92 Search Results for "Watson, Thomas"

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.2026.11
Improved Approximation of Two Watchmen’s Routes in Simple Polygons

Authors: Anna Brötzner, Bengt J. Nilsson, and Christiane Schmidt

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

Abstract
We study the watchman route problem for a set of two watchmen for the objective of minimizing the length of the longest route (min-max) inside a simple polygon P having n vertices, which is known to be weakly NP-hard. First, we consider seeing a discrete set of m points in the interior of P. We show that even this problem is weakly NP-hard and present an approximation algorithm with approximation ratio 2+ε that runs in O(m⁵n) time, assuming that a starting point for each of the two routes is given. We generalize the algorithm to see all of the interior of P in O(n⁶) time with approximation ratio 2 + π/2 ≈ 3.571, improving on the previously known best algorithm that has an approximation ratio of ≈ 6.922 and runtime O(n²) [Bengt J. Nilsson and Eli Packer, 2024]. Finally, we describe how to extend this algorithm to the case where no starting points are given, this taking O(n⁸) time, yielding an approximation ratio of 3 + π/2 ≈ 4.571, improving on the previously known best approximation algorithm with ratio ≈ 5.969 also having runtime O(n⁸) [Bengt J. Nilsson and Eli Packer, 2024].
Cite as

Anna Brötzner, Bengt J. Nilsson, and Christiane Schmidt. Improved Approximation of Two Watchmen’s Routes in Simple Polygons. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{brotzner_et_al:LIPIcs.SWAT.2026.11,
  author =	{Br\"{o}tzner, Anna and Nilsson, Bengt J. and Schmidt, Christiane},
  title =	{{Improved Approximation of Two Watchmen’s Routes in Simple Polygons}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{11:1--11:16},
  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.2026.11},
  URN =		{urn:nbn:de:0030-drops-260472},
  doi =		{10.4230/LIPIcs.SWAT.2026.11},
  annote =	{Keywords: Art gallery problem, watchman route problem, multiple watchmen, path planning, polygons}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.5
Bifunction and Interlevel Delaunay Trifiltrations

Authors: Ángel Javier Alonso, Michael Kerber, Tung Lam, Michael Lesnick, and Abhishek Rathod

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

Abstract
A key property of the Delaunay filtration is that it is topologically (i.e., weakly) equivalent to the offset (union-of-balls) filtration. Recently, this filtration has been extended to point clouds equipped with an ℝ-valued function, yielding a computable 2-parameter filtration that satisfies an analogous weak equivalence. Motivated in part by the study of time-varying data, we introduce a 3-parameter extension of the Delaunay filtration for point clouds equipped with an ℝ²-valued function, also satisfying an analogous weak equivalence. For a point cloud X ⊂ ℝ^d, our trifiltration has size O(|X|^{⌈(d+1)/2⌉+1}). We present an algorithm that computes this trifiltration in time O(|X|^{⌈d/2⌉+2}), together with an implementation. Our experiments demonstrate that the implementation can handle thousands of points in ℝ³, with memory growth that is nearly linear.
Cite as

Ángel Javier Alonso, Michael Kerber, Tung Lam, Michael Lesnick, and Abhishek Rathod. Bifunction and Interlevel Delaunay Trifiltrations. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{alonso_et_al:LIPIcs.SoCG.2026.5,
  author =	{Alonso, \'{A}ngel Javier and Kerber, Michael and Lam, Tung and Lesnick, Michael and Rathod, Abhishek},
  title =	{{Bifunction and Interlevel Delaunay Trifiltrations}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{5:1--5:20},
  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.2026.5},
  URN =		{urn:nbn:de:0030-drops-258118},
  doi =		{10.4230/LIPIcs.SoCG.2026.5},
  annote =	{Keywords: Delaunay triangulation, Multiparameter persistent homology, Interlevel, Bowyer-Watson}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.5
Token Positional Games

Authors: Guillaume Bagan, Quentin Deschamps, Florian Galliot, Mirjana Mikalački, and Nacim Oijid

