15 Search Results for "Bezáková, Ivona"

Document
DOI: 10.4230/LIPIcs.SWAT.2026.8
Submodular Max-Min Allocation Under Identical Valuations

Authors: Kimon Boehmer

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

Abstract
In the problem of Submodular Max-Min Allocation, we are given a set of items, a set of players, and monotone submodular valuation functions that represent the satisfaction of a player with a certain subset of items. The goal is to find an allocation of the items to the players that maximizes the lowest satisfaction among all players. We study this problem in the special case where all players have the same valuation function. We devise a greedy algorithm which gives a 0.4-approximation, improving the previously best factor of 10/27 ≈ 0.37 by Uziahu and Feige. Furthermore, we study the integrality gap of the configuration LP when players have identical valuations. By constructing a variable assignment to the dual from a primal integral solution, we give the first constant upper bound on the integrality gap for submodular valuations. Generalizing the result to the case where players' allocations must be independent in k given matroids, we derive a 𝒪(k)-estimation algorithm for max-min allocation subject to k matroid constraints under identical valuations.
Cite as

Kimon Boehmer. Submodular Max-Min Allocation Under Identical Valuations. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{boehmer:LIPIcs.SWAT.2026.8,
  author =	{Boehmer, Kimon},
  title =	{{Submodular Max-Min Allocation Under Identical Valuations}},
  booktitle =	{20th Scandinavian Symposium on Algorithm Theory (SWAT 2026)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-421-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{370},
  editor =	{Fraigniaud, Pierre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2026.8},
  URN =		{urn:nbn:de:0030-drops-260446},
  doi =		{10.4230/LIPIcs.SWAT.2026.8},
  annote =	{Keywords: Submodularity, Approximation algorithms, Allocation, Configuration LP}
}
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
DOI: 10.4230/LIPIcs.ITCS.2026.114
Zero-Freeness Is All You Need: A Weitz-Type FPTAS for the Entire Lee-Yang Zero-Free Region

Authors: Shuai Shao and Ke Shi

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

Abstract
We present a Weitz-type FPTAS for the ferromagnetic Ising model across the entire Lee–Yang zero-free region, without relying on the strong spatial mixing (SSM) property. Our algorithm is Weitz-type for two reasons. First, it expresses the partition function as a telescoping product of ratios, with the key being to approximate each ratio. Second, it uses Weitz’s self-avoiding walk tree, and truncates it at logarithmic depth to give a good and efficient approximation. The key difference from the standard Weitz algorithm is that we approximate a carefully designed edge-deletion ratio instead of the marginal probability of a vertex being assigned a particular spin, ensuring our algorithm does not require SSM. Furthermore, by establishing local dependence of coefficients (LDC), we indeed prove a novel form of SSM for these edge-deletion ratios, which, in turn, implies the standard SSM for the random cluster model. This is the first SSM result for the random cluster model on general graphs, beyond lattices. Our proof of LDC is based on a new division relation, and we show such relations hold quite universally. This leads to a broadly applicable framework for proving LDC across a variety of models, including the Potts model, the hypergraph independence polynomial, and Holant problems. Combined with existing zero-freeness results for these models, we derive new SSM results for them.
Cite as

Shuai Shao and Ke Shi. Zero-Freeness Is All You Need: A Weitz-Type FPTAS for the Entire Lee-Yang Zero-Free Region. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 114:1-114:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{shao_et_al:LIPIcs.ITCS.2026.114,
  author =	{Shao, Shuai and Shi, Ke},
  title =	{{Zero-Freeness Is All You Need: A Weitz-Type FPTAS for the Entire Lee-Yang Zero-Free Region}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{114:1--114:17},
  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.2026.114},
  URN =		{urn:nbn:de:0030-drops-254010},
  doi =		{10.4230/LIPIcs.ITCS.2026.114},
  annote =	{Keywords: Ferromagnetic Ising Model, Lee–Yang Theorem, Weitz-Type FPTAS, Strong Spatial Mixing, Random Cluster Model}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2025.65
Brief Announcement: Congested Clique Counting for Local Gibbs Distributions

