10 Search Results for "Hébert-Johnson, Úrsula"

Document
DOI: 10.4230/LIPIcs.IPEC.2025.9
An ETH-Tight FPT Algorithm for Rejection-Proof Set Packing with Applications to Kidney Exchange

Authors: Bart M. P. Jansen, Jeroen S. K. Lamme, and Ruben F. A. Verhaegh

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
We study the parameterized complexity of a recently introduced multi-agent variant of the Kidney Exchange problem. Given a directed graph G and integers d and k, the standard problem asks whether G contains a packing of vertex-disjoint cycles, each of length ≤ d, covering at least k vertices in total. In the multi-agent setting we consider, the vertex set is partitioned over several agents who reject a cycle packing as solution if it can be modified into an alternative packing that covers more of their own vertices. A cycle packing is called rejection-proof if no agent rejects it and the problem asks whether such a packing exists that covers at least k vertices. We exploit the sunflower lemma on a set packing formulation of the problem to give a kernel for this Σ₂^P-complete problem that is polynomial in k for all constant values of d. We also provide a 2^𝒪(k log k) + n^𝒪(1) algorithm based on it and show that this FPT algorithm is asymptotically optimal under the ETH. Further, we generalize the problem by including an additional positive integer c in the input that naturally captures how much agents can modify a given cycle packing to reject it. For every constant c, the resulting problem simplifies from being Σ₂^P-complete to NP-complete. The super-exponential lower bound already holds for c = 2, though. We present an ad-hoc single-exponential algorithm for c = 1. These results reveal an interesting discrepancy between the classical and parameterized complexity of the problem and give a good view of what makes it hard.
Cite as

Bart M. P. Jansen, Jeroen S. K. Lamme, and Ruben F. A. Verhaegh. An ETH-Tight FPT Algorithm for Rejection-Proof Set Packing with Applications to Kidney Exchange. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.IPEC.2025.9,
  author =	{Jansen, Bart M. P. and Lamme, Jeroen S. K. and Verhaegh, Ruben F. A.},
  title =	{{An ETH-Tight FPT Algorithm for Rejection-Proof Set Packing with Applications to Kidney Exchange}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.9},
  URN =		{urn:nbn:de:0030-drops-251414},
  doi =		{10.4230/LIPIcs.IPEC.2025.9},
  annote =	{Keywords: Parameterized complexity, Multi-agent kidney exchange, Kernelization, Set packing}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.19
Characterizing the Distinguishability of Product Distributions Through Multicalibration

Authors: Cassandra Marcussen, Aaron Putterman, and Salil Vadhan

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Given a sequence of samples x_1, … , x_k promised to be drawn from one of two distributions X₀, X₁, a well-studied problem in statistics is to decide which distribution the samples are from. Information theoretically, the maximum advantage in distinguishing the two distributions given k samples is captured by the total variation distance between X₀^{⊗k} and X₁^{⊗k}. However, when we restrict our attention to efficient distinguishers (i.e., small circuits) of these two distributions, exactly characterizing the ability to distinguish X₀^{⊗k} and X₁^{⊗k} is more involved and less understood. In this work, we give a general way to reduce bounds on the computational indistinguishability of X₀ and X₁ to bounds on the information-theoretic indistinguishability of some specific, related variables X̃₀ and X̃₁. As a consequence, we prove a new, tight characterization of the number of samples k needed to efficiently distinguish X₀^{⊗k} and X₁^{⊗k} with constant advantage as k = Θ(d_H^{-2}(X̃₀, X̃₁)), which is the inverse of the squared Hellinger distance d_H between two distributions X̃₀ and X̃₁ that are computationally indistinguishable from X₀ and X₁. Likewise, our framework can be used to re-derive a result of Halevi and Rabin (TCC 2008) and Geier (TCC 2022), proving nearly-tight bounds on how computational indistinguishability scales with the number of samples for arbitrary product distributions. At the heart of our work is the use of the Multicalibration Theorem (Hébert-Johnson, Kim, Reingold, Rothblum 2018) in a way inspired by recent work of Casacuberta, Dwork, and Vadhan (STOC 2024). Multicalibration allows us to relate the computational indistinguishability of X₀, X₁ to the statistical indistinguishability of X̃₀, X̃₁ (for lower bounds on k) and construct explicit circuits to distinguish between X̃₀, X̃₁ and consequently X₀, X₁ (for upper bounds on k).
Cite as