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
The classical Maker-Breaker positional game is played on a board which is a hypergraph ℋ, with two players, Maker and Breaker, alternately claiming vertices of ℋ until all the vertices are claimed. When the game ends, Maker wins if she has claimed all the vertices of some edge of ℋ; otherwise, Breaker wins. Playing this game in real life can be done by placing tokens on the vertices of the board. In this paper, we study the unfortunate case in which one or both players do not have enough tokens to cover all the vertices and, as such, will have to move their tokens around at some point instead of placing new ones. There may be a bias, in that Maker and Breaker do not necessarily have the same amount of tokens. The present paper initiates the study of this generalization of positional games, called token positional games. A particularly interesting case is when Maker has a winning strategy in the classical game: what is the lowest number of tokens with which she still wins against Breaker’s unlimited stock? We notably show that, for k-uniform hypergraphs on an arbitrarily large number n of vertices, this number equals k if k ∈ {2,3} but can vary from k to Ω(n) if k ≥ 4. From an algorithmic point of view, PSPACE-hardness in general is inherited from classical positional games, but we get a polynomial-time algorithm to solve the case where Breaker only has one token. We also establish EXPTIME-completeness for a "token sliding" variation of the game.
Cite as

Guillaume Bagan, Quentin Deschamps, Florian Galliot, Mirjana Mikalački, and Nacim Oijid. Token Positional Games. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bagan_et_al:LIPIcs.FUN.2026.5,
  author =	{Bagan, Guillaume and Deschamps, Quentin and Galliot, Florian and Mikala\v{c}ki, Mirjana and Oijid, Nacim},
  title =	{{Token Positional Games}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.5},
  URN =		{urn:nbn:de:0030-drops-257240},
  doi =		{10.4230/LIPIcs.FUN.2026.5},
  annote =	{Keywords: positional games, token games, hypergraphs, algorithmic complexity}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.24
On the Complexity of the Maker-Breaker Happy Vertex Game

Authors: Mathieu Hilaire, Perig Montfort, and Nacim Oijid

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
Given a c-colored graph G, a vertex v of G is said to be happy if it has the same color as all its neighbors. The notion of happy vertices was introduced by Zhang and Li [Peng Zhang and Angsheng Li, 2015] to compute the homophily of a graph. Eto, Fujimoto, Kiya, Matsushita, Miyano, Murao and Saitoh [Hiroshi Eto et al., 2025] introduced the Maker-Maker version of the Happy vertex game, where two players compete to claim more happy vertices than their opponent. We introduce here the Maker-Breaker happy vertex game: two players, Maker and Breaker, alternately color the vertices of a graph with their respective colors. Maker aims to maximize the number of happy vertices at the end, while Breaker aims to prevent her. This game is also a scoring version of the Maker-Breaker domination game introduced by Duchene, Gledel, Parreau and Renault [Duchene et al., 2020], as a happy vertex corresponds exactly to a vertex that is not dominated in the domination game. Therefore, this game is a very natural game on graphs and can be studied within the scope of scoring positional games [Bagan et al., 2024]. We initiate here the complexity study of this game, by proving that computing its score is PSPACE-complete on trees, NP-hard on caterpillars, and polynomial on subdivided stars. Finally, we provide the exact value of the score on graphs of maximum degree 2, and we provide an FPT-algorithm to compute the score on graphs of bounded neighborhood diversity. An important contribution of the paper is that, to achieve our hardness results, we introduce a new type of incidence graph called the literal-clause incidence graph for 2-SAT formulas. We prove that QMAX 2-SAT remains PSPACE-complete even if this graph is acyclic, and that MAX 2-SAT remains NP-complete, even if this graph is acyclic and has maximum degree 2, i.e. is a union of paths. We demonstrate the importance of this contribution by proving that Incidence, the scoring positional game played on a graph is also PSPACE-complete when restricted to forests.
Cite as

