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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2026.130

Lower Bounds on Pure Dynamic Programming for Connectivity Problems on Graphs of Bounded Path-Width

Authors: Kacper Kluk and Jesper Nederlof

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

Abstract

We give unconditional parameterized complexity lower bounds on pure dynamic programming algorithms - as modeled by tropical circuits - for connectivity problems such as the Traveling Salesperson Problem. Our lower bounds are higher than the currently fastest algorithms that rely on algebra and give evidence that these algebraic aspects are unavoidable for competitive worst case running times. Specifically, we study input graphs with a small width parameter such as treewidth and pathwidth and show that for any k there exists a graph G of pathwidth at most k and k^𝒪(1) vertices such that any tropical circuit calculating the optimal value of a Traveling Salesperson round tour uses at least 2^Ω(k log log k) gates. We establish this result by linking tropical circuit complexity to the nondeterministic communication complexity of specific compatibility matrices. These matrices encode whether two partial solutions combine into a full solution, and Raz and Spieker [Combinatorica 1995] previously proved a lower bound for this complexity measure.

Cite as

Kacper Kluk and Jesper Nederlof. Lower Bounds on Pure Dynamic Programming for Connectivity Problems on Graphs of Bounded Path-Width. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 130:1-130:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kluk_et_al:LIPIcs.ICALP.2026.130,
  author =	{Kluk, Kacper and Nederlof, Jesper},
  title =	{{Lower Bounds on Pure Dynamic Programming for Connectivity Problems on Graphs of Bounded Path-Width}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{130:1--130:23},
  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.2026.130},
  URN =		{urn:nbn:de:0030-drops-265196},
  doi =		{10.4230/LIPIcs.ICALP.2026.130},
  annote =	{Keywords: Parameterized Complexity, treewidth, tropical circuits, connectivity problems}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.5

BuffCut: Prioritized Buffered Streaming Graph Partitioning

Authors: Linus Baumgärtner, Adil Chhabra, Marcelo Fonseca Faraj, and Christian Schulz

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

Abstract

Streaming graph partitioners enable resource-efficient and massively scalable partitioning, but one-pass assignment heuristics are highly sensitive to stream order and often yield substantially higher edge cuts than in-memory methods. We present BuffCut, a buffered streaming partitioner that narrows this quality gap, particularly when stream ordering is adversarial, by combining prioritized buffering with batch-wise multilevel assignment. BuffCut maintains a bounded priority buffer to delay poorly informed decisions and regulate the order in which nodes are considered for assignment. It incrementally constructs high-locality batches of configurable size by iteratively inserting the highest-priority nodes from the buffer into the batch, effectively recovering locality structure from the stream. Each batch is then assigned via a multilevel partitioning algorithm. Experiments on diverse real-world and synthetic graphs show that BuffCut consistently outperforms state-of-the-art buffered streaming methods. Compared to the strongest prioritized buffering baseline, BuffCut achieves 20.8% fewer edge cuts while running 2.9× faster and using 11.3× less memory. Against the next-best batched method, it reduces edge cut by 15.8% with only modest overheads of 1.8× runtime and 1.09× memory.

Cite as

Linus Baumgärtner, Adil Chhabra, Marcelo Fonseca Faraj, and Christian Schulz. BuffCut: Prioritized Buffered Streaming Graph Partitioning. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{baumgartner_et_al:LIPIcs.SEA.2026.5,
  author =	{Baumg\"{a}rtner, Linus and Chhabra, Adil and Faraj, Marcelo Fonseca and Schulz, Christian},
  title =	{{BuffCut: Prioritized Buffered Streaming Graph Partitioning}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{5:1--5:20},
  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.2026.5},
  URN =		{urn:nbn:de:0030-drops-260097},
  doi =		{10.4230/LIPIcs.SEA.2026.5},
  annote =	{Keywords: graph partitioning, streaming, online, buffered, prioritized partitioning}
}

Document

DOI: 10.4230/LIPIcs.SEA.2026.4

Integer Programming Models for the Median of a 0-1 String Set Under Levenshtein Distance

Authors: Claudio Arbib, Andrea D'Ascenzo, Oya E. Karaşan, and Andrea Pizzuti

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

Abstract

The Median String Problem calls for finding a string that minimizes the average distance from a given set of strings. Under the Levenshtein (or edit) metric, the problem is NP-hard even for binary strings. We devised two novel integer linear programming models for this case and tested them against the only formulation we are aware of in the literature. Our numerical experiments attest to the efficacy of the proposed approach.

