265 Search Results for "Mitzenmacher, Michael"

Volume

OASIcs, Volume 69

2nd Symposium on Simplicity in Algorithms (SOSA 2019)

SOSA 2019, January 8-9, 2019, San Diego, CA, USA

Editors: Jeremy T. Fineman and Michael Mitzenmacher

Volume

LIPIcs, Volume 55

43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

ICALP 2016, July 11-15, 2016, Rome, Italy

Editors: Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani, and Davide Sangiorgi

Document
DOI: 10.4230/LIPIcs.STACS.2026.6
Threshold-Driven Streaming Graph: Expansion and Rumor Spreading

Authors: Flora Angileri, Andrea Clementi, Emanuele Natale, Michele Salvi, and Isabella Ziccardi

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

Abstract
A randomized distributed algorithm called RAES was introduced in [Becchetti et al., 2020] to extract a bounded-degree expander from a dense n-vertex expander graph G = (V, E). The algorithm relies on a simple threshold-based procedure. A key assumption in [Becchetti et al., 2020] is that the input graph G is static - i.e., both its vertex set V and edge set E remain unchanged throughout the process - while the analysis of raes in dynamic models is left as a major open question. In this work, we investigate the behavior of RAES under a dynamic graph model induced by a streaming node-churn process (also known as the sliding window model), where, at each discrete round, a new node joins the graph and the oldest node departs. This process yields a bounded-degree dynamic graph 𝒢 = {G_t = (V_t, E_t) : t ∈ ℕ} that captures essential characteristics of peer-to-peer networks - specifically, node churn and threshold on the number of connections each node can manage. We prove that every snapshot G_t in the dynamic graph sequence has good expansion properties with high probability. Furthermore, we leverage this property to establish a logarithmic upper bound on the completion time of the well-known PUSH and PULL rumor spreading protocols over the dynamic graph 𝒢.
Cite as

Flora Angileri, Andrea Clementi, Emanuele Natale, Michele Salvi, and Isabella Ziccardi. Threshold-Driven Streaming Graph: Expansion and Rumor Spreading. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 6:1-6:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{angileri_et_al:LIPIcs.STACS.2026.6,
  author =	{Angileri, Flora and Clementi, Andrea and Natale, Emanuele and Salvi, Michele and Ziccardi, Isabella},
  title =	{{Threshold-Driven Streaming Graph: Expansion and Rumor Spreading}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{6:1--6:21},
  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.2026.6},
  URN =		{urn:nbn:de:0030-drops-254957},
  doi =		{10.4230/LIPIcs.STACS.2026.6},
  annote =	{Keywords: Distributed Algorithms, Randomized Algorithms, Dynamic Random Graphs, Graph Expansion, Rumor Spreading}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.38
Fully Dynamic Spectral Sparsification for Directed Hypergraphs

Authors: Sebastian Forster, Gramoz Goranci, and Ali Momeni

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

Abstract
There has been a surge of interest in spectral hypergraph sparsification, a natural generalization of spectral sparsification for graphs. In this paper, we present a simple fully dynamic algorithm for maintaining spectral hypergraph sparsifiers of directed hypergraphs. Our algorithm achieves a near-optimal size of O(n² / ε ² log ⁷ m) and amortized update time of O(r² log ³ m), where n is the number of vertices, and m and r respectively upper bound the number of hyperedges and the rank of the hypergraph at any time. We also extend our approach to the parallel batch-dynamic setting, where a batch of any k hyperedge insertions or deletions can be processed with O(kr² log ³ m) amortized work and O(log ² m) depth. This constitutes the first spectral-based sparsification algorithm in this setting.
Cite as

Sebastian Forster, Gramoz Goranci, and Ali Momeni. Fully Dynamic Spectral Sparsification for Directed Hypergraphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 38:1-38:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{forster_et_al:LIPIcs.STACS.2026.38,
  author =	{Forster, Sebastian and Goranci, Gramoz and Momeni, Ali},
  title =	{{Fully Dynamic Spectral Sparsification for Directed Hypergraphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{38:1--38:20},
  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.2026.38},
  URN =		{urn:nbn:de:0030-drops-255272},
  doi =		{10.4230/LIPIcs.STACS.2026.38},
  annote =	{Keywords: Spectral sparsification, Dynamic algorithms, (Directed) hypergraphs, Data structures}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.63
Generalised Quantifiers Based on Rabin-Mostowski Index