Mathieu Hilaire, Perig Montfort, and Nacim Oijid. On the Complexity of the Maker-Breaker Happy Vertex Game. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hilaire_et_al:LIPIcs.FUN.2026.24,
  author =	{Hilaire, Mathieu and Montfort, Perig and Oijid, Nacim},
  title =	{{On the Complexity of the Maker-Breaker Happy Vertex Game}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{24:1--24:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.24},
  URN =		{urn:nbn:de:0030-drops-257434},
  doi =		{10.4230/LIPIcs.FUN.2026.24},
  annote =	{Keywords: Maker-Breaker game, Domination game, happy vertex game, scoring game, complexity}
}
Document
DOI: 10.4230/OASIcs.NINeS.2026.9
Tight Loops, Smooth Streams: Responsive Congestion Control for Real-Time Video

Authors: Pantea Karimi, Sadjad Fouladi, Vibhaalakshmi Sivaraman, and Mohammad Alizadeh

Published in: OASIcs, Volume 139, 1st New Ideas in Networked Systems (NINeS 2026)

Abstract
Real-time video streaming relies on rate control to match video bitrate to network capacity while keeping latency low. Existing deployed video rate controllers react slowly to network changes, causing under-utilization and latency spikes. In contrast, modern delay-sensitive congestion control algorithms (CCAs) adapt on round-trip-time timescales, maintaining a tight feedback loop that achieves both high utilization and low latency. We introduce Vidaptive, a lightweight framework that enables real-time video to leverage responsive CCAs without codec changes. Vidaptive decouples encoding from transmission: it paces video frames at the CCA’s rate and injects dummy packets when the encoder output is insufficient, preserving a continuous feedback loop. An online algorithm dynamically adjusts the encoder’s target bitrate to align with CCA capacity while bounding frame latency. Implemented in Google WebRTC, Vidaptive improves both video quality and tail latency on diverse cellular traces. Compared to GCC, it delivers 1.5× higher bitrate, +40% VMAF, +1.4 dB SSIM, +1.3 dB PSNR, and reduces 95th-percentile frame latency by 57% (2.2 seconds). Against Salsify, it achieves lower tail latency without invasive codec modifications. These results show that coupling existing CCAs with a thin adaptation layer can outperform specialized video rate controllers while remaining deployable in practice.
Cite as

Pantea Karimi, Sadjad Fouladi, Vibhaalakshmi Sivaraman, and Mohammad Alizadeh. Tight Loops, Smooth Streams: Responsive Congestion Control for Real-Time Video. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 9:1-9:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{karimi_et_al:OASIcs.NINeS.2026.9,
  author =	{Karimi, Pantea and Fouladi, Sadjad and Sivaraman, Vibhaalakshmi and Alizadeh, Mohammad},
  title =	{{Tight Loops, Smooth Streams: Responsive Congestion Control for Real-Time Video}},
  booktitle =	{1st New Ideas in Networked Systems (NINeS 2026)},
  pages =	{9:1--9:29},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-414-7},
  ISSN =	{2190-6807},
  year =	{2026},
  volume =	{139},
  editor =	{Argyraki, Katerina and Panda, Aurojit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NINeS.2026.9},
  URN =		{urn:nbn:de:0030-drops-255942},
  doi =		{10.4230/OASIcs.NINeS.2026.9},
  annote =	{Keywords: real-time video, congestion control, transport protocols, video rate control, low-latency video communication, tight feedback loop}
}
Document
DOI: 10.4230/OASIcs.NINeS.2026.21
Accio: Rethinking OS-Architecture Co-Design for Next-Gen I/O

Authors: Amirmohammad Nazari, Rajit Manohar, and Robert Soulé

Published in: OASIcs, Volume 139, 1st New Ideas in Networked Systems (NINeS 2026)

Abstract
In this paper, we propose a novel software/hardware design to improve I/O performance while maintaining existing POSIX-standard APIs. Our approach stands in contrast to existing kernel-bypass strategies that improve performance at the expense of abandoning familiar programming abstractions. Our key insight is that navigating the performance-functionality trade-off requires changes to the processor; it cannot be done without support of the CPU micro-architecture. Our design, called Accio, includes: dedicated hardware for interrupt management, a hardware assist for thread scheduling, tables in hardware that manage I/O state, and modifications to the operating system to support the new hardware. Our evaluation demonstrates that Accio saturates the bus bandwidth, reduces CPU usage by up to 66% compared to state-of-the-art kernel-bypass systems, and reduces latency to 1/12th of that of the Linux kernel, matching that of kernel-bypass systems.
Cite as