Cite as

Claudio Arbib, Andrea D'Ascenzo, Oya E. Karaşan, and Andrea Pizzuti. Integer Programming Models for the Median of a 0-1 String Set Under Levenshtein Distance. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{arbib_et_al:LIPIcs.SEA.2026.4,
  author =	{Arbib, Claudio and D'Ascenzo, Andrea and Kara\c{s}an, Oya E. and Pizzuti, Andrea},
  title =	{{Integer Programming Models for the Median of a 0-1 String Set Under Levenshtein Distance}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{4:1--4:15},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-260081},
  doi =		{10.4230/LIPIcs.SEA.2026.4},
  annote =	{Keywords: Levenshtein Distance, Median String Problem, Integer Programming}
}

Document

DOI: 10.4230/LIPIcs.CPM.2026.12

Maximizing Diversity in (Near-)Median String Selection

Authors: Diptarka Chakraborty, Rudrayan Kundu, Nidhi Purohit, and Aravinda Kanchana Ruwanpathirana

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

Abstract

Given a set of strings over a specified alphabet, identifying a median or consensus string that minimizes the total distance to all input strings is a fundamental data aggregation problem. When the Hamming distance is considered as the underlying metric, this problem has extensive applications, ranging from bioinformatics to pattern recognition. However, modern applications often require the generation of multiple (near-)optimal yet diverse median strings to enhance flexibility and robustness in decision-making. In this study, we address this need by focusing on two prominent diversity measures: sum dispersion and min dispersion. We first introduce an exact algorithm for the diameter variant of the problem, which identifies pairs of near-optimal medians that are maximally diverse. Subsequently, we propose a (1-ε)-approximation algorithm (for any ε > 0) for sum dispersion, as well as a bi-criteria approximation algorithm for the more challenging min dispersion case, allowing the generation of multiple (more than two) diverse near-optimal Hamming medians. Our approach primarily leverages structural insights into the Hamming median space and also draws on techniques from error-correcting code construction to establish these results.

Cite as

Diptarka Chakraborty, Rudrayan Kundu, Nidhi Purohit, and Aravinda Kanchana Ruwanpathirana. Maximizing Diversity in (Near-)Median String Selection. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chakraborty_et_al:LIPIcs.CPM.2026.12,
  author =	{Chakraborty, Diptarka and Kundu, Rudrayan and Purohit, Nidhi and Ruwanpathirana, Aravinda Kanchana},
  title =	{{Maximizing Diversity in (Near-)Median String Selection}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{12:1--12:15},
  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.2026.12},
  URN =		{urn:nbn:de:0030-drops-259382},
  doi =		{10.4230/LIPIcs.CPM.2026.12},
  annote =	{Keywords: Diversity maximization, Hamming median, diameter, dispersion, approximation algorithms}
}

Document

DOI: 10.4230/LITES.11.1.1

A Survey of Real-Time Support, Analysis, and Advancements in ROS 2

Authors: Daniel Casini, Jian-Jia Chen, Jing Li, Federico Reghenzani, and Harun Teper

Published in: LITES, Volume 11, Issue 1 (2026). Leibniz Transactions on Embedded Systems, Volume 11, Issue 1

Abstract

The Robot Operating System 2 (ROS 2) has emerged as a relevant middleware framework for robotic applications, offering modularity, distributed execution, and communication. In the last six years, ROS 2 has drawn increasing attention from the real-time systems community and industry. This survey presents a comprehensive overview of research efforts that analyze, enhance, and extend ROS 2 to support real-time execution. We first provide a detailed description of the internal scheduling mechanisms of ROS 2 and its layered architecture, including the interaction with DDS-based communication and other communication middleware. We then review key contributions from the literature, covering timing analysis for both single- and multi-threaded executors, metrics such as response time, reaction time, and data age, and different communication modes. The survey also discusses community-driven enhancements to the ROS 2 runtime, including new executor algorithm designs, real-time GPU management, and microcontroller support via micro-ROS. Furthermore, we summarize techniques for bounding DDS communication delays, message filters, and profiling tools that have been developed to support analysis and experimentation. To help systematize this growing body of work, we introduce taxonomies that classify the surveyed contributions based on different criteria. This survey aims to guide both researchers and practitioners in understanding and improving the real-time capabilities of ROS 2.