Authors: Denis Kuperberg, Damian Niwiński, Paweł Parys, and Michał Skrzypczak

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

Abstract
In this work we introduce new generalised quantifiers which allow us to express the Rabin-Mostowski index of automata. Our main results study expressive power and decidability of the monadic second-order (MSO) logic extended with these quantifiers. We study these problems in the realm of both ω-words and infinite trees. As it turns out, the pictures in these two cases are very different. In the case of ω-words the new quantifiers can be effectively expressed in pure MSO logic. In contrast, in the case of infinite trees, addition of these quantifiers leads to an undecidable formalism. To realise index-quantifier elimination, we consider the extension of MSO by game quantifiers. As a tool, we provide a specific quantifier-elimination procedure for them. Moreover, we introduce a novel construction of transducers realising strategies in ω-regular games with monadic parameters.
Cite as

Denis Kuperberg, Damian Niwiński, Paweł Parys, and Michał Skrzypczak. Generalised Quantifiers Based on Rabin-Mostowski Index. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 63:1-63:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kuperberg_et_al:LIPIcs.STACS.2026.63,
  author =	{Kuperberg, Denis and Niwi\'{n}ski, Damian and Parys, Pawe{\l} and Skrzypczak, Micha{\l}},
  title =	{{Generalised Quantifiers Based on Rabin-Mostowski Index}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{63:1--63:22},
  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.2026.63},
  URN =		{urn:nbn:de:0030-drops-255526},
  doi =		{10.4230/LIPIcs.STACS.2026.63},
  annote =	{Keywords: monadic quantifiers, decidability, quantifier elimination, parity automata, game quantifier, Rabin-Mostowski index}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.71
Broadcast in Almost Mixing Time

Authors: Anton Paramonov and Roger Wattenhofer

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

Abstract
We study the problem of broadcasting multiple messages in the CONGEST model. In this problem, a dedicated source node s possesses a set M of messages with every message of size O(log n) where n is the total number of nodes. The objective is to ensure that every node in the network learns all messages in M. The execution of an algorithm progresses in rounds, and we focus on optimizing the round complexity of broadcasting multiple messages. Our primary contribution is a randomized algorithm for networks with expander topology. The algorithm succeeds with high probability and achieves a round complexity that is optimal up to a factor of the network’s mixing time and polylogarithmic terms. It leverages a multi-COBRA primitive, which uses multiple branching random walks running in parallel. A crucial aspect of our method is the use of these branching random walks to construct an optimal (up to a polylogarithmic factor) tree packing of a random graph, which is then used for efficient broadcasting. We also prove the problem to be NP-hard in a centralized setting and provide insights into why lower bounds that can be matched in expanders, namely graph diameter and |M|/minCut, cannot be tight in general graphs.
Cite as

Anton Paramonov and Roger Wattenhofer. Broadcast in Almost Mixing Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 71:1-71:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{paramonov_et_al:LIPIcs.STACS.2026.71,
  author =	{Paramonov, Anton and Wattenhofer, Roger},
  title =	{{Broadcast in Almost Mixing Time}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{71:1--71:20},
  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.2026.71},
  URN =		{urn:nbn:de:0030-drops-255603},
  doi =		{10.4230/LIPIcs.STACS.2026.71},
  annote =	{Keywords: Distributed algorithms, Expander Graphs, Random graphs, Broadcast, Branching random walks, Tree packing, CONGEST model}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.69
Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time