Amirmohammad Nazari, Rajit Manohar, and Robert Soulé. Accio: Rethinking OS-Architecture Co-Design for Next-Gen I/O. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{nazari_et_al:OASIcs.NINeS.2026.21,
  author =	{Nazari, Amirmohammad and Manohar, Rajit and Soul\'{e}, Robert},
  title =	{{Accio: Rethinking OS-Architecture Co-Design for Next-Gen I/O}},
  booktitle =	{1st New Ideas in Networked Systems (NINeS 2026)},
  pages =	{21:1--21:24},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-414-7},
  ISSN =	{2190-6807},
  year =	{2026},
  volume =	{139},
  editor =	{Argyraki, Katerina and Panda, Aurojit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NINeS.2026.21},
  URN =		{urn:nbn:de:0030-drops-256063},
  doi =		{10.4230/OASIcs.NINeS.2026.21},
  annote =	{Keywords: Networks, Operating Systems, I/O Optimization}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.40
Maker-Maker Games of Rank 4 Are PSPACE-Complete

Authors: Florian Galliot and Jonas Sénizergues

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

Abstract
The Maker-Maker convention of positional games is played on a hypergraph whose edges are interpreted as winning sets. Two players take turns picking a previously unpicked vertex, aiming at being first to pick all the vertices of some edge. Optimal play can only lead to a first player win or a draw, and deciding between the two is known to be PSPACE-complete even for 6-uniform hypergraphs. We establish PSPACE-completeness for hypergraphs of rank 4. As an intermediary, we use the recently introduced achievement positional games, a more general convention in which each player has their own winning sets (blue and red). We show that deciding whether the blue player has a winning strategy as the first player is PSPACE-complete even with blue edges of size 2 or 3 and pairwise disjoint red edges of size 2. The result for hypergraphs of rank 4 in the Maker-Maker convention follows as a simple corollary.
Cite as

Florian Galliot and Jonas Sénizergues. Maker-Maker Games of Rank 4 Are PSPACE-Complete. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{galliot_et_al:LIPIcs.STACS.2026.40,
  author =	{Galliot, Florian and S\'{e}nizergues, Jonas},
  title =	{{Maker-Maker Games of Rank 4 Are PSPACE-Complete}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{40:1--40:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.40},
  URN =		{urn:nbn:de:0030-drops-255298},
  doi =		{10.4230/LIPIcs.STACS.2026.40},
  annote =	{Keywords: Game theory, Positional games, Combinatorial games, Complexity, Hypergraphs}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.23
Simple Circuit Extensions for XOR in PTIME

Authors: Marco Carmosino, Ngu Dang, and Tim Jackman

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

Abstract
The Minimum Circuit Size Problem for Partial Functions (MCSP^*) is hard assuming the Exponential Time Hypothesis (ETH) (Ilango, 2020). This breakthrough result leveraged a characterization of the optimal {∧, ∨, ¬} circuits for n-bit OR (OR_n) and a reduction from the partial f-Simple Extension Problem where f = OR_n. It remains open to extend that reduction to show ETH-hardness of total MCSP. However, Ilango observed that the total f-Simple Extension Problem is easy whenever f is computed by read-once formulas (like OR_n). Therefore, extending Ilango’s proof to total MCSP would require replacing OR_n with a more complex but similarly well-understood Boolean function. This work shows that the f-Simple Extension problem remains easy when f is the next natural candidate: XOR_n. We first develop a fixed-parameter tractable algorithm for the f-Simple Extension Problem that is efficient whenever the optimal circuits for f are (1) linear in size, (2) polynomially "few" and efficiently enumerable in the truth-table size (up to isomorphism and permutation of inputs), and (3) all have constant bounded fan-out. XOR_n satisfies all three of these conditions. When ¬ gates count towards circuit size, optimal XOR_n circuits are binary trees of n-1 subcircuits computing (¬)XOR₂ (Kombarov, 2011). We extend this characterization when ¬ gates do not contribute the circuit size. Thus, the XOR-Simple Extension Problem is in polynomial time under both measures of circuit complexity. We conclude by discussing conjectures about the complexity of the f-Simple Extension problem for each explicit function f with known and unrestricted circuit lower bounds over the DeMorgan basis. Examining the conditions under which our Simple Extension Solver is efficient, we argue that multiplexer functions (MUX) are the most promising candidate for ETH-hardness of a Simple Extension Problem, towards proving ETH-hardness of total MCSP.
Cite as

