53 Search Results for "Cook, James"

Document
DOI: 10.4230/LIPIcs.CCC.2026.29
Frontier Space-Time Algorithms Using Only Full Memory

Authors: Petr Chmel, Aditi Dudeja, Michal Koucký, Ian Mertz, and Ninad Rajgopal

Published in: LIPIcs, Volume 383, 41st Computational Complexity Conference (CCC 2026)

Abstract
We develop catalytic algorithms for fundamental problems in algorithm design that run in polynomial time, use only 𝒪(log(n)) workspace, and use sublinear catalytic space matching the best-known space bounds of non-catalytic algorithms running in polynomial time. First, we design a polynomial time algorithm for directed s-t connectivity using n / 2^{Θ(√{log n})} catalytic space, which matches the state-of-the-art time-space bounds in the non-catalytic setting [Barnes et al., 1998], and improves the catalytic space usage of the best known algorithm [James Cook and Edward Pyne, 2026]. Furthermore, using only 𝒪(log(n)) random bits we get a randomized algorithm whose running time nearly matches the fastest time bounds known for space-unrestricted algorithms. Second, we design polynomial time algorithms for the problems of computing Edit Distance, Longest Common Subsequence, and the Discrete Fréchet Distance, again using n / 2^{Θ(√{log n})} catalytic space. This again matches non-catalytic time-space frontier for Edit Distance and Least Common Subsequence [Kiyomi et al., 2021].
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Petr Chmel, Aditi Dudeja, Michal Koucký, Ian Mertz, and Ninad Rajgopal. Frontier Space-Time Algorithms Using Only Full Memory. In 41st Computational Complexity Conference (CCC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 383, pp. 29:1-29:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chmel_et_al:LIPIcs.CCC.2026.29,
  author =	{Chmel, Petr and Dudeja, Aditi and Kouck\'{y}, Michal and Mertz, Ian and Rajgopal, Ninad},
  title =	{{Frontier Space-Time Algorithms Using Only Full Memory}},
  booktitle =	{41st Computational Complexity Conference (CCC 2026)},
  pages =	{29:1--29:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-437-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{383},
  editor =	{Moshkovitz, Dana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2026.29},
  URN =		{urn:nbn:de:0030-drops-270710},
  doi =		{10.4230/LIPIcs.CCC.2026.29},
  annote =	{Keywords: Catalytic computation, Connectivity, Edit distance, Discrete Fr\'{e}chet distance}
}
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.
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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.2026.3
Reachability with Restricted Reactions in Inhibitory Chemical Reaction Networks

Authors: Divya Bajaj, Bin Fu, Ryan Knobel, Austin Luchsinger, Aiden Massie, Pablo Santos, Ramiro Santos, Robert Schweller, Evan Tomai, and Tim Wylie

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

Abstract
Chemical Reaction Networks (CRNs) are a well-established model of distributed computing characterized by quantities of molecular species that can transform or change through applications of reactions. A fundamental problem in CRNs is the reachability problem, which asks if an initial configuration of species can transition to a target configuration through an applicable sequence of reactions. It is well-known that the reachability problem in general CRNs was recently proven to be Ackermann-complete. However, if the CRN’s reactions are restricted in both power, such as only deleting species (deletion-only rules) or consuming and producing an equal number of species (volume-preserving rules), and size (unimolecular or bimolecular rules), then reachability falls below Ackermann-completeness, and is even solvable in polynomial time for deletion-only systems. In this paper, we investigate reachability under this set of restricted unimolecular and bimolecular reactions, but in the Priority-Inhibitory CRN and Inhibitory CRN models. These models extend a traditional CRN by allowing some reactions to be inhibited from firing in a configuration if certain species are present; the exact inhibition behavior varies between the models. We first show that reachability with Priority iCRNs mostly remains in P for deletion-only systems, but becomes NP-complete for one case. We then show that reachability with deletion-only reactions for iCRNs is mostly NP-complete, and PSPACE-complete even for (1,1)-size (general) reactions. We also provide FPT algorithms for solving most of the reachability problems for the iCRN model. Finally, we show reachability for CRNs with states is already NP-hard for the simplest deletion-only systems, and is PSPACE-complete even for (general) (1,1)-size reactions.
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Divya Bajaj, Bin Fu, Ryan Knobel, Austin Luchsinger, Aiden Massie, Pablo Santos, Ramiro Santos, Robert Schweller, Evan Tomai, and Tim Wylie. Reachability with Restricted Reactions in Inhibitory Chemical Reaction Networks. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bajaj_et_al:LIPIcs.SWAT.2026.3,
  author =	{Bajaj, Divya and Fu, Bin and Knobel, Ryan and Luchsinger, Austin and Massie, Aiden and Santos, Pablo and Santos, Ramiro and Schweller, Robert and Tomai, Evan and Wylie, Tim},
  title =	{{Reachability with Restricted Reactions in Inhibitory Chemical Reaction Networks}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{3:1--3:18},
  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.2026.3},
  URN =		{urn:nbn:de:0030-drops-260399},
  doi =		{10.4230/LIPIcs.SWAT.2026.3},
  annote =	{Keywords: Chemical Reaction Networks, Vector Addition Systems, Petri-nets, Reachability, Inhibitors, Void Reactions}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2026.30
Parallel Algorithms for Group Isomorphism via Code Equivalence