Authors: Joshua Z. Sobel

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
There are well established reductions between combinatorial sampling and counting problems (Jerrum, Valiant, Vazirani TCS 1986). Building off of a very recent parallel algorithm utilizing this connection (Liu, Yin, Zhang arxiv 2024), we demonstrate the first approximate counting algorithm in the CongestedClique for a wide range of problems. Most interestingly, we present an algorithm for approximating the number of q-colorings of a graph within ε-multiplicative error, when q > αΔ for any constant α > 2, in Õ((n^{1/3})/ε²) rounds. More generally, we achieve a runtime of Õ((n^{1/3})/ε²) rounds for approximating the partition function of Gibbs distributions defined over graphs when simple locality and fast mixing conditions hold. Gibbs distributions are widely used in fields such as machine learning and statistical physics. We obtain our result by providing an algorithm to draw n random samples from a distributed Markov chain in parallel, using similar ideas to triangle counting (Dolev, Lenzen, Peled DISC 2012) and semiring matrix multiplication (Censor-Hillel, Kaski, Korhonen, Lenzen, Paz, Suomela PODC 2015). Aside from counting problems, this result may be interesting for other applications requiring a large number of samples.
Cite as

Joshua Z. Sobel. Brief Announcement: Congested Clique Counting for Local Gibbs Distributions. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 65:1-65:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sobel:LIPIcs.DISC.2025.65,
  author =	{Sobel, Joshua Z.},
  title =	{{Brief Announcement: Congested Clique Counting for Local Gibbs Distributions}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{65:1--65:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.65},
  URN =		{urn:nbn:de:0030-drops-248811},
  doi =		{10.4230/LIPIcs.DISC.2025.65},
  annote =	{Keywords: Distributed Sampling, Approximate Counting, Markov Chains, Gibbs Distributions}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.83
Low-Temperature Sampling on Sparse Random Graphs

Authors: Andreas Galanis, Leslie Ann Goldberg, and Paulina Smolarova

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We consider sampling in the so-called low-temperature regime, which is typically characterised by non-local behaviour and strong global correlations. Canonical examples include sampling independent sets on bipartite graphs and sampling from the ferromagnetic q-state Potts model. Low-temperature sampling is computationally intractable for general graphs, but recent advances based on the polymer method have made significant progress for graph families that exhibit certain expansion properties that reinforce the correlations, including for example expanders, lattices and dense graphs. One of the most natural graph classes that has so far escaped this algorithmic framework is the class of sparse Erdős-Rényi random graphs whose expansion only manifests for sufficiently large subsets of vertices; small sets of vertices on the other hand have vanishing expansion which makes them behave independently from the bulk of the graph and therefore weakens the correlations. At a more technical level, the expansion of small sets is crucial for establishing the Kotecky-Priess condition which underpins the applicability of the framework. Our main contribution is to develop the polymer method in the low-temperature regime for sparse random graphs. As our running example, we use the Potts and random-cluster models on G(n,d/n) for d = Θ(1), where we show a polynomial-time sampling algorithm for all sufficiently large q and d, at all temperatures. Our approach applies more generally for models that are monotone. Key to our result is a simple polymer definition that blends easily with the connectivity properties of the graph and allows us to show that polymers have size at most O(log n).
Cite as

Andreas Galanis, Leslie Ann Goldberg, and Paulina Smolarova. Low-Temperature Sampling on Sparse Random Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 83:1-83:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{galanis_et_al:LIPIcs.ICALP.2025.83,
  author =	{Galanis, Andreas and Goldberg, Leslie Ann and Smolarova, Paulina},
  title =	{{Low-Temperature Sampling on Sparse Random Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{83:1--83:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.83},
  URN =		{urn:nbn:de:0030-drops-234606},
  doi =		{10.4230/LIPIcs.ICALP.2025.83},
  annote =	{Keywords: approximate counting, Glauber dynamics, random cluster model, approximate sampling, Erd\H{o}s-R\'{e}nyi Graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.84
One-Shot Learning for k-SAT

Authors: Andreas Galanis, Leslie Ann Goldberg, and Xusheng Zhang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Consider a k-SAT formula Φ where every variable appears at most d times, and let σ be a satisfying assignment of Φ sampled proportionally to e^{β m(σ)} where m(σ) is the number of variables set to true and β is a real parameter. Given Φ and σ, can we learn the value of β efficiently? This problem falls into a recent line of works about single-sample ("one-shot") learning of Markov random fields. The k-SAT setting we consider here was recently studied by Galanis, Kandiros, and Kalavasis (SODA'24) where they showed that single-sample learning is possible when roughly d ≤ 2^{k/6.45} and impossible when d ≥ (k+1) 2^{k-1}. Crucially, for their impossibility results they used the existence of unsatisfiable instances which, aside from the gap in d, left open the question of whether the feasibility threshold for one-shot learning is dictated by the satisfiability threshold of k-SAT formulas of bounded degree. Our main contribution is to answer this question negatively. We show that one-shot learning for k-SAT is infeasible well below the satisfiability threshold; in fact, we obtain impossibility results for degrees d as low as k² when β is sufficiently large, and bootstrap this to small values of β when d scales exponentially with k, via a probabilistic construction. On the positive side, we simplify the analysis of the learning algorithm and obtain significantly stronger bounds on d in terms of β. In particular, for the uniform case β → 0 that has been studied extensively in the sampling literature, our analysis shows that learning is possible under the condition d≲ 2^{k/2}. This is nearly optimal (up to constant factors) in the sense that it is known that sampling a uniformly-distributed satisfying assignment is NP-hard for d≳ 2^{k/2}.
Cite as