Cassandra Marcussen, Aaron Putterman, and Salil Vadhan. Characterizing the Distinguishability of Product Distributions Through Multicalibration. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{marcussen_et_al:LIPIcs.CCC.2025.19,
  author =	{Marcussen, Cassandra and Putterman, Aaron and Vadhan, Salil},
  title =	{{Characterizing the Distinguishability of Product Distributions Through Multicalibration}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.19},
  URN =		{urn:nbn:de:0030-drops-237130},
  doi =		{10.4230/LIPIcs.CCC.2025.19},
  annote =	{Keywords: Multicalibration, computational distinguishability}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.16
Smooth Calibration and Decision Making

Authors: Jason Hartline, Yifan Wu, and Yunran Yang

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Calibration requires predictor outputs to be consistent with their Bayesian posteriors. For machine learning predictors that do not distinguish between small perturbations, calibration errors are continuous in predictions, e.g. smooth calibration error [Foster and Hart, 2018], distance to calibration [Błasiok et al., 2023]. On the contrary, decision-makers who use predictions make optimal decisions discontinuously in probabilistic space, experiencing loss from miscalibration discontinuously. Calibration errors for decision-making are thus discontinuous, e.g., Expected Calibration Error [Foster and Vohra, 1997], and Calibration Decision Loss [Hu and Wu, 2024]. Thus, predictors with a low calibration error for machine learning may suffer a high calibration error for decision-making, i.e. they may not be trustworthy for decision-makers optimizing assuming their predictions are correct. It is natural to ask if post-processing a predictor with a low calibration error for machine learning is without loss to achieve a low calibration error for decision-making. In our paper, we show post-processing an online predictor with ε distance to calibration achieves O(√{ε}) ECE and CDL, which is asymptotically optimal. The post-processing algorithm adds noise to make predictions differentially private. The optimal bound from low distance to calibration predictors from post-processing is non-optimal compared with existing online calibration algorithms that directly optimize for ECE and CDL.
Cite as

Jason Hartline, Yifan Wu, and Yunran Yang. Smooth Calibration and Decision Making. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 16:1-16:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hartline_et_al:LIPIcs.FORC.2025.16,
  author =	{Hartline, Jason and Wu, Yifan and Yang, Yunran},
  title =	{{Smooth Calibration and Decision Making}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{16:1--16:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.16},
  URN =		{urn:nbn:de:0030-drops-231438},
  doi =		{10.4230/LIPIcs.FORC.2025.16},
  annote =	{Keywords: Calibration, calibration errors, decision making, differential privacy}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.14
Model Ensembling for Constrained Optimization

Authors: Ira Globus Harris, Varun Gupta, Michael Kearns, and Aaron Roth

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Many instances of decision making under objective uncertainty can be decomposed into two steps: predicting the objective function and then optimizing for the best feasible action under the estimate of the objective vector. We study the problem of ensembling models for optimization of uncertain linear objectives under arbitrary constraints. We imagine we are given a collection of predictive models mapping a feature space to multi-dimensional real-valued predictions, which form the coefficients of a linear objective that we would like to optimize. We give two ensembling methods that can provably result in transparent decisions that strictly improve on all initial policies. The first method operates in the "white box" setting in which we have access to the underlying prediction models and the second in the "black box" setting in which we only have access to the induced decisions (in the downstream optimization problem) of the constituent models, but not their underlying point predictions. They are transparent or trustworthy in the sense that the user can reliably predict long-term ensemble rewards even if the instance by instance predictions are imperfect.
Cite as

