries for standard union-complexity arguments. We construct a support graph for arbitrary distance ball systems as contractions of Voronoi cells; the sparseness comes as a byproduct. 2) We present an assignment of each depth-(≥3) cell to a unique 3-tuple of ball centers. This allows us to use standard Clarkson-Shor techniques to reduce the counting to cells of depth exactly 3, which we prove to be size O(n) by a novel geometric argument based on our support being a Voronoi contraction.
Cite as

Reilly Browne and Hsien-Chih Chang. Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{browne_et_al:LIPIcs.SoCG.2026.24,
  author =	{Browne, Reilly and Chang, Hsien-Chih},
  title =	{{Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.24},
  URN =		{urn:nbn:de:0030-drops-258300},
  doi =		{10.4230/LIPIcs.SoCG.2026.24},
  annote =	{Keywords: Minimum dominating set, planar graphs, shallow cell complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.36
Upward Book Embeddings of Partitioned Digraphs

Authors: Giordano Da Lozzo, Fabrizio Frati, and Ignaz Rutter

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
In 1999, Heath, Pemmaraju, and Trenk [SIAM J. Comput. 28(4), 1999] extended the classic notion of book embeddings to digraphs, introducing the concept of upward book embeddings, in which the vertices must appear along the spine in a topological order and the edges are partitioned into pages, so that no two edges in the same page cross. For a partitioned digraph G = (V, ⋃^k_{i=1} E_i), that is, a digraph whose edge set is partitioned into k subsets, an upward book embedding is required to assign edges to pages as prescribed by the given partition. In a companion paper, Heath and Pemmaraju [SIAM J. Comput. 28(5), 1999] proved that the problem of testing the existence of an upward book embedding of a partitioned digraph is linear-time solvable for k = 1 and recently Akitaya, Demaine, Hesterberg, and Liu [GD, 2017] have shown the problem NP-complete for k ≥ 3. In this paper, we study upward book embeddings of partitioned digraphs and focus on the unsolved case k = 2. Our first main result is a novel characterization of the upward embeddings that support an upward book embedding in two pages. We exploit this characterization in several ways, and obtain a rich picture of the complexity landscape of the problem. First, we show that the problem remains NP-complete when k = 2, thus closing the complexity gap for the problem. Second, we show that, for an n-vertex partitioned digraph with a prescribed planar embedding, the existence of an upward book embedding that respects the given planar embedding can be tested in O(n log³ n) time. Finally, leveraging the SPQ(R)-tree decomposition of biconnected graphs into triconnected components, we present a cubic-time testing algorithm for biconnected directed partial 2-trees.
Cite as

Giordano Da Lozzo, Fabrizio Frati, and Ignaz Rutter. Upward Book Embeddings of Partitioned Digraphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 36:1-36:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dalozzo_et_al:LIPIcs.SoCG.2026.36,
  author =	{Da Lozzo, Giordano and Frati, Fabrizio and Rutter, Ignaz},
  title =	{{Upward Book Embeddings of Partitioned Digraphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{36:1--36:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.36},
  URN =		{urn:nbn:de:0030-drops-258424},
  doi =		{10.4230/LIPIcs.SoCG.2026.36},
  annote =	{Keywords: upward book embeddings, partitioned digraphs, SPQ-trees, 2-trees}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.51
First-Order Logic and Twin-Width for Some Geometric Graphs

Authors: Colin Geniet, Gunwoo Kim, and Lucas Meijer

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
For some geometric graph classes, tractability of testing first-order formulas is precisely characterised by the graph parameter twin-width. This was first proved for interval graphs among others in [BCKKLT, IPEC '22], where the equivalence is called delineation, and more generally holds for circle graphs, rooted directed path graphs, and H-graphs when H is a forest. Delineation is based on the key idea that geometric graphs often admit natural vertex orderings, allowing to use the very rich theory of twin-width for ordered graphs. Answering two questions raised in their work, we prove that delineation holds for intersection graphs of non-degenerate axis-parallel unit segment graphs, but fails for visibility graphs of 1.5D terrains. We also prove delineation for intersection graphs of circular arcs.
Cite as

Colin Geniet, Gunwoo Kim, and Lucas Meijer. First-Order Logic and Twin-Width for Some Geometric Graphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 51:1-51:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{geniet_et_al:LIPIcs.SoCG.2026.51,
  author =	{Geniet, Colin and Kim, Gunwoo and Meijer, Lucas},
  title =	{{First-Order Logic and Twin-Width for Some Geometric Graphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{51:1--51:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.51},
  URN =		{urn:nbn:de:0030-drops-258575},
  doi =		{10.4230/LIPIcs.SoCG.2026.51},
  annote =	{Keywords: Twin-width, axis-parallel unit segment graphs, circular arc graphs, terrain visibility graphs, first-order logic, model checking, FPT}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICDT.2026.1
Query Decompositions and All That (Invited Talk)