Andreas Galanis, Leslie Ann Goldberg, and Xusheng Zhang. One-Shot Learning for k-SAT. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 84:1-84:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{galanis_et_al:LIPIcs.ICALP.2025.84,
  author =	{Galanis, Andreas and Goldberg, Leslie Ann and Zhang, Xusheng},
  title =	{{One-Shot Learning for k-SAT}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{84:1--84:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.84},
  URN =		{urn:nbn:de:0030-drops-234610},
  doi =		{10.4230/LIPIcs.ICALP.2025.84},
  annote =	{Keywords: Computational Learning Theory, k-SAT, Maximum likelihood estimation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.98
The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization

Authors: Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study the online allocation of divisible items to n agents with additive valuations for p-mean welfare maximization, a problem introduced by Barman, Khan, and Maiti (2022). Our algorithmic and hardness results characterize the optimal competitive ratios for the entire spectrum of -∞ ≤ p ≤ 1. Surprisingly, our improved algorithms for all p ≤ (1)/(log n) are simply the greedy algorithm for the Nash welfare, supplemented with two auxiliary components to ensure all agents have non-zero utilities and to help a small number of agents with low utilities. In this sense, the long arm of Nashian allocation achieves near-optimal competitive ratios not only for Nash welfare but also all the way to egalitarian welfare.
Cite as

Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang. The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 98:1-98:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.ICALP.2025.98,
  author =	{Huang, Zhiyi and Lee, Chui Shan and Shu, Xinkai and Wang, Zhaozi},
  title =	{{The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{98:1--98:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.98},
  URN =		{urn:nbn:de:0030-drops-234754},
  doi =		{10.4230/LIPIcs.ICALP.2025.98},
  annote =	{Keywords: Online Algorithms, Fair Division, Nash Welfare}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.61
Hardness of Sampling for the Anti-Ferromagnetic Ising Model on Random Graphs

Authors: Neng Huang, Will Perkins, and Aaron Potechin

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We prove a hardness of sampling result for the anti-ferromagnetic Ising model on random graphs of average degree d for large constant d, proving that when the normalized inverse temperature satisfies β > 1 (asymptotically corresponding to the condensation threshold), then w.h.p. over the random graph there is no stable sampling algorithm that can output a sample close in W₂ distance to the Gibbs measure. The results also apply to a fixed-magnetization version of the model, showing that there are no stable sampling algorithms for low but positive temperature max and min bisection distributions. These results show a gap in the tractability of search and sampling problems: while there are efficient algorithms to find near optimizers, stable sampling algorithms cannot access the Gibbs distribution concentrated on such solutions. Our techniques involve extensions of the interpolation technique relating behavior of the mean field Sherrington-Kirkpatrick model to behavior of Ising models on random graphs of average degree d for large d. While previous interpolation arguments compared the free energies of the two models, our argument compares the average energies and average overlaps in the two models.
Cite as

Neng Huang, Will Perkins, and Aaron Potechin. Hardness of Sampling for the Anti-Ferromagnetic Ising Model on Random Graphs. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 61:1-61:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.ITCS.2025.61,
  author =	{Huang, Neng and Perkins, Will and Potechin, Aaron},
  title =	{{Hardness of Sampling for the Anti-Ferromagnetic Ising Model on Random Graphs}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{61:1--61:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.61},
  URN =		{urn:nbn:de:0030-drops-226899},
  doi =		{10.4230/LIPIcs.ITCS.2025.61},
  annote =	{Keywords: Random graph, spin glass, sampling algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.21
Fast Sampling via Spectral Independence Beyond Bounded-Degree Graphs

Authors: Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, and Daniel Štefankovič