Authors: Etienne Objois and Adrian Vladu

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

Abstract
We provide the first nearly-linear time algorithm for approximating 𝓁_{q → p}-norms of non-negative matrices, for q ≥ p ≥ 1. Our algorithm returns a (1-ε)-approximation to the matrix norm in time Õ(1/(q ε) ⋅ nnz(A)), where A is the input matrix, and improves upon the previous state of the art, which either proved convergence only in the limit [Boyd '74], or had very high polynomial running times [Bhaskara-Vijayraghavan, SODA '11]. Our algorithm is extremely simple, and is largely inspired from the coordinate-scaling approach used for positive linear program solvers. Our algorithm can readily be used in the [Englert-Räcke, FOCS '09] to improve the running time of constructing O(log n)-competitive 𝓁_p-oblivious routings.
Cite as

Etienne Objois and Adrian Vladu. Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 69:1-69:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{objois_et_al:LIPIcs.STACS.2026.69,
  author =	{Objois, Etienne and Vladu, Adrian},
  title =	{{Approximating q → p Norms of Non-Negative Matrices in Nearly-Linear Time}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{69:1--69:19},
  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.2026.69},
  URN =		{urn:nbn:de:0030-drops-255585},
  doi =		{10.4230/LIPIcs.STACS.2026.69},
  annote =	{Keywords: matrix norm, Perron-Frobenius theory, oblivious routings, input-sparsity time, lp norm}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.43
Stealing from the Dragon’s Hoard: Online Unbounded Knapsack With Removal

Authors: Matthias Gehnen and Moritz Stocker

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

Abstract
We introduce the Online Unbounded Knapsack Problem with Removal, a variation of the well-known Online Knapsack Problem. Items, each with a weight and value, arrive online and an algorithm must decide on whether or not to pack them into a knapsack with a fixed weight limit. An item may be packed an arbitrary number of times and items may be removed from the knapsack at any time without cost. The goal is to maximize the total value of items packed, while respecting a weight limit. We show that this is one of the very few natural online knapsack variants that allow for competitive deterministic algorithms in the general setting, by providing an algorithm with competitivity 1.6911. We complement this with a lower bound of 1.5877. We also analyze the proportional setting, where the weight and value of any single item agree, and show that deterministic algorithms can be exactly 3/2-competitive. Lastly, we give lower and upper bounds of 6/5 and 4/3 on the competitivity of randomized algorithms in this setting.
Cite as

Matthias Gehnen and Moritz Stocker. Stealing from the Dragon’s Hoard: Online Unbounded Knapsack With Removal. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gehnen_et_al:LIPIcs.STACS.2026.43,
  author =	{Gehnen, Matthias and Stocker, Moritz},
  title =	{{Stealing from the Dragon’s Hoard: Online Unbounded Knapsack With Removal}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{43:1--43:17},
  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.2026.43},
  URN =		{urn:nbn:de:0030-drops-255327},
  doi =		{10.4230/LIPIcs.STACS.2026.43},
  annote =	{Keywords: online problems, online knapsack, unbounded knapsack, removal}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.40
A Simple and Robust Protocol for Distributed Counting

Authors: Edith Cohen, Moshe Shechner, and Uri Stemmer

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

Abstract
We revisit the distributed counting problem, where a server must continuously approximate the total number of events occurring across k sites while minimizing communication. The communication complexity of this problem is known to be Θ(k/(ε)log N) for deterministic protocols. Huang, Yi, and Zhang (2012) showed that randomization can reduce this to Θ((√k)/ε log N), but their analysis is restricted to the oblivious setting, where the stream of events is independent of the protocol’s outputs. Xiong, Zhu, and Huang (2023) presented a robust protocol for distributed counting that removes the oblivious assumption. However, their communication complexity is suboptimal by a polylog(k) factor and their protocol is substantially more complex than the oblivious protocol of Huang et al. (2012). This left open a natural question: could it be that the simple protocol of Huang et al. (2012) is already robust? We resolve this question with two main contributions. First, we show that the protocol of Huang et al. (2012) is itself not robust by constructing an explicit adaptive attack that forces it to lose its accuracy. Second, we present a new, surprisingly simple, robust protocol for distributed counting that achieves the optimal communication complexity of O((√k)/ε log N). Our protocol is simpler than that of Xiong et al. (2023), perhaps even simpler than that of Huang et al. (2012), and is the first to match the optimal oblivious complexity in the adaptive setting.
Cite as