Cite as

Daniel Casini, Jian-Jia Chen, Jing Li, Federico Reghenzani, and Harun Teper. A Survey of Real-Time Support, Analysis, and Advancements in ROS 2. In LITES, Volume 11, Issue 1 (2026). Leibniz Transactions on Embedded Systems, Volume 11, Issue 1, pp. 1:1-1:37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@Article{casini_et_al:LITES.11.1.1,
  author =	{Casini, Daniel and Chen, Jian-Jia and Li, Jing and Reghenzani, Federico and Teper, Harun},
  title =	{{A Survey of Real-Time Support, Analysis, and Advancements in ROS 2}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{1:1--1:37},
  ISSN =	{2199-2002},
  year =	{2026},
  volume =	{11},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.11.1.1},
  URN =		{urn:nbn:de:0030-drops-257914},
  doi =		{10.4230/LITES.11.1.1},
  annote =	{Keywords: ROS 2, middleware, real-time, timing predictability, publish-subscribe}
}

Document

DOI: 10.4230/OASIcs.NINeS.2026.5

OrbitalBrain: A Distributed Framework for Training ML Models in Space

Authors: Om Chabra, Chenning Li, Kevin Hsieh, Santiago Segarra, Behnaz Arzani, Peder Olsen, and Ranveer Chandra

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

Abstract

Earth observation nanosatellites capture high-resolution photos of the Earth in near real-time. These images increasingly support ML applications that are critical for safety and response, such as forest fire and flood detection. However, the downlink bandwidth is limited, resulting in days or weeks of delay from image capture to training. In this work, we propose OrbitalBrain, an efficient in-space distributed ML training framework that leverages limited and predictable satellite compute, bandwidth, and power to intelligently balance data transfer, model aggregation, and local training. Our evaluations demonstrate that OrbitalBrain achieves 1.52×-12.4× speedup in time-to-accuracy while always reaching a higher final model accuracy compared to state-of-the-art ground-based or federated learning baselines. Furthermore, our approach is complementary to satellite imagery capturing and downloading, enhancing the overall efficiency of satellite-based applications.

Cite as

Om Chabra, Chenning Li, Kevin Hsieh, Santiago Segarra, Behnaz Arzani, Peder Olsen, and Ranveer Chandra. OrbitalBrain: A Distributed Framework for Training ML Models in Space. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 5:1-5:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chabra_et_al:OASIcs.NINeS.2026.5,
  author =	{Chabra, Om and Li, Chenning and Hsieh, Kevin and Segarra, Santiago and Arzani, Behnaz and Olsen, Peder and Chandra, Ranveer},
  title =	{{OrbitalBrain: A Distributed Framework for Training ML Models in Space}},
  booktitle =	{1st New Ideas in Networked Systems (NINeS 2026)},
  pages =	{5:1--5:32},
  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.2026.5},
  URN =		{urn:nbn:de:0030-drops-255907},
  doi =		{10.4230/OASIcs.NINeS.2026.5},
  annote =	{Keywords: Satellite networks, Distributed machine learning, Federated learning, Earth observation, In-orbit computing}
}

Document

DOI: 10.4230/OASIcs.NINeS.2026.10

Scalable Routing in a City-Scale Wi-Fi Network for Disaster Recovery

Authors: Ziqian Liu, Om Chabra, James Lynch, Aaron Martin, Chenning Li, and Hari Balakrishnan

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

Abstract

This paper presents CityMesh, a city-scale decentralized mesh network designed for disaster recovery and emergency scenarios. When wide-area Internet connectivity is unavailable or severely degraded, CityMesh leverages both static access points and mobile devices equipped with Wi-Fi to provide intra-city connectivity and reach opportunistic gateways to the Internet (e.g., via satellite links). The main contribution of this paper is a scalable routing protocol that supports millions of devices, addressing a long-standing limitation of wireless mesh and mobile ad hoc networks. Unlike prior approaches, CityMesh exploits rich building-location and building-geometry data from widely available city maps to guide route computation, improving packet delivery while significantly reducing transmission overhead. Simulation results from 70 cities show that CityMesh improves packet delivery rates by 88% over WEAVE (a state-of-the-art geographic routing protocol). A campus-scale deployment of 300 Wi-Fi devices across 31 buildings shows the practical deployability of CityMesh. These results demonstrate the promise of map-aware routing as a foundation for scalable, resilient city-wide Wi-Fi networks.