Ira Globus Harris, Varun Gupta, Michael Kearns, and Aaron Roth. Model Ensembling for Constrained Optimization. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{globusharris_et_al:LIPIcs.FORC.2025.14,
  author =	{Globus Harris, Ira and Gupta, Varun and Kearns, Michael and Roth, Aaron},
  title =	{{Model Ensembling for Constrained Optimization}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.14},
  URN =		{urn:nbn:de:0030-drops-231412},
  doi =		{10.4230/LIPIcs.FORC.2025.14},
  annote =	{Keywords: model ensembling, trustworthy AI, decision-making under uncertainty}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.19
Mapping the Tradeoffs and Limitations of Algorithmic Fairness

Authors: Etam Benger and Katrina Ligett

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Sufficiency and separation are two fundamental criteria in classification fairness. For binary classifiers, these concepts correspond to subgroup calibration and equalized odds, respectively, and are known to be incompatible except in trivial cases. In this work, we explore a relaxation of these criteria based on f-divergences between distributions - essentially the same relaxation studied in the literature on approximate multicalibration - analyze their relationships, and derive implications for fair representations and downstream uses (post-processing) of representations. We show that when a protected attribute is determinable from features present in the data, the (relaxed) criteria of sufficiency and separation exhibit a tradeoff, forming a convex Pareto frontier. Moreover, we prove that when a protected attribute is not fully encoded in the data, achieving full sufficiency may be impossible. This finding not only strengthens the case against "fairness through unawareness" but also highlights an important caveat for work on (multi-)calibration.
Cite as

Etam Benger and Katrina Ligett. Mapping the Tradeoffs and Limitations of Algorithmic Fairness. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{benger_et_al:LIPIcs.FORC.2025.19,
  author =	{Benger, Etam and Ligett, Katrina},
  title =	{{Mapping the Tradeoffs and Limitations of Algorithmic Fairness}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{19:1--19:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.19},
  URN =		{urn:nbn:de:0030-drops-231465},
  doi =		{10.4230/LIPIcs.FORC.2025.19},
  annote =	{Keywords: Algorithmic fairness, information theory, sufficiency-separation tradeoff}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.22
When Does a Predictor Know Its Own Loss?

Authors: Aravind Gollakota, Parikshit Gopalan, Aayush Karan, Charlotte Peale, and Udi Wieder

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Given a predictor and a loss function, how well can we predict the loss that the predictor will incur on an input? This is the problem of loss prediction, a key computational task associated with uncertainty estimation for a predictor. In a classification setting, a predictor will typically predict a distribution over labels and hence have its own estimate of the loss that it will incur, given by the entropy of the predicted distribution. Should we trust this estimate? In other words, when does the predictor know what it knows and what it does not know? In this work we study the theoretical foundations of loss prediction. Our main contribution is to establish tight connections between nontrivial loss prediction and certain forms of multicalibration [Ursula Hébert-Johnson et al., 2018], a multigroup fairness notion that asks for calibrated predictions across computationally identifiable subgroups. Formally, we show that a loss predictor that is able to improve on the self-estimate of a predictor yields a witness to a failure of multicalibration, and vice versa. This has the implication that nontrivial loss prediction is in effect no easier or harder than auditing for multicalibration. We support our theoretical results with experiments that show a robust positive correlation between the multicalibration error of a predictor and the efficacy of training a loss predictor.
Cite as

Aravind Gollakota, Parikshit Gopalan, Aayush Karan, Charlotte Peale, and Udi Wieder. When Does a Predictor Know Its Own Loss?. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gollakota_et_al:LIPIcs.FORC.2025.22,
  author =	{Gollakota, Aravind and Gopalan, Parikshit and Karan, Aayush and Peale, Charlotte and Wieder, Udi},
  title =	{{When Does a Predictor Know Its Own Loss?}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{22:1--22:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.22},
  URN =		{urn:nbn:de:0030-drops-231490},
  doi =		{10.4230/LIPIcs.FORC.2025.22},
  annote =	{Keywords: loss prediction, multicalibration, active learning, algorithmic fairness, calibration, predictive uncertainty, uncertainty estimation, machine learning theory}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.7
Kernel Multiaccuracy

Authors: Carol Xuan Long, Wael Alghamdi, Alexander Glynn, Yixuan Wu, and Flavio P. Calmon