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal O(n log n) sampling algorithms on bounded-degree graphs for a large class of problems throughout the so-called uniqueness regime, including, for example, the problems of sampling independent sets, matchings, and Ising-model configurations. Our main contribution is to relax the bounded-degree assumption that has so far been important in establishing and applying spectral independence. Previous methods for avoiding degree bounds rely on using L^p-norms to analyse contraction on graphs with bounded connective constant (Sinclair, Srivastava, Yin; FOCS'13). The non-linearity of L^p-norms is an obstacle to applying these results to bound spectral independence. Our solution is to capture the L^p-analysis recursively by amortising over the subtrees of the recurrence used to analyse contraction. Our method generalises previous analyses that applied only to bounded-degree graphs. As a main application of our techniques, we consider the random graph G(n,d/n), where the previously known algorithms run in time n^O(log d) or applied only to large d. We refine these algorithmic bounds significantly, and develop fast nearly linear algorithms based on Glauber dynamics that apply to all constant d, throughout the uniqueness regime.
Cite as

Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, and Daniel Štefankovič. Fast Sampling via Spectral Independence Beyond Bounded-Degree Graphs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bezakova_et_al:LIPIcs.ICALP.2022.21,
  author =	{Bez\'{a}kov\'{a}, Ivona and Galanis, Andreas and Goldberg, Leslie Ann and \v{S}tefankovi\v{c}, Daniel},
  title =	{{Fast Sampling via Spectral Independence Beyond Bounded-Degree Graphs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{21:1--21:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.21},
  URN =		{urn:nbn:de:0030-drops-163622},
  doi =		{10.4230/LIPIcs.ICALP.2022.21},
  annote =	{Keywords: Hard-core model, Random graphs, Markov chains}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.29
Detours in Directed Graphs

Authors: Fedor V. Fomin, Petr A. Golovach, William Lochet, Danil Sagunov, Kirill Simonov, and Saket Saurabh

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
We study two "above guarantee" versions of the classical Longest Path problem on undirected and directed graphs and obtain the following results. In the first variant of Longest Path that we study, called Longest Detour, the task is to decide whether a graph has an (s,t)-path of length at least dist_G(s,t)+k (where dist_G(s,t) denotes the length of a shortest path from s to t). Bezáková et al. [Ivona Bezáková et al., 2019] proved that on undirected graphs the problem is fixed-parameter tractable (FPT) by providing an algorithm of running time 2^{O(k)}⋅ n. Further, they left the parameterized complexity of the problem on directed graphs open. Our first main result establishes a connection between Longest Detour on directed graphs and 3-Disjoint Paths on directed graphs. Using these new insights, we design a 2^{O (k)}· n^{O(1)} time algorithm for the problem on directed planar graphs. Further, the new approach yields a significantly faster FPT algorithm on undirected graphs. In the second variant of Longest Path, namely Longest Path above Diameter, the task is to decide whether the graph has a path of length at least diam(G)+k(diam(G)denotes the length of a longest shortest path in a graph G). We obtain dichotomy results about Longest Path above Diameter on undirected and directed graphs. For (un)directed graphs, Longest Path above Diameter is NP-complete even for k=1. However, if the input undirected graph is 2-connected, then the problem is FPT. On the other hand, for 2-connected directed graphs, we show that Longest Path above Diameter is solvable in polynomial time for each k ∈ {1,..., 4} and is NP-complete for every k ≥ 5. The parameterized complexity of Longest Detour on general directed graphs remains an interesting open problem.
Cite as

Fedor V. Fomin, Petr A. Golovach, William Lochet, Danil Sagunov, Kirill Simonov, and Saket Saurabh. Detours in Directed Graphs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fomin_et_al:LIPIcs.STACS.2022.29,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Lochet, William and Sagunov, Danil and Simonov, Kirill and Saurabh, Saket},
  title =	{{Detours in Directed Graphs}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{29:1--29:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.29},
  URN =		{urn:nbn:de:0030-drops-158390},
  doi =		{10.4230/LIPIcs.STACS.2022.29},
  annote =	{Keywords: longest path, longest detour, diameter, directed graphs, parameterized complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.22
The Complexity of Approximating the Matching Polynomial in the Complex Plane

Authors: Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, and Daniel Štefankovič