Authors: Michael Levet

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

Abstract
In this paper, we exhibit AC³ isomorphism tests for coprime extensions H ⋉ N where H is elementary Abelian and N is Abelian; and groups where Rad(G) = Z(G) is elementary Abelian and G = Soc^{*}(G). The fact that isomorphism testing for these families is in P was established respectively by Qiao, Sarma, and Tang (STACS 2011), and Grochow and Qiao (CCC 2014, SIAM J. Comput. 2017). The polynomial-time isomorphism tests for both of these families crucially leveraged small (size O(log |G|)) instances of Linear Code Equivalence (Babai, SODA 2011). Here, we combine Luks' group-theoretic method for Graph Isomorphism (FOCS 1980, J. Comput. Syst. Sci. 1982) with the fact that G is given by its multiplication table, to implement the corresponding instances of Linear Code Equivalence in AC³. As a byproduct of our work, we show that isomorphism testing of arbitrary central-radical groups is decidable using AC circuits of depth O(log³ n) and size n^{O(log log n)}. This improves upon the previous bound of n^{O(log log n)}-time due to Grochow and Qiao (ibid.).
Cite as

Michael Levet. Parallel Algorithms for Group Isomorphism via Code Equivalence. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{levet:LIPIcs.SWAT.2026.30,
  author =	{Levet, Michael},
  title =	{{Parallel Algorithms for Group Isomorphism via Code Equivalence}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{30:1--30:19},
  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.2026.30},
  URN =		{urn:nbn:de:0030-drops-260660},
  doi =		{10.4230/LIPIcs.SWAT.2026.30},
  annote =	{Keywords: Group Isomorphism, Circuit Complexity, Code Equivalence}
}
Document
DOI: 10.4230/OASIcs.NINeS.2026.24
SwiftQueue: Optimizing Low-Latency Applications with Swift Packet Queuing

Authors: Siddhant Ray, Xi Jiang, Jack Luo, Nick Feamster, and Junchen Jiang

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

Abstract
Low Latency, Low Loss, and Scalable Throughput (L4S), as an emerging router-queue management technique, has seen steady deployment in the industry. An L4S-enabled router assigns each packet to the queue based on the packet header marking. Currently, L4S employs per-flow queue selection, i.e., all packets of a flow are marked the same way and thus use the same queues, even though each packet is marked separately. However, this may hurt tail latency and latency-sensitive applications because transient congestion and queue buildups may only affect a fraction of packets in a flow. We present SwiftQueue, a new L4S queue-selection strategy in which a sender uses a novel per-packet latency predictor to pinpoint which packets likely have latency spikes or drops. The insight is that many packet-level latency variations result from complex interactions among recent packets at shared router queues. Yet, these intricate packet-level latency patterns are hard to learn efficiently by traditional models. Instead, SwiftQueue uses a custom Transformer, which is well-studied for its expressiveness on sequential patterns, to predict the next packet’s latency based on the latencies of recently received ACKs. Based on the predicted latency of each outgoing packet, SwiftQueue’s sender dynamically marks the L4S packet header to assign packets to potentially different queues, even within the same flow. Using real network traces, we show that SwiftQueue is 45-65% more accurate in predicting latency and its variations than state-of-art methods. Based on its latency prediction, SwiftQueue reduces the tail latency for L4S-enabled flows by 36-45%, compared with the existing L4S queue-selection method.
Cite as