Authors: Kyle Deeds, Timo Camillo Merkl, Reinhard Pichler, and Dan Suciu

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
The close relationship between Conjunctive Queries (CQs) and Constraint Satisfaction Problems (CSPs) has long been known. Nevertheless, apart from decomposition methods, research on efficient query evaluation or constraint solving algorithms has developed rather independently. In this article, we illustrate how search algorithms originating from the CSP community can be fruitfully applied to query evaluation - either by further developing the original search algorithms or by combining them with query decomposition methods. It turns out that the resulting approaches may indeed lead to lower time and/or space complexity than previous query evaluation methods.
Cite as

Kyle Deeds, Timo Camillo Merkl, Reinhard Pichler, and Dan Suciu. Query Decompositions and All That (Invited Talk). In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{deeds_et_al:LIPIcs.ICDT.2026.1,
  author =	{Deeds, Kyle and Merkl, Timo Camillo and Pichler, Reinhard and Suciu, Dan},
  title =	{{Query Decompositions and All That}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.1},
  URN =		{urn:nbn:de:0030-drops-256158},
  doi =		{10.4230/LIPIcs.ICDT.2026.1},
  annote =	{Keywords: Query evaluation, Query decompositions, Complexity}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICDT.2026.3
Building Relational Circuits (Invited Talk)

Authors: Florent Capelli

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
We review two algorithms which allow to build a factorized representation of the answers set of join queries. In a nutshell, the representation builds a circuit representing the answers set of a join query by starting from atomic relations and iteratively combine them by either constructing the Cartesian product or the disjoint union of previously computed relations. The first one can be seen as the trace of the celebrated Yannakakis algorithm, building the answer set from the inputs to the output of the circuit while the second adopts a top-down approach which can be seen as a generalization of the exhaustive DPLL algorithm, originally designed to solve the #SAT problem.
Cite as

Florent Capelli. Building Relational Circuits (Invited Talk). In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{capelli:LIPIcs.ICDT.2026.3,
  author =	{Capelli, Florent},
  title =	{{Building Relational Circuits}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.3},
  URN =		{urn:nbn:de:0030-drops-256172},
  doi =		{10.4230/LIPIcs.ICDT.2026.3},
  annote =	{Keywords: Conjunctive queries, factorized databases, knowledge compilation}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2026.7
The Importance of Parameters in Ranking Functions

Authors: Christoph Standke, Nikolaos Tziavelis, Wolfgang Gatterbauer, and Benny Kimelfeld

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
How important is the weight of a given column in determining the ranking of tuples in a table? To address such an explanation question about a ranking function, we investigate the computation of SHAP scores for column weights, adopting a recent framework by Grohe et al. [ICDT'24]. The exact definition of this score depends on three key components: (1) the ranking function in use, (2) an effect function that quantifies the impact of using alternative weights on the ranking, and (3) an underlying weight distribution. We analyze the computational complexity of different instantiations of this framework for a range of fundamental ranking and effect functions, focusing on probabilistically independent finite distributions for individual columns. For the ranking functions, we examine lexicographic orders and score-based orders defined by the summation, minimum, and maximum functions. For the effect functions, we consider global, top-k, and local perspectives: global measures quantify the divergence between the perturbed and original rankings, top-k measures inspect the change in the set of top-k answers, and local measures capture the impact on an individual tuple of interest. Although all cases admit an additive fully polynomial-time randomized approximation scheme (FPRAS), we establish the complexity of exact computation, identifying which cases are solvable in polynomial time and which are #P-hard. We further show that all complexity results, lower bounds and upper bounds, extend to a related task of computing the Shapley value of whole columns (regardless of their weight).
Cite as

Christoph Standke, Nikolaos Tziavelis, Wolfgang Gatterbauer, and Benny Kimelfeld. The Importance of Parameters in Ranking Functions. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{standke_et_al:LIPIcs.ICDT.2026.7,
  author =	{Standke, Christoph and Tziavelis, Nikolaos and Gatterbauer, Wolfgang and Kimelfeld, Benny},
  title =	{{The Importance of Parameters in Ranking Functions}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.7},
  URN =		{urn:nbn:de:0030-drops-256217},
  doi =		{10.4230/LIPIcs.ICDT.2026.7},
  annote =	{Keywords: Ranking, Explanation, Shapley value, SHAP scores}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2026.8
Neither Cover nor Pack: Distributed Worst-Case Optimality of Degree-2 Joins

Authors: Heba Aamer, Xiao Hu, and Bas Ketsman

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
We study the worst-case communication complexity of the join query evaluation problem over large-scale data in distributed shared-nothing systems under the MPC model. We focus on multi-round MPC algorithms that run in constant number of rounds. The problem is well-understood for a few classes of queries, mainly the class of acyclic queries and the class of graph-like queries. For queries not belonging to either class, the complexity picture is much less clear. We study the class of degree-two queries and fragments thereof. In this paper, we tighten the gap between the upper and lower bounds for the studied classes and establish worst-case optimality for some fragments of the considered classes. We also debunk a well-believed conjecture about which query-related quantity, in the worst-case, optimally captures the communication complexity of the studied problem.
Cite as