Edith Cohen, Moshe Shechner, and Uri Stemmer. A Simple and Robust Protocol for Distributed Counting. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 40:1-40:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cohen_et_al:LIPIcs.ITCS.2026.40,
  author =	{Cohen, Edith and Shechner, Moshe and Stemmer, Uri},
  title =	{{A Simple and Robust Protocol for Distributed Counting}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{40:1--40:24},
  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.2026.40},
  URN =		{urn:nbn:de:0030-drops-253272},
  doi =		{10.4230/LIPIcs.ITCS.2026.40},
  annote =	{Keywords: Distributed Streaming, Adversarial Streaming}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.102
Smoothed Analysis of Dynamic Graph Algorithms

Authors: Uri Meir and Ami Paz

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

Abstract
Recent years have seen significant progress in the study of dynamic graph algorithms, and most notably, the introduction of strong lower bound techniques for them (e.g., Henzinger, Krinninger, Nanongkai and Saranurak, STOC 2015; Larsen and Yu, FOCS 2023). As worst-case analysis (adversarial inputs) may lead to the necessity of high running times, a natural question arises: in which cases are high running times really necessary, and in which cases these inputs merely manifest unique pathological cases? Early attempts to tackle this question were made by Nikoletseas, Reif, Spirakis and Yung (ICALP 1995) and by Alberts and Henzinger (Algorithmica 1998), who considered models with very little adversarial control over the inputs, and showed fast algorithms exist for them. The question was then overlooked for decades, until Henzinger, Lincoln and Saha (SODA 2022) recently addressed uniformly random inputs, and presented algorithms and impossibility results for several subgraph counting problems. To tackle the above question more thoroughly, we employ smoothed analysis, a celebrated framework introduced by Spielman and Teng (J. ACM, 2004). An input is proposed by an adversary but then a noisy version of it is processed by the algorithm instead. This model of inputs is parameterized by the amount of adversarial control, and fully interpolates between worst-case inputs and a uniformly random input. Doing so, we extend impossibility results for some problems to the smoothed model with only a minor quantitative loss. That is, we show that partially-adversarial inputs suffice to impose high running times for certain problems. In contrast, we show that other problems become easy even with the slightest amount of noise. In addition, we study the interplay between the adversary and the noise, leading to three natural models of smoothed inputs, for which we show a hierarchy of increasing difficulty stretching between the average-case and the worst-case complexities.
Cite as

Uri Meir and Ami Paz. Smoothed Analysis of Dynamic Graph Algorithms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 102:1-102:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{meir_et_al:LIPIcs.ITCS.2026.102,
  author =	{Meir, Uri and Paz, Ami},
  title =	{{Smoothed Analysis of Dynamic Graph Algorithms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{102:1--102:20},
  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.2026.102},
  URN =		{urn:nbn:de:0030-drops-253896},
  doi =		{10.4230/LIPIcs.ITCS.2026.102},
  annote =	{Keywords: Dynamic graph algorithms, Smoothed analysis, Shortest paths}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.7
An Unholy Trinity: TFNP, Polynomial Systems, and the Quantum Satisfiability Problem

Authors: Marco Aldi, Sevag Gharibian, and Dorian Rudolph

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

Abstract
The theory of Total Function NP (TFNP) and its subclasses says that, even if one is promised an efficiently verifiable proof exists for a problem, finding this proof can be intractable. Despite the success of the theory at showing intractability of problems such as computing Brouwer fixed points and Nash equilibria, subclasses of TFNP remain arguably few and far between. In this work, we define two new subclasses of TFNP borne of the study of complex polynomial systems: Multi-homogeneous Systems (MHS) and Sparse Fundamental Theorem of Algebra (SFTA). The first of these is based on Bézout’s theorem from algebraic geometry, marking the first TFNP subclass based on an algebraic geometric principle. At the heart of our study is the computational problem known as Quantum SAT (QSAT) with a System of Distinct Representatives (SDR), first studied by [Laumann, Läuchli, Moessner, Scardicchio, and Sondhi 2010]. Among other results, we show that QSAT with SDR is MHS-complete, thus giving not only the first link between quantum complexity theory and TFNP, but also the first TFNP problem whose classical variant (SAT with SDR) is easy but whose quantum variant is hard. We also show how to embed the roots of a sparse, high-degree, univariate polynomial into QSAT with SDR, obtaining that SFTA is contained in a zero-error version of MHS. We conjecture this construction also works in the low-error setting, which would imply SFTA ⊆ MHS.
Cite as