Siddhant Ray, Xi Jiang, Jack Luo, Nick Feamster, and Junchen Jiang. SwiftQueue: Optimizing Low-Latency Applications with Swift Packet Queuing. In 1st New Ideas in Networked Systems (NINeS 2026). Open Access Series in Informatics (OASIcs), Volume 139, pp. 24:1-24:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ray_et_al:OASIcs.NINeS.2026.24,
  author =	{Ray, Siddhant and Jiang, Xi and Luo, Jack and Feamster, Nick and Jiang, Junchen},
  title =	{{SwiftQueue: Optimizing Low-Latency Applications with Swift Packet Queuing}},
  booktitle =	{1st New Ideas in Networked Systems (NINeS 2026)},
  pages =	{24:1--24:29},
  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.2026.24},
  URN =		{urn:nbn:de:0030-drops-256093},
  doi =		{10.4230/OASIcs.NINeS.2026.24},
  annote =	{Keywords: Latency prediction, L4S Queue Management}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.41
On the Complexity of Computing Strahler Numbers

Authors: Moses Ganardi and Markus Lohrey

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

Abstract
It is shown that the problem of computing the Strahler number of a binary tree given as a term is complete for the circuit complexity class uniform NC¹. For several variants, where the binary tree is given by a pointer structure or in a succinct form by a directed acyclic graph or a tree straight-line program, the complexity of computing the Strahler number is determined as well. The problem, whether a given context-free grammar in Chomsky normal form produces a derivation tree (resp., an acyclic derivation tree), whose Strahler number is at least a given number k is shown to be P-complete (resp., PSPACE-complete).
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Moses Ganardi and Markus Lohrey. On the Complexity of Computing Strahler Numbers. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 41:1-41:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2026.41,
  author =	{Ganardi, Moses and Lohrey, Markus},
  title =	{{On the Complexity of Computing Strahler Numbers}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{41:1--41:22},
  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.2026.41},
  URN =		{urn:nbn:de:0030-drops-255301},
  doi =		{10.4230/LIPIcs.STACS.2026.41},
  annote =	{Keywords: Strahler number, circuit complexity classes, context-free grammars}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.25
Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing

Authors: Marek Černý and Tim Seppelt

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

Abstract
Two graphs G and H are homomorphism indistinguishable over a graph class ℱ if they admit the same number of homomorphisms from every graph F ∈ ℱ. Many graph isomorphism relaxations such as (quantum) isomorphism and cospectrality can be characterised as homomorphism indistinguishability over specific graph classes. Thereby, the problems HomInd(ℱ) of deciding homomorphism indistinguishability over ℱ subsume diverse graph isomorphism relaxations whose complexities range from logspace to undecidable. Establishing the first general result on the complexity of HomInd(ℱ), Seppelt (MFCS 2024) showed that HomInd(ℱ) is in randomised polynomial time for every graph class ℱ of bounded treewidth that can be defined in counting monadic second-order logic CMSO₂. We show that this algorithm is conditionally optimal, i.e. it cannot be derandomised unless polynomial identity testing is in P. For CMSO₂-definable graph classes ℱ of bounded pathwidth, we improve the previous complexity upper bound for HomInd(ℱ) from P to C_ = L and show that this is tight. Secondarily, we establish a connection between homomorphism indistinguishability and multiplicity automata equivalence which allows us to pinpoint the complexity of the latter problem as C_ = L-complete.
Cite as