Marco Carmosino, Ngu Dang, and Tim Jackman. Simple Circuit Extensions for XOR in PTIME. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{carmosino_et_al:LIPIcs.STACS.2026.23,
  author =	{Carmosino, Marco and Dang, Ngu and Jackman, Tim},
  title =	{{Simple Circuit Extensions for XOR in PTIME}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.23},
  URN =		{urn:nbn:de:0030-drops-255127},
  doi =		{10.4230/LIPIcs.STACS.2026.23},
  annote =	{Keywords: Minimum Circuit Size Problem, Circuit Lower Bounds, Exponential Time Hypothesis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.66
Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds

Authors: Yupan Liu

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

Abstract
We investigate the computational hardness of estimating the quantum α-Rényi entropy S^𝚁_α(ρ) = (ln Tr(ρ^α))/(1-α) and the quantum q-Tsallis entropy S^𝚃_q(ρ) = (1-Tr(ρ^q))/(q-1), both converging to the von Neumann entropy as the order approaches 1. The promise problems Quantum α-Rényi Entropy Approximation (RényiQEA_α) and Quantum q-Tsallis Entropy Approximation (TsallisQEA_q) ask whether S^𝚁_α(ρ) or S^𝚃_q(ρ), respectively, is at least τ_Y or at most τ_N, where τ_Y - τ_N is typically a positive constant. Previous hardness results cover only the von Neumann entropy (order 1) and some cases of the quantum q-Tsallis entropy, while existing approaches do not readily extend to other orders. We establish that for all positive real orders, the rank-2 variants Rank2RényiQEA_α and Rank2TsallisQEA_q are BQP-hard. Combined with prior (rank-dependent) quantum query algorithms in Wang, Guan, Liu, Zhang, and Ying (TIT 2024), Wang, Zhang, and Li (TIT 2024), and Liu and Wang (SODA 2025), our results imply: - For all real order α > 0 and 0 < q ≤ 1, LowRankRényiQEA_α and LowRankTsallisQEA_q are BQP-complete, where both are restricted versions of RényiQEA_α and TsallisQEA_q with ρ of polynomial rank. - For all real order q > 1, TsallisQEA_q is BQP-complete. Our hardness results stem from reductions based on new inequalities relating the α-Rényi or q-Tsallis binary entropies of different orders, where the reductions differ substantially from previous approaches, and the inequalities are also of independent interest.
Cite as

Yupan Liu. Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 66:1-66:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{liu:LIPIcs.STACS.2026.66,
  author =	{Liu, Yupan},
  title =	{{Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{66:1--66:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.66},
  URN =		{urn:nbn:de:0030-drops-255550},
  doi =		{10.4230/LIPIcs.STACS.2026.66},
  annote =	{Keywords: computational hardness, quantum state testing, quantum R\'{e}nyi entropy, quantum Tsallis entropy, von Neumann entropy}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.54
A 13/6-Approximation for Strip Packing via the Bottom-Left Algorithm