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
We study the problem of approximating the value of the matching polynomial on graphs with edge parameter gamma, where gamma takes arbitrary values in the complex plane. When gamma is a positive real, Jerrum and Sinclair showed that the problem admits an FPRAS on general graphs. For general complex values of gamma, Patel and Regts, building on methods developed by Barvinok, showed that the problem admits an FPTAS on graphs of maximum degree Delta as long as gamma is not a negative real number less than or equal to -1/(4(Delta-1)). Our first main result completes the picture for the approximability of the matching polynomial on bounded degree graphs. We show that for all Delta >= 3 and all real gamma less than -1/(4(Delta-1)), the problem of approximating the value of the matching polynomial on graphs of maximum degree Delta with edge parameter gamma is #P-hard. We then explore whether the maximum degree parameter can be replaced by the connective constant. Sinclair et al. showed that for positive real gamma it is possible to approximate the value of the matching polynomial using a correlation decay algorithm on graphs with bounded connective constant (and potentially unbounded maximum degree). We first show that this result does not extend in general in the complex plane; in particular, the problem is #P-hard on graphs with bounded connective constant for a dense set of gamma values on the negative real axis. Nevertheless, we show that the result does extend for any complex value gamma that does not lie on the negative real axis. Our analysis accounts for complex values of gamma using geodesic distances in the complex plane in the metric defined by an appropriate density function.
Cite as

Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, and Daniel Štefankovič. The Complexity of Approximating the Matching Polynomial in the Complex Plane. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 22:1-22:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bezakova_et_al:LIPIcs.ICALP.2019.22,
  author =	{Bez\'{a}kov\'{a}, Ivona and Galanis, Andreas and Goldberg, Leslie Ann and \v{S}tefankovi\v{c}, Daniel},
  title =	{{The Complexity of Approximating the Matching Polynomial in the Complex Plane}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{22:1--22:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.22},
  URN =		{urn:nbn:de:0030-drops-105983},
  doi =		{10.4230/LIPIcs.ICALP.2019.22},
  annote =	{Keywords: matchings, partition function, correlation decay, connective constant}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.56
On Counting Oracles for Path Problems

Authors: Ivona Bezáková and Andrew Searns

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We initiate the study of counting oracles for various path problems in graphs. Distance oracles have gained a lot of attention in recent years, with studies of the underlying space and time tradeoffs. For a given graph G, a distance oracle is a data structure which can be used to answer distance queries for pairs of vertices s,t in V(G). In this work, we extend the set up to answering counting queries: for a pair of vertices s,t, the oracle needs to provide the number of (shortest or all) paths from s to t. We present O(n^{1.5}) preprocessing time, O(n^{1.5}) space, and O(sqrt{n}) query time algorithms for oracles counting shortest paths in planar graphs and for counting all paths in planar directed acyclic graphs. We extend our results to other graphs which admit small balanced separators and present applications where our oracle improves the currently best known running times.
Cite as

Ivona Bezáková and Andrew Searns. On Counting Oracles for Path Problems. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 56:1-56:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bezakova_et_al:LIPIcs.ISAAC.2018.56,
  author =	{Bez\'{a}kov\'{a}, Ivona and Searns, Andrew},
  title =	{{On Counting Oracles for Path Problems}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{56:1--56:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.56},
  URN =		{urn:nbn:de:0030-drops-100042},
  doi =		{10.4230/LIPIcs.ISAAC.2018.56},
  annote =	{Keywords: Counting oracle, Path problems, Shortest paths, Separators}
}
Document
DOI: 10.4230/DagRep.7.8.23
Computational Counting (Dagstuhl Seminar 17341)

Authors: Ivona Bezáková, Leslie Ann Goldberg, and Mark R. Jerrum

Published in: Dagstuhl Reports, Volume 7, Issue 8 (2018)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 17341 "Computational Counting". The seminar was held from 20th to 25th August 2017, at Schloss Dagstuhl -- Leibnitz Center for Informatics. A total of 43 researchers from all over the world, with interests and expertise in different aspects of computational counting, actively participated in the meeting.
Cite as

Ivona Bezáková, Leslie Ann Goldberg, and Mark R. Jerrum. Computational Counting (Dagstuhl Seminar 17341). In Dagstuhl Reports, Volume 7, Issue 8, pp. 23-44, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Article{bezakova_et_al:DagRep.7.8.23,
  author =	{Bez\'{a}kov\'{a}, Ivona and Goldberg, Leslie Ann and Jerrum, Mark R.},
  title =	{{Computational Counting (Dagstuhl Seminar 17341)}},
  pages =	{23--44},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2018},
  volume =	{7},
  number =	{8},
  editor =	{Bez\'{a}kov\'{a}, Ivona and Goldberg, Leslie Ann and Jerrum, Mark R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.7.8.23},
  URN =		{urn:nbn:de:0030-drops-84283},
  doi =		{10.4230/DagRep.7.8.23},
  annote =	{Keywords: approximation algorithms, computational complexity, counting problems, partition functions, phase transitions}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.54
Finding Detours is Fixed-Parameter Tractable