Heba Aamer, Xiao Hu, and Bas Ketsman. Neither Cover nor Pack: Distributed Worst-Case Optimality of Degree-2 Joins. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{aamer_et_al:LIPIcs.ICDT.2026.8,
  author =	{Aamer, Heba and Hu, Xiao and Ketsman, Bas},
  title =	{{Neither Cover nor Pack: Distributed Worst-Case Optimality of Degree-2 Joins}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.8},
  URN =		{urn:nbn:de:0030-drops-256226},
  doi =		{10.4230/LIPIcs.ICDT.2026.8},
  annote =	{Keywords: degree-two joins, worst-case optimality, distributed algorithms}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2026.9
Acyclic Join Sampling Under Selections: Dichotomy, Union Sampling, and Enumeration

Authors: Jinchao Huang, Yufei Tao, and Sibo Wang

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
Previous research on join sampling has focused on joins without selection conditions, even though such conditions are prevalent in everyday queries in database systems. Motivated by this, we undertake a systematic investigation on the complexity of sampling from the result of an acyclic join under equality conditions given only at runtime. When conditions are conjunctive, the goal is to understand when it is possible to precompute a feasible structure that uses Õ(IN) space and supports sampling in Õ(1) time, where IN is the input size. We present a dichotomy to characterize (subject to a widely-accepted conjecture) the existence of such structures based on the conditions supplied and, in every feasible scenario, give an optimal structure of O(IN) space and O(1) sample time. We then extend our investigation to conditions expressed in disjunctive normal form, where the core challenge reduces to the fundamental set union sampling problem. We overcome the challenge with an optimal algorithm and utilize it to develop optimal sampling structures. Our findings also lead to new results on the closely-related random enumeration problem.
Cite as

Jinchao Huang, Yufei Tao, and Sibo Wang. Acyclic Join Sampling Under Selections: Dichotomy, Union Sampling, and Enumeration. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{huang_et_al:LIPIcs.ICDT.2026.9,
  author =	{Huang, Jinchao and Tao, Yufei and Wang, Sibo},
  title =	{{Acyclic Join Sampling Under Selections: Dichotomy, Union Sampling, and Enumeration}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.9},
  URN =		{urn:nbn:de:0030-drops-256231},
  doi =		{10.4230/LIPIcs.ICDT.2026.9},
  annote =	{Keywords: Conjunctive Queries, Acyclic Joins, Sampling, Lower Bounds}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2026.11
Factorised Representations of Join Queries: Tight Bounds and a New Dichotomy

Authors: Christoph Berkholz and Harry Vinall-Smeeth

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
A common theme in factorised databases and knowledge compilation is the representation of solution sets in a useful yet succinct data structure. In this paper, we study the representation of the result of join queries (or, equivalently, the set of homomorphisms between two relational structures). We focus on the very general format of {∪,×}-circuits - also known as d-representations or DNNF circuits - and aim to find the limits of this approach. In prior work, it has been shown that there always exists a {∪,×}-circuit of size N^O(subw) representing the query result, where N is the size of the database and subw the submodular width of the query. If the arity of all relations is bounded by a constant, then subw is linear in the treewidth tw of the query. In this setting, the authors of this paper proved a lower bound of N^Ω(tw^ε) on the circuit size (ICALP 2023), where ε > 0 depends on the excluded grid theorem. Our first main contribution is to improve this lower bound to N^Ω(tw), which is tight up to a constant factor in the exponent. Our second contribution is a N^Ω(subw^{1/4}) lower bound on the circuit size for join queries over relations of unbounded arity. Both lower bounds are unconditional lower bounds on the circuit size for well-chosen database instances. Their proofs use a combination of structural (hyper)graph theory with communication complexity in a simple yet novel way. While the second lower bound is asymptotically equivalent to Marx’s conditional bound on the decision complexity (JACM 2013), our N^Θ(tw) bound in the bounded arity setting is tight, while the best conditional bound on the decision complexity is N^Ω(tw/log tw). Note that removing this logarithmic factor in the decision setting is a major open problem.
Cite as

Christoph Berkholz and Harry Vinall-Smeeth. Factorised Representations of Join Queries: Tight Bounds and a New Dichotomy. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{berkholz_et_al:LIPIcs.ICDT.2026.11,
  author =	{Berkholz, Christoph and Vinall-Smeeth, Harry},
  title =	{{Factorised Representations of Join Queries: Tight Bounds and a New Dichotomy}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.11},
  URN =		{urn:nbn:de:0030-drops-256255},
  doi =		{10.4230/LIPIcs.ICDT.2026.11},
  annote =	{Keywords: join queries, homomorphisms, factorised databases, succinct representation, knowledge compilation, lower bounds}
}
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