Marco Aldi, Sevag Gharibian, and Dorian Rudolph. An Unholy Trinity: TFNP, Polynomial Systems, and the Quantum Satisfiability Problem. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{aldi_et_al:LIPIcs.ITCS.2026.7,
  author =	{Aldi, Marco and Gharibian, Sevag and Rudolph, Dorian},
  title =	{{An Unholy Trinity: TFNP, Polynomial Systems, and the Quantum Satisfiability Problem}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{7:1--7:24},
  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.2026.7},
  URN =		{urn:nbn:de:0030-drops-252946},
  doi =		{10.4230/LIPIcs.ITCS.2026.7},
  annote =	{Keywords: quantum complexity theory, Quantum Merlin Arthur (QMA), Quantum Satisfiability Problem (QSAT), total function NP (TFNP)}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.80
FPT Approximations for Connected Maximum Coverage

Authors: Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi

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

Abstract
We revisit connectivity-constrained coverage through a unifying model, Partial Connected Red-Blue Dominating Set (PartialConRBDS). Given a bipartite graph G = (R∪ B,E) with red vertices R and blue vertices B, an auxiliary connectivity graph G_{conn} on R, and integers k,t, the task is to find a set S ⊆ R with |S| ≤ k such that G_{conn}[S] is connected and S dominates at least t blue vertices. This formulation captures connected variants of Maximum Coverage [Hochbaum-Rao, Inf. Proc. Lett., 2020; D'Angelo-Delfaraz, AAMAS 2025], Partial Vertex Cover, and Partial Dominating Set [Khuller et al., SODA 2014; Lamprou et al., TCS 2021] via standard encodings. Limits to parameterized tractability. PartialConRBDS is W[1]-hard parameterized by k even under strong restrictions: it remains hard when G_{conn} is a clique or a star and the incidence graph G is 3-degenerate, or when G is K_{2,2}-free. Inapproximability. For every ε > 0, there is no polynomial-time (1, 1-1/e+ε)-approximation unless 𝖯 = NP. Moreover, under ETH, no algorithm running in f(k)⋅ n^{o(k)} time achieves an g(k)-approximation for k for any computable function g(⋅), or for any ε > 0, a (1-1/e+ε)-approximation for t. Graphical special cases. Partial Connected Dominating Set is W[2]-hard parameterized by k and inherits the same ETH-based f(k)⋅ n^{o(k)} inapproximability bound as above; Partial Connected Vertex Cover is W[1]-hard parameterized by k. These hardness boundaries delineate a natural "sweet spot" for study: within appropriate structural restrictions on the incidence graph, one can still aim for fine-grained (FPT) approximations. Our algorithms. We solve PartialConRBDS exactly by reducing it to Relaxed Directed Steiner Out-Tree in time (2e)^t ⋅ n^{𝒪(1)}. For biclique-free incidences (i.e., when G excludes K_{d,d} as an induced subgraph), we obtain two complementary parameterized schemes: - An Efficient Parameterized Approximation Scheme (EPAS) running in time 2^{𝒪(k² d/ε)}⋅ n^{𝒪(1)} that either returns a connected solution of size at most k covering at least (1-ε)t blue vertices, or correctly reports that no connected size-k solution covers t; and - A Parameterized Approximation Scheme (PAS) running in time 2^{𝒪(kd(k²+log d))}⋅ n^{𝒪(1/ε)} that either returns a connected solution of size at most (1+ε)k covering at least t blue vertices, or correctly reports that no connected size-k solution covers t. Together, these results chart the boundary between hardness and FPT-approximability for connectivity-constrained coverage.
Cite as