Authors: Ivona Bezáková, Radu Curticapean, Holger Dell, and Fedor V. Fomin

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
We consider the following natural "above guarantee" parameterization of the classical longest path problem: For given vertices s and t of a graph G, and an integer k, the longest detour problem asks for an (s,t)-path in G that is at least k longer than a shortest (s,t)-path. Using insights into structural graph theory, we prove that the longest detour problem is fixed-parameter tractable (FPT) on undirected graphs and actually even admits a single-exponential algorithm, that is, one of running time exp(O(k)) * poly(n). This matches (up to the base of the exponential) the best algorithms for finding a path of length at least k. Furthermore, we study a related problem, exact detour, that asks whether a graph G contains an (s,t)-path that is exactly k longer than a shortest (s,t)-path. For this problem, we obtain a randomized algorithm with running time about 2.746^k * poly(n), and a deterministic algorithm with running time about 6.745^k * poly(n), showing that this problem is FPT as well. Our algorithms for the exact detour problem apply to both undirected and directed graphs.
Cite as

Ivona Bezáková, Radu Curticapean, Holger Dell, and Fedor V. Fomin. Finding Detours is Fixed-Parameter Tractable. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 54:1-54:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bezakova_et_al:LIPIcs.ICALP.2017.54,
  author =	{Bez\'{a}kov\'{a}, Ivona and Curticapean, Radu and Dell, Holger and Fomin, Fedor V.},
  title =	{{Finding Detours is Fixed-Parameter Tractable}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{54:1--54:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.54},
  URN =		{urn:nbn:de:0030-drops-74790},
  doi =		{10.4230/LIPIcs.ICALP.2017.54},
  annote =	{Keywords: longest path, fixed-parameter tractable algorithms, above-guarantee parameterization, graph minors}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.45
Approximation via Correlation Decay When Strong Spatial Mixing Fails

Authors: Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, Heng Guo, and Daniel Stefankovic

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin models. Previous analyses of correlation-decay algorithms implicitly depended on the occurrence of strong spatial mixing. This, roughly, means that one uses worst-case analysis of the recursive procedure that creates the sub-instances. In this paper, we develop a new analysis method that is more refined than the worst-case analysis. We take the shape of instances in the computation tree into consideration and we amortise against certain "bad" instances that are created as the recursion proceeds. This enables us to show correlation decay and to obtain an FPTAS even when strong spatial mixing fails. We apply our technique to the problem of approximately counting independent sets in hypergraphs with degree upper-bound Delta and with a lower bound k on the arity of hyperedges. Liu and Lin gave an FPTAS for k >= 2 and Delta <= 5 (lack of strong spatial mixing was the obstacle preventing this algorithm from being generalised to Delta = 6). Our technique gives a tight result for Delta = 6, showing that there is an FPTAS for k >= 3 and Delta <= 6. The best previously-known approximation scheme for Delta = 6 is the Markov-chain simulation based FPRAS of Bordewich, Dyer and Karpinski, which only works for k >= 8. Our technique also applies for larger values of k, giving an FPTAS for k >= 1.66 Delta. This bound is not as strong as existing randomised results, for technical reasons that are discussed in the paper. Nevertheless, it gives the first deterministic approximation schemes in this regime. We further demonstrate that in the hypergraph independent set model, approximating the partition function is NP-hard even within the uniqueness regime.
Cite as

Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, Heng Guo, and Daniel Stefankovic. Approximation via Correlation Decay When Strong Spatial Mixing Fails. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 45:1-45:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bezakova_et_al:LIPIcs.ICALP.2016.45,
  author =	{Bez\'{a}kov\'{a}, Ivona and Galanis, Andreas and Goldberg, Leslie Ann and Guo, Heng and Stefankovic, Daniel},
  title =	{{Approximation via Correlation Decay When Strong Spatial Mixing Fails}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{45:1--45:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.45},
  URN =		{urn:nbn:de:0030-drops-63257},
  doi =		{10.4230/LIPIcs.ICALP.2016.45},
  annote =	{Keywords: approximate counting, independent sets in hypergraphs, correlation decay}
}
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