Marek Černý and Tim Seppelt. Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cerny_et_al:LIPIcs.STACS.2026.25,
  author =	{\v{C}ern\'{y}, Marek and Seppelt, Tim},
  title =	{{Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{25:1--25:20},
  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.2026.25},
  URN =		{urn:nbn:de:0030-drops-255144},
  doi =		{10.4230/LIPIcs.STACS.2026.25},
  annote =	{Keywords: treewidth, Courcelle’s theorem, logspace, multiplicity automata, polynomial identity testing}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.16
On the Entailment Problem in Dynamic Separation Logic with Inductive Definitions

Authors: Nicolas Peltier

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
Separation Logic (SL) is a well-established framework for reasoning about programs that manipulate dynamic memory. To express and verify properties of custom recursive data structures, SL is extended with spatial predicates defined by user-specified inductive rules. Many verification problems reduce to deciding entailments between formulas involving these predicates. While the general entailment problem is undecidable, a broad class of inductive rules - known as PCE (Progressing, Connected, and Established) - has been identified for which entailment is decidable. In this work, we extend the study of the entailment problem to Dynamic Separation Logic (DSL), an extension of SL that includes dynamic modalities for reasoning about actions on the heap and store. We show that entailment in DSL remains decidable for PCE rules by proving that dynamic modalities can be automatically eliminated.
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Nicolas Peltier. On the Entailment Problem in Dynamic Separation Logic with Inductive Definitions. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{peltier:LIPIcs.CSL.2026.16,
  author =	{Peltier, Nicolas},
  title =	{{On the Entailment Problem in Dynamic Separation Logic with Inductive Definitions}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{16:1--16:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.16},
  URN =		{urn:nbn:de:0030-drops-254402},
  doi =		{10.4230/LIPIcs.CSL.2026.16},
  annote =	{Keywords: Separation logic, Dynamic logic, Entailment problem}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.43
Efficient Catalytic Graph Algorithms

Authors: James Cook and Edward Pyne

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

Abstract
We give fast, simple, and implementable catalytic logspace algorithms for two fundamental graph problems. First, a randomized catalytic algorithm for s → t connectivity running in Õ(nm) time, and a deterministic catalytic algorithm for the same running in Õ(n³ m) time. The former algorithm is the first algorithmic use of randomization in CL. The algorithm uses one register per vertex and repeatedly "pushes" values along the edges in the graph. Second, a deterministic catalytic algorithm for simulating random walks which in Õ(m T² / ε) time estimates the probability a T-step random walk ends at a given vertex within ε additive error. The algorithm uses one register for each vertex and increments it at each visit to ensure repeated visits follow different outgoing edges. Prior catalytic algorithms for both problems did not have explicit runtime bounds beyond being polynomial in n.
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James Cook and Edward Pyne. Efficient Catalytic Graph Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 43:1-43:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cook_et_al:LIPIcs.ITCS.2026.43,
  author =	{Cook, James and Pyne, Edward},
  title =	{{Efficient Catalytic Graph Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{43:1--43:22},
  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.2026.43},
  URN =		{urn:nbn:de:0030-drops-253305},
  doi =		{10.4230/LIPIcs.ITCS.2026.43},
  annote =	{Keywords: catalytic computing, graph algorithms, catalytic logspace}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.60
Total Search Problems in ZPP

Authors: Noah Fleming, Stefan Grosser, Siddhartha Jain, Jiawei Li, Hanlin Ren, Morgan Shirley, and Weiqiang Yuan

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

Abstract
We initiate a systematic study of TFZPP, the class of total NP search problems solvable by polynomial time randomized algorithms. TFZPP contains a variety of important search problems such as Bertrand-Chebyshev (finding a prime between N and 2N), refuter problems for many circuit lower bounds, and Lossy-Code. The Lossy-Code problem has found prominence due to its fundamental connections to derandomization, catalytic computing, and the metamathematics of complexity theory, among other areas. While TFZPP collapses to FP under standard derandomization assumptions in the white-box setting, we are able to separate TFZPP from the major TFNP subclasses in the black-box setting. In fact, we are able to separate it from every uniform TFNP class assuming that NP is not in quasi-polynomial time. To do so, we extend the connection between proof complexity and black-box TFNP to randomized proof systems and randomized reductions. Next, we turn to developing a taxonomy of TFZPP problems. We highlight a problem called Nephew, originating from an infinity axiom in set theory. We show that Nephew is in PWPP∩ TFZPP and conjecture that it is not reducible to Lossy-Code. Intriguingly, except for some artificial examples, most other black-box TFZPP problems that we are aware of reduce to Lossy-Code: - We define a problem called Empty-Child capturing finding a leaf in a rooted (binary) tree, and show that this problem is equivalent to Lossy-Code. We also show that a variant of Empty-Child with "heights" is complete for the intersection of SOPL and Lossy-Code. - We strengthen Lossy-Code with several combinatorial inequalities such as the AM-GM inequality. Somewhat surprisingly, we show the resulting new problems are still reducible to Lossy-Code. A technical highlight of this result is that they are proved by formalizations in bounded arithmetic, specifically in Jeřábek’s theory APC₁ (JSL 2007). - Finally, we show that the Dense-Linear-Ordering problem reduces to Lossy-Code.
Cite as