Authors: Stefan Hougardy and Bart Zondervan

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

Abstract
In the Strip Packing problem, we are given a vertical strip of fixed width and unbounded height, along with a set of axis‑parallel rectangles. The task is to place all rectangles within the strip, without overlaps, while minimizing the height of the packing. This problem is known to be NP-hard. The Bottom-Left Algorithm is a simple and widely used heuristic for Strip Packing. Given a fixed order of the rectangles, it places them one by one, always choosing the lowest feasible position in the strip and, in case of ties, the leftmost one. Baker, Coffman, and Rivest proved in 1980 that the Bottom-Left Algorithm has approximation ratio 3 if the rectangles are sorted by decreasing width [Brenda S. Baker et al., 1980]. For the past 45 years, no alternative ordering has been found that improves this bound. We introduce a new rectangle ordering and show that with this ordering the Bottom-Left Algorithm achieves a 13/6 approximation for the Strip Packing problem.
Cite as

Stefan Hougardy and Bart Zondervan. A 13/6-Approximation for Strip Packing via the Bottom-Left Algorithm. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 54:1-54:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hougardy_et_al:LIPIcs.STACS.2026.54,
  author =	{Hougardy, Stefan and Zondervan, Bart},
  title =	{{A 13/6-Approximation for Strip Packing via the Bottom-Left Algorithm}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{54:1--54:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.54},
  URN =		{urn:nbn:de:0030-drops-255432},
  doi =		{10.4230/LIPIcs.STACS.2026.54},
  annote =	{Keywords: Approximation Algorithm, Strip Packing, Bottom-Left Algorithm, Rectangle Packing}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.59
When Is Local Search Both Effective and Efficient?

Authors: Artem Kaznatcheev and Sofia Vazquez Alferez

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

Abstract
Combinatorial optimization problems implicitly define fitness landscapes that combine the numeric structure of the "fitness" function to be maximized with the combinatorial structure of which assignments are "adjacent". Local search starts at an assignment in this landscape and successively moves assignments until no further improvement is possible among the adjacent assignments. Classic analyses of local search algorithms have focused more on the question of effectiveness ("did we find a good solution?") and often implicitly assumed that there are no doubts about their efficiency ("did we find it quickly?"). But there are many reasons to doubt the efficiency of local search. Even if we focus on fitness landscapes on the hypercube that are single peaked on every subcube (known as semismooth fitness landscapes, completely unimodal pseudo-Boolean functions, or acyclic unique sink orientations) where effectiveness is obvious, many local search algorithms are known to be inefficient. Since fitness landscapes are unwieldy exponentially large objects, we focus on their polynomial-sized representations by instances of valued constraint satisfaction problems (VCSP). We define a "direction" for valued constraints such that directed VCSPs generate semismooth fitness landscapes. We call directed VCSPs oriented if they do not have any pair of variables with arcs in both directions. Since recognizing if a VCSP-instance is directed or oriented is coNP-complete, we generalized oriented VCSPs as conditionally-smooth fitness landscapes where the structural property of "conditionally-smooth" is recognizable in polynomial time for a VCSP-instance. We prove that many popular local search algorithms like random ascent, simulated annealing, history-based rules, jumping rules, and the Kernighan-Lin heuristic are very efficient on conditionally-smooth landscapes. But conditionally-smooth landscapes are still expressive enough so that other well-regarded local search algorithms like steepest ascent and random facet require a super-polynomial number of steps to find the fitness peak.
Cite as

Artem Kaznatcheev and Sofia Vazquez Alferez. When Is Local Search Both Effective and Efficient?. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 59:1-59:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kaznatcheev_et_al:LIPIcs.STACS.2026.59,
  author =	{Kaznatcheev, Artem and Vazquez Alferez, Sofia},
  title =	{{When Is Local Search Both Effective and Efficient?}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{59:1--59:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.59},
  URN =		{urn:nbn:de:0030-drops-255480},
  doi =		{10.4230/LIPIcs.STACS.2026.59},
  annote =	{Keywords: valued constraint satisfaction problem, local search, algorithm analysis, constraint graphs, pseudo-Boolean functions, parameterized complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.37
New Algebrization Barriers to Circuit Lower Bounds via Communication Complexity of Missing-String