Tanmay Inamdar, Satyabrata Jana, Madhumita Kundu, Daniel Lokshtanov, Saket Saurabh, and Meirav Zehavi. FPT Approximations for Connected Maximum Coverage. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 80:1-80:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{inamdar_et_al:LIPIcs.ITCS.2026.80,
  author =	{Inamdar, Tanmay and Jana, Satyabrata and Kundu, Madhumita and Lokshtanov, Daniel and Saurabh, Saket and Zehavi, Meirav},
  title =	{{FPT Approximations for Connected Maximum Coverage}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{80:1--80:24},
  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.2026.80},
  URN =		{urn:nbn:de:0030-drops-253674},
  doi =		{10.4230/LIPIcs.ITCS.2026.80},
  annote =	{Keywords: Partial Dominating Set, Connectivity, Maximum Coverage, FPT Approximation, Fixed-parameter Tractability}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.63
Perfect Simulation of Las Vegas Algorithms via Local Computation

Authors: Xinyu Fu, Yonggang Jiang, and Yitong Yin

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

Abstract
The notion of Las Vegas algorithms was introduced by Babai (1979) and can be defined in two ways: - In Babai’s original definition, a randomized algorithm is called Las Vegas if it has a finitely bounded running time and certifiable random failure. - Another definition widely accepted today is that Las Vegas algorithms refer to zero-error randomized algorithms with random running times. The equivalence between the two definitions is straightforward. Specifically, for randomized algorithms with certifiable failures, repeatedly running the algorithm until no failure is encountered allows for faithful simulation of the correct output when it executes successfully. We show that a similar perfect simulation can also be achieved in distributed local computation. Specifically, in the LOCAL model, with a polylogarithmic overhead in time complexity, any Las Vegas algorithm with finitely bounded running time and locally certifiable failures can be converted to a zero error Las Vegas algorithm. This transformed algorithm faithfully reproduces the correct output of the original algorithm in successful executions. This is achieved by a reduction to a distributed sampling problem under the Lovász Local Lemma (LLL), where the objective is to sample from the joint distribution of random variables avoiding all bad events. We then design the first efficient algorithm to solve this sampling problem in the LOCAL model.
Cite as

Xinyu Fu, Yonggang Jiang, and Yitong Yin. Perfect Simulation of Las Vegas Algorithms via Local Computation. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 63:1-63:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fu_et_al:LIPIcs.ITCS.2026.63,
  author =	{Fu, Xinyu and Jiang, Yonggang and Yin, Yitong},
  title =	{{Perfect Simulation of Las Vegas Algorithms via Local Computation}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{63:1--63:22},
  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.2026.63},
  URN =		{urn:nbn:de:0030-drops-253503},
  doi =		{10.4230/LIPIcs.ITCS.2026.63},
  annote =	{Keywords: Las Vegas algorithms, perfect simulation, Lov\'{a}sz Local Lemma, sampling}
}
Document
Extended Abstract
DOI: 10.4230/LIPIcs.ITCS.2026.29
The Mixed Birth-Death/death-Birth Moran Process (Extended Abstract)

Authors: David A. Brewster, Yichen Huang, Michael Mitzenmacher, and Martin A. Nowak