Noah Fleming, Stefan Grosser, Siddhartha Jain, Jiawei Li, Hanlin Ren, Morgan Shirley, and Weiqiang Yuan. Total Search Problems in ZPP. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 60:1-60:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fleming_et_al:LIPIcs.ITCS.2026.60,
  author =	{Fleming, Noah and Grosser, Stefan and Jain, Siddhartha and Li, Jiawei and Ren, Hanlin and Shirley, Morgan and Yuan, Weiqiang},
  title =	{{Total Search Problems in ZPP}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{60:1--60:26},
  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.2026.60},
  URN =		{urn:nbn:de:0030-drops-253473},
  doi =		{10.4230/LIPIcs.ITCS.2026.60},
  annote =	{Keywords: TFNP, lossy code, randomized proof systems, query complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.3
Linear Matroid Intersection Is in Catalytic Logspace

Authors: Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra

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

Abstract
Linear matroid intersection is an important problem in combinatorial optimization. Given two linear matroids over the same ground set, the linear matroid intersection problem asks you to find a common independent set of maximum size. The deep interest in linear matroid intersection is due to the fact that it generalises many classical problems in theoretical computer science, such as bipartite matching, edge disjoint spanning trees, rainbow spanning tree, and many more. We study this problem in the model of catalytic computation: space-bounded machines are granted access to catalytic space, which is additional working memory that is full with arbitrary data that must be preserved at the end of its computation. Although linear matroid intersection has had a polynomial time algorithm for over 50 years, it remains an important open problem to show that linear matroid intersection belongs to any well studied subclass of {P}. We address this problem for the class catalytic logspace (CL) with a polynomial time bound (CLP). Recently, Agarwala and Mertz (2025) showed that bipartite maximum matching can be computed in the class CLP ⊆ {P}. This was the first subclass of {P} shown to contain bipartite matching, and additionally the first problem outside TC¹ shown to be contained in CL. We significantly improve the result of Agarwala and Mertz by showing that linear matroid intersection can be computed in CLP.
Cite as

Aryan Agarwala, Yaroslav Alekseev, and Antoine Vinciguerra. Linear Matroid Intersection Is in Catalytic Logspace. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{agarwala_et_al:LIPIcs.ITCS.2026.3,
  author =	{Agarwala, Aryan and Alekseev, Yaroslav and Vinciguerra, Antoine},
  title =	{{Linear Matroid Intersection Is in Catalytic Logspace}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{3:1--3:23},
  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.2026.3},
  URN =		{urn:nbn:de:0030-drops-252908},
  doi =		{10.4230/LIPIcs.ITCS.2026.3},
  annote =	{Keywords: Catalytic Computing, Computational Complexity, Matroid Theory, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.79
Range Avoidance and Remote Point: New Algorithms and Hardness