Cite as

Ziqian Liu, Om Chabra, James Lynch, Aaron Martin, Chenning Li, and Hari Balakrishnan. Scalable Routing in a City-Scale Wi-Fi Network for Disaster Recovery. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 10:1-10:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{liu_et_al:OASIcs.NINeS.2026.10,
  author =	{Liu, Ziqian and Chabra, Om and Lynch, James and Martin, Aaron and Li, Chenning and Balakrishnan, Hari},
  title =	{{Scalable Routing in a City-Scale Wi-Fi Network for Disaster Recovery}},
  booktitle =	{1st New Ideas in Networked Systems (NINeS 2026)},
  pages =	{10:1--10:31},
  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.2026.10},
  URN =		{urn:nbn:de:0030-drops-255954},
  doi =		{10.4230/OASIcs.NINeS.2026.10},
  annote =	{Keywords: mesh networking, disaster recovery, geographic routing, scalability, Wi-Fi}
}

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.2026.62

Relative Compressed Reverse Suffix Array

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

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

Abstract

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

Cite as

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

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

Document

DOI: 10.4230/LIPIcs.ITCS.2026.49

Debordering Closure Results in Determinantal and Pfaffian Ideals

Authors: Anakin Dey and Zeyu Guo

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

Abstract

One important question in algebraic complexity is understanding the complexity of polynomial ideals (Grochow, Bulletin of EATCS 131, 2020). Andrews and Forbes (STOC 2022) studied the determinantal ideals I^{det}_{n,m,r} generated by the r× r minors of n× m matrices. Over fields of characteristic zero or of sufficiently large characteristic, they showed that for any nonzero f ∈ I^{det}_{n,m,r}, the determinant of a t × t matrix of variables with t = Θ{r^{1/3}} is approximately computed by a constant-depth, polynomial-size f-oracle algebraic circuit, in the sense that the determinant lies in the border of such circuits. An analogous result was also obtained for Pfaffians in the same paper. In this work, we deborder the result of Andrews and Forbes by showing that when f has polynomial degree, the determinant is in fact exactly computed by a constant-depth, polynomial-size f-oracle algebraic circuit. We further establish an analogous result for Pfaffian ideals. Our results are established using the isolation lemma, combined with a careful analysis of straightening-law expansions of polynomials in determinantal and Pfaffian ideals.

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Anakin Dey and Zeyu Guo. Debordering Closure Results in Determinantal and Pfaffian Ideals. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 49:1-49:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dey_et_al:LIPIcs.ITCS.2026.49,
  author =	{Dey, Anakin and Guo, Zeyu},
  title =	{{Debordering Closure Results in Determinantal and Pfaffian Ideals}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{49:1--49:24},
  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.2026.49},
  URN =		{urn:nbn:de:0030-drops-253363},
  doi =		{10.4230/LIPIcs.ITCS.2026.49},
  annote =	{Keywords: Algebraic circuit complexity, Isolation lemma, Debordering}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.32

Vanishing Signatures, Orbit Closure, and the Converse of the Holant Theorem

Authors: Jin-Yi Cai and Ben Young

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

Abstract

Valiant’s Holant theorem is a powerful tool for algorithms and reductions for counting problems. It states that if two sets ℱ and 𝒢 of tensors (a.k.a. constraint functions or signatures) are related by a holographic transformation, then ℱ and 𝒢 are Holant-indistinguishable, i.e., every tensor network using tensors from ℱ, respectively from 𝒢, contracts to the same value. Xia (ICALP 2010) conjectured the converse of the Holant theorem, but a counterexample was found based on vanishing signatures, those which are Holant-indistinguishable from 0. We prove two near-converses of the Holant theorem using techniques from invariant theory. (I) Holant-indistinguishable ℱ and 𝒢 always admit two sequences of holographic transformations mapping them arbitrarily close to each other, i.e., their GL_q-orbit closures intersect. (II) We show that vanishing signatures are the only true obstacle to a converse of the Holant theorem. As corollaries of the two theorems we obtain the first characterization of homomorphism-indistinguishability over graphs of bounded degree, a long standing open problem, and show that two graphs with invertible adjacency matrices are isomorphic if and only if they are homomorphism-indistinguishable over graphs with maximum degree at most three. We also show that Holant-indistinguishability is complete for a complexity class TOCI introduced by Lysikov and Walter [Vladimir Lysikov and Michael Walter, 2024], and hence hard for graph isomorphism.