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

Abstract
We study evolutionary dynamics on graphs in which each step consists of one birth and one death, referred to generally as Moran processes. In standard simplified models, there are two types of individuals: residents, who have a fitness of 1, and mutants, who have a fitness of r. Two standard update rules are used in the literature. In Birth–death (Bd), a vertex is chosen to reproduce proportional to fitness, and one of its neighbors is selected uniformly at random to die and be replaced by the offspring. In death–Birth (dB), a vertex is chosen uniformly to die, and then one of its neighbors is chosen, proportional to fitness, to place an offspring into the vacancy. Two crucial quantities are: the unconditional absorption time, which is the expected time until only residents or only mutants remain, and the fixation probability of the mutant, which is the probability that at some time the mutants occupy the whole graph. Birth-death and death-Birth rules can yield significantly different outcomes for these quantities on the same graph, rendering conclusions dependent on the update rule. We formalize and study a unified model, the λ-mixed Moran process, in which each step is independently a Bd step with probability λ ∈ [0,1] and a dB step otherwise. We analyze this mixed process and establish a few results that form a starting point for its further study. All of our results are for undirected, connected graphs. As an interesting special case, we show at λ = 1/2 for any graph that the fixation probability when r = 1 with a single mutant initially on the graph is exactly 1/n, and also at λ = 1/2 that the absorption time for any r is O_r(n⁴) (that is, with an r-dependent constant). We also show results for graphs that are "almost regular," in a manner defined in the paper. We use this to show that for suitable random graphs from G∼ G(n,p) and fixed r > 1, with high probability over the choice of graph, the absorption time is O_r(n⁴), the fixation probability is Ω_r(n^{-2}), and we can approximate the fixation probability in polynomial time. Another special case is when the graph has only two possible values for the degree {d₁, d₂} with d₁ ≤ d₂. For those graphs, we give exact formulas for fixation probabilities under r = 1 and any λ, and establish O_r(n⁴ α⁴) absorption time regardless of λ, where α = d₂/d₁. We also provide explicit formulas for the star and cycle under any r or λ.
Cite as

David A. Brewster, Yichen Huang, Michael Mitzenmacher, and Martin A. Nowak. The Mixed Birth-Death/death-Birth Moran Process (Extended Abstract). In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 29:1-29:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{brewster_et_al:LIPIcs.ITCS.2026.29,
  author =	{Brewster, David A. and Huang, Yichen and Mitzenmacher, Michael and Nowak, Martin A.},
  title =	{{The Mixed Birth-Death/death-Birth Moran Process}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{29:1--29:2},
  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.2026.29},
  URN =		{urn:nbn:de:0030-drops-253161},
  doi =		{10.4230/LIPIcs.ITCS.2026.29},
  annote =	{Keywords: Moran process, Approximation algorithms, Random graphs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.31
Delaunay Triangulations with Predictions

Authors: Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos

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

Abstract
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set P of n points in the plane and a triangulation G that serves as a "prediction" of the Delaunay triangulation, we would like to use G to compute the correct Delaunay triangulation DT(P) more quickly when G is "close" to DT(P). We obtain a variety of results of this type, under different deterministic and probabilistic settings, including the following: 1) Define D to be the number of edges in G that are not in DT(P). We present a deterministic algorithm to compute DT(P) from G in O(n + Dlog³ n) time, and a randomized algorithm in O(n+Dlog n) expected time, the latter of which is optimal in terms of D. 2) Let R be a random subset of the edges of DT(P), where each edge is chosen independently with probability ρ. Suppose G is any triangulation of P that contains R. We present an algorithm to compute DT(P) from G in O(nlog log n + nlog(1/ρ)) time with high probability. 3) Define d_{vio} to be the maximum number of points of P strictly inside the circumcircle of a triangle in G (the number is 0 if G is equal to DT(P)). We present a deterministic algorithm to compute DT(P) from G in O(nlog^*n + nlog d_{vio}) time. We also obtain results in similar settings for related problems such as 2D Euclidean minimum spanning trees, and hope that our work will open up a fruitful line of future research.
Cite as

Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos. Delaunay Triangulations with Predictions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cabello_et_al:LIPIcs.ITCS.2026.31,
  author =	{Cabello, Sergio and Chan, Timothy M. and Giannopoulos, Panos},
  title =	{{Delaunay Triangulations with Predictions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{31:1--31:23},
  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.2026.31},
  URN =		{urn:nbn:de:0030-drops-253186},
  doi =		{10.4230/LIPIcs.ITCS.2026.31},
  annote =	{Keywords: Delaunay Triangulation, Minimum Spanning Tree, Algorithms with Predictions}
}
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