Authors: Lijie Chen, Yang Hu, and Hanlin Ren

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

Abstract
The algebrization barrier, proposed by Aaronson and Wigderson (STOC '08, ToCT '09), captures the limitations of many complexity-theoretic techniques based on arithmetization. Notably, several circuit lower bounds that overcome the relativization barrier (Buhrman-Fortnow-Thierauf, CCC '98; Vinodchandran, TCS '05; Santhanam, STOC '07, SICOMP '09) remain subject to the algebrization barrier. In this work, we establish several new algebrization barriers to circuit lower bounds by studying the communication complexity of the following problem, called XOR-Missing-String: For m < 2^{n/2}, Alice gets a list of m strings x₁, … , x_m ∈ {0, 1}ⁿ, Bob gets a list of m strings y₁, … , y_m ∈ {0, 1}ⁿ, and the goal is to output a string s ∈ {0, 1}ⁿ that is not equal to x_i⊕ y_j for any i, j ∈ [m]. 1) We construct an oracle A₁ and its multilinear extension A₁̃ such that PostBPE^{A₁̃} has linear-size A₁-oracle circuits on infinitely many input lengths. That is, proving PostBPE ̸ ⊆ i.o.- SIZE[O(n)] requires non-algebrizing techniques. This barrier follows from a PostBPP communication lower bound for XOR-Missing-String. This is in contrast to the well-known algebrizing lower bound MA_E (⊆ PostBPE) ̸ ⊆ P/_poly. 2) We construct an oracle A₂ and its multilinear extension A₂̃ such that BPE^{A₂̃} has linear-size A₂-oracle circuits on all input lengths. Previously, a similar barrier was demonstrated by Aaronson and Wigderson, but in their result, A₂̃ is only a multiquadratic extension of A₂. Our results show that communication complexity is more useful than previously thought for proving algebrization barriers, as Aaronson and Wigderson wrote that communication-based barriers were "more contrived". This serves as an example of how XOR-Missing-String forms new connections between communication lower bounds and algebrization barriers. 3) Finally, we study algebrization barriers to circuit lower bounds for MA_E. Buhrman, Fortnow, and Thierauf proved a sub-half-exponential circuit lower bound for MA_E via algebrizing techniques. Toward understanding whether the half-exponential bound can be improved, we define a natural subclass of MA_E that includes their hard MA_E language, and prove the following result: For every super-half-exponential function h(n), we construct an oracle A₃ and its multilinear extension A₃̃ such that this natural subclass of MA_E^{A₃̃} has h(n)-size A₃-oracle circuits on all input lengths. This suggests that half-exponential might be the correct barrier for MA_E circuit lower bounds w.r.t. algebrizing techniques.
Cite as

Lijie Chen, Yang Hu, and Hanlin Ren. New Algebrization Barriers to Circuit Lower Bounds via Communication Complexity of Missing-String. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 37:1-37:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2026.37,
  author =	{Chen, Lijie and Hu, Yang and Ren, Hanlin},
  title =	{{New Algebrization Barriers to Circuit Lower Bounds via Communication Complexity of Missing-String}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{37:1--37:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.37},
  URN =		{urn:nbn:de:0030-drops-253246},
  doi =		{10.4230/LIPIcs.ITCS.2026.37},
  annote =	{Keywords: circuit lower bound, algebrization barrier, missing string, communication complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.112
Lower Bounds Beyond DNF of Parities

Authors: Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov

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

Abstract
We consider a subclass of AC⁰[2] circuits that simultaneously captures DNF∘Xor and depth-3 AC⁰ circuits. For this class we show a technique for proving lower bounds inspired by the top-down approach. We give lower bounds for the middle slice function, inner product function, and affine dispersers.
Cite as

Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov. Lower Bounds Beyond DNF of Parities. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{riazanov_et_al:LIPIcs.ITCS.2026.112,
  author =	{Riazanov, Artur and Sofronova, Anastasia and Sokolov, Dmitry},
  title =	{{Lower Bounds Beyond DNF of Parities}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{112:1--112:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.112},
  URN =		{urn:nbn:de:0030-drops-253996},
  doi =		{10.4230/LIPIcs.ITCS.2026.112},
  annote =	{Keywords: boolean circuits, top-down, unpredictability}
}
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