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Jin-Yi Cai and Ben Young. Vanishing Signatures, Orbit Closure, and the Converse of the Holant Theorem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cai_et_al:LIPIcs.ITCS.2026.32,
  author =	{Cai, Jin-Yi and Young, Ben},
  title =	{{Vanishing Signatures, Orbit Closure, and the Converse of the Holant Theorem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{32:1--32:20},
  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.2026.32},
  URN =		{urn:nbn:de:0030-drops-253198},
  doi =		{10.4230/LIPIcs.ITCS.2026.32},
  annote =	{Keywords: Holant, Orbit Closure Intersection, Homomorphism Indistinguishability, Tensor Network}
}

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}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.4

Pseudodeterministic Algorithms for Minimum Cut Problems

Authors: Aryan Agarwala and Nithin Varma

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

Abstract

In this paper we present efficient pseudodeterministic algorithms for both the global minimum cut and minimum s-t cut problems. The running time of our algorithm for the global minimum cut problem is asymptotically better than the fastest sequential deterministic global minimum cut algorithm (Henzinger, Li, Rao, Wang; SODA 2024). Furthermore, we implement our algorithm in streaming, PRAM, and cut-query models, where no efficient deterministic global minimum cut algorithms are known.

Cite as

Aryan Agarwala and Nithin Varma. Pseudodeterministic Algorithms for Minimum Cut Problems. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.4,
  author =	{Agarwala, Aryan and Varma, Nithin},
  title =	{{Pseudodeterministic Algorithms for Minimum Cut Problems}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{4:1--4:15},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-252917},
  doi =		{10.4230/LIPIcs.ITCS.2026.4},
  annote =	{Keywords: Minimum Cut, Pseudodeterministic Algorithms}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.56

The Hardness of Learning Quantum Circuits and Its Cryptographic Applications

Authors: Bill Fefferman, Soumik Ghosh, Makrand Sinha, and Henry Yuen

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

Abstract

We show that concrete hardness assumptions about learning or cloning the output state of a random quantum circuit can be used as the foundation for secure quantum cryptography. In particular, under these assumptions we construct secure one-way state generators (OWSGs), digital signature schemes, quantum bit commitments, and private key encryption schemes. We also discuss evidence for these hardness assumptions by analyzing the best-known quantum learning algorithms, as well as proving black-box lower bounds for cloning and learning given state preparation oracles. Our random circuit-based constructions provide concrete instantiations of quantum cryptographic primitives whose security do not depend on the existence of one-way functions. The use of random circuits in our constructions also opens the door to {NISQ-friendly quantum cryptography}. We discuss noise tolerant versions of our OWSG and digital signature constructions which can potentially be implementable on noisy quantum computers connected by a quantum network. On the other hand, they are still secure against {noiseless} quantum adversaries, raising the intriguing possibility of a useful implementation of an end-to-end cryptographic protocol on near-term quantum computers. Finally, our explorations suggest that the rich interconnections between learning theory and cryptography in classical theoretical computer science also extend to the quantum setting.

Cite as

Bill Fefferman, Soumik Ghosh, Makrand Sinha, and Henry Yuen. The Hardness of Learning Quantum Circuits and Its Cryptographic Applications. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 56:1-56:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fefferman_et_al:LIPIcs.ITCS.2026.56,
  author =	{Fefferman, Bill and Ghosh, Soumik and Sinha, Makrand and Yuen, Henry},
  title =	{{The Hardness of Learning Quantum Circuits and Its Cryptographic Applications}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{56:1--56:21},
  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.2026.56},
  URN =		{urn:nbn:de:0030-drops-253431},
  doi =		{10.4230/LIPIcs.ITCS.2026.56},
  annote =	{Keywords: quantum learning, quantum circuits, cryptographic hardness, one-way state generators}
}

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