Authors: Shengtang Huang, Xin Li, and Yan Zhong

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

Abstract
The Range Avoidance (Avoid) problem C-Avoid[n,m(n)] asks that, given a circuit in a class C with input length n and output length m(n) > n, find a string not in the range of the circuit. This problem has been a central piece in several recent frameworks for proving circuit lower bounds and constructing explicit combinatorial objects. Previous work by Korten (FOCS' 21) and by Ren, Santhanam, and Wang (FOCS' 22) showed that algorithms for Avoid are closely related to circuit lower bounds. In particular, Korten’s work reinterpreted an earlier result from bounded arithmetic, originally proved by Jeřábek (Ann. Pure Appl. Log. 2004), as an equivalence in computational complexity between the existence of FP^NP algorithms for the general Avoid problem and 2^{Ω(n)} lower bounds against general Boolean circuits for the class 𝐄^NP. In this work, we significantly complement these works by generalizing the equivalence result to restricted circuit classes and obtain the following: - For any constant depth unbounded fan-in circuit class C ⊇ AC⁰, there is an FP^NP algorithm for C-Avoid[n,n^{1+ε}] (for any constant ε > 0) if and only if 𝐄^NP cannot be computed by C circuits of size 2^{o(n)}. This addresses an open problem by Korten (Bulletin of EATCS' 25). - If 𝐄^NP cannot be computed by o(2ⁿ/n) size formulas, then there is an FP^NP algorithm for NC⁰-Avoid[n,2n]. Note that by an extension of Ren, Santhanam, and Wang (FOCS' 22), an FP^NP algorithm for NC⁰₄-Avoid[n,n+n^δ] for any constant δ ∈ (0,1) implies 𝐄^NP cannot be computed by o(2ⁿ/n) size formulas. These results yield the first characterizations of FP^NP C-Avoid algorithms for low-complexity circuit classes such as AC⁰. We also consider the average-case analog of Avoid, the Remote Point (Remote-Point) problem, and establish: - For some suitable function c(n) and constant γ > 0, there is an FP^NP algorithm for Remote-Point[n,n^{6+γ},c(O_{γ}(log n))] if and only if 𝐄^NP cannot be (1/2-c(n))-approximated by circuits of size 2^{o(n)}. Finally, we also present two improved algorithms for NC⁰-Avoid: - A family of 2^{n^{1 - ε/(k-1) +o(1)}} time algorithms for NC⁰_k-Avoid[n,n^{1+ε}] for any ε > 0, exhibiting the first subexponential-time algorithm for any super-linear stretch. - Faster local algorithms for NC⁰_k-Avoid[n,n+1] running in time O(n2^{(k-2)/(k-1) n}), improving the naive 2ⁿ⋅ poly(n) bound.
Cite as

Shengtang Huang, Xin Li, and Yan Zhong. Range Avoidance and Remote Point: New Algorithms and Hardness. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{huang_et_al:LIPIcs.ITCS.2026.79,
  author =	{Huang, Shengtang and Li, Xin and Zhong, Yan},
  title =	{{Range Avoidance and Remote Point: New Algorithms and Hardness}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{79:1--79:19},
  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.2026.79},
  URN =		{urn:nbn:de:0030-drops-253662},
  doi =		{10.4230/LIPIcs.ITCS.2026.79},
  annote =	{Keywords: Circuit Lower Bounds, Range Avoidance Problem, Remote Point Problem}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.42
Degrees of Second and Higher-Order Polynomials

Authors: Donghyun Lim and Martin Ziegler

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
Second-order polynomials generalize classical (=first-order) ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory, extending for instance discrete classes (like P/FP or PSPACE/FPSPACE) to operators in Analysis [http://doi.org/10.1137/S0097539794263452], [http://doi.org/10.1145/2189778.2189780]. The degree subclassifies ordinary polynomial growth into linear, quadratic, cubic, etc. To similarly classify second-order polynomials, we (well-)define their degree by structural induction as an "arctic" first-order polynomial: a term/expression over integer variable D and operations + and ⋅ and binary max(). This generalized degree turns out to transform nicely under (now two kinds of) polynomial composition. As examples, we collect and determine the degrees of previous and new asymptotic analyses of algorithms and operators receiving function/oracle arguments. Then we motivate and introduce third-order polynomials and their degrees as arctic second-order polynomials, along with their transformations under three kinds of composition. Proceeding to fourth order and beyond yields a hierarchy, with characterization in Simply Typed Lambda Calculus.
Cite as

Donghyun Lim and Martin Ziegler. Degrees of Second and Higher-Order Polynomials. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 42:1-42:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lim_et_al:LIPIcs.FSTTCS.2025.42,
  author =	{Lim, Donghyun and Ziegler, Martin},
  title =	{{Degrees of Second and Higher-Order Polynomials}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{42:1--42:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.42},
  URN =		{urn:nbn:de:0030-drops-251225},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.42},
  annote =	{Keywords: Logic in Computer Science, Higher Order Program Analysis, Asymptotic Type Theory}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.7
Polynomial Equivalence of Extended Chemical Reaction Models

Authors: Divya Bajaj, Jose-Luis Castellanos, Ryan Knobel, Austin Luchsinger, Aiden Massie, Adrian Salinas, Pablo Santos, Ramiro Santos, Robert Schweller, and Tim Wylie

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
The ability to detect whether a species (or dimension) is zero in Chemical Reaction Networks (CRN), Vector Addition Systems, or Petri Nets is known to increase the power of these models - making them capable of universal computation. While this ability may appear in many forms, such as extending the models to allow transitions to be inhibited, prioritized, or synchronized, we present an extension that directly performs this zero checking. We introduce a new void genesis CRN variant with a simple design that merely increments the count of a specific species when any other species' count goes to zero. As with previous extensions, we show that the model is Turing Universal. We then analyze several other studied CRN variants and show that they are all equivalent through a polynomial simulation with the void genesis model, which does not merely follow from Turing-universality. Thus, inhibitor species, reactions that occur at different rates, being allowed to run reactions in parallel, or even being allowed to continually add more volume to the CRN, does not add additional simulation power beyond simply detecting if a species count becomes zero.
Cite as

Divya Bajaj, Jose-Luis Castellanos, Ryan Knobel, Austin Luchsinger, Aiden Massie, Adrian Salinas, Pablo Santos, Ramiro Santos, Robert Schweller, and Tim Wylie. Polynomial Equivalence of Extended Chemical Reaction Models. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 7:1-7:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bajaj_et_al:LIPIcs.ISAAC.2025.7,
  author =	{Bajaj, Divya and Castellanos, Jose-Luis and Knobel, Ryan and Luchsinger, Austin and Massie, Aiden and Salinas, Adrian and Santos, Pablo and Santos, Ramiro and Schweller, Robert and Wylie, Tim},
  title =	{{Polynomial Equivalence of Extended Chemical Reaction Models}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{7:1--7:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.7},
  URN =		{urn:nbn:de:0030-drops-249158},
  doi =		{10.4230/LIPIcs.ISAAC.2025.7},
  annote =	{Keywords: Chemical Reaction Networks, Simulations, Petri-nets, Vector Addition Systems, Bi-simulation, Turing-universality, Inhibitors}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.9
Small Space Encoding and Recognition of k-Palindromic Prefixes

Authors: Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Palindromes are non-empty strings that read the same forward and backward. We study the problem of recognizing so-called k-palindromic strings, which can be represented as the concatenation of exactly k palindromes. [Rubinchik and Shur, MFCS 2020] showed that the problem is solvable in linear space and time. We present a read-only algorithm that recognizes all k-palindromic prefixes of a string T of length n in O(n ⋅ 6^{k²} ⋅ log^k n) time and O(6^{k²} ⋅ log^k n) space. As a corollary, we also obtain a read-only algorithm for computing the palindromic length of T, i.e., the smallest k such that T is k-palindromic, in O(n ⋅ 6^{k²} ⋅ log^⌈k/2⌉ n) time and O(6^{k²} ⋅ log^⌈k/2⌉ n) space.
Cite as

Gabriel Bathie, Jonas Ellert, and Tatiana Starikovskaya. Small Space Encoding and Recognition of k-Palindromic Prefixes. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bathie_et_al:LIPIcs.ISAAC.2025.9,
  author =	{Bathie, Gabriel and Ellert, Jonas and Starikovskaya, Tatiana},
  title =	{{Small Space Encoding and Recognition of k-Palindromic Prefixes}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.9},
  URN =		{urn:nbn:de:0030-drops-249178},
  doi =		{10.4230/LIPIcs.ISAAC.2025.9},
  annote =	{Keywords: palindromic length, read-only algorithms, palindromes}
}
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