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract
Predefined demographic groups often overlook the subpopulations most impacted by model errors, leading to a growing emphasis on data-driven methods that pinpoint where models underperform. The emerging field of multi-group fairness addresses this by ensuring models perform well across a wide range of group-defining functions, rather than relying on fixed demographic categories. We demonstrate that recently introduced notions of multi-group fairness can be equivalently formulated as integral probability metrics (IPM). IPMs are the common information-theoretic tool that underlie definitions such as multiaccuracy, multicalibration, and outcome indistinguishably. For multiaccuracy, this connection leads to a simple, yet powerful procedure for achieving multiaccuracy with respect to an infinite-dimensional class of functions defined by a reproducing kernel Hilbert space (RKHS): first perform a kernel regression of a model’s errors, then subtract the resulting function from a model’s predictions. We combine these results to develop a post-processing method that improves multiaccuracy with respect to bounded-norm functions in an RKHS, enjoys provable performance guarantees, and, in binary classification benchmarks, achieves favorable multiaccuracy relative to competing methods.
Cite as

Carol Xuan Long, Wael Alghamdi, Alexander Glynn, Yixuan Wu, and Flavio P. Calmon. Kernel Multiaccuracy. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 7:1-7:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{long_et_al:LIPIcs.FORC.2025.7,
  author =	{Long, Carol Xuan and Alghamdi, Wael and Glynn, Alexander and Wu, Yixuan and Calmon, Flavio P.},
  title =	{{Kernel Multiaccuracy}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{7:1--7:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.7},
  URN =		{urn:nbn:de:0030-drops-231341},
  doi =		{10.4230/LIPIcs.FORC.2025.7},
  annote =	{Keywords: algorithmic fairness, integral probability metrics, information theory}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.46
Sampling Unlabeled Chordal Graphs in Expected Polynomial Time

Authors: Úrsula Hébert-Johnson and Daniel Lokshtanov

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We design an algorithm that generates an n-vertex unlabeled chordal graph uniformly at random in expected polynomial time. Along the way, we develop the following two results: (1) an FPT algorithm for counting and sampling labeled chordal graphs with a given automorphism π, parameterized by the number of moved points of π, and (2) a proof that the probability that a random n-vertex labeled chordal graph has a given automorphism π ∈ S_n is at most 1/2^{c max{μ²,n}}, where μ is the number of moved points of π and c is a constant. Our algorithm for sampling unlabeled chordal graphs calls the aforementioned FPT algorithm as a black box with potentially large values of the parameter μ, but the probability of calling this algorithm with a large value of μ is exponentially small.
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Úrsula Hébert-Johnson and Daniel Lokshtanov. Sampling Unlabeled Chordal Graphs in Expected Polynomial Time. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hebertjohnson_et_al:LIPIcs.STACS.2025.46,
  author =	{H\'{e}bert-Johnson, \'{U}rsula and Lokshtanov, Daniel},
  title =	{{Sampling Unlabeled Chordal Graphs in Expected Polynomial Time}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{46:1--46:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.46},
  URN =		{urn:nbn:de:0030-drops-228726},
  doi =		{10.4230/LIPIcs.STACS.2025.46},
  annote =	{Keywords: Chordal graphs, graph sampling, graph counting, unlabeled graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.58
Counting and Sampling Labeled Chordal Graphs in Polynomial Time

Authors: Úrsula Hébert-Johnson, Daniel Lokshtanov, and Eric Vigoda

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We present the first polynomial-time algorithm to exactly compute the number of labeled chordal graphs on n vertices. Our algorithm solves a more general problem: given n and ω as input, it computes the number of ω-colorable labeled chordal graphs on n vertices, using O(n⁷) arithmetic operations. A standard sampling-to-counting reduction then yields a polynomial-time exact sampler that generates an ω-colorable labeled chordal graph on n vertices uniformly at random. Our counting algorithm improves upon the previous best result by Wormald (1985), which computes the number of labeled chordal graphs on n vertices in time exponential in n. An implementation of the polynomial-time counting algorithm gives the number of labeled chordal graphs on up to 30 vertices in less than three minutes on a standard desktop computer. Previously, the number of labeled chordal graphs was only known for graphs on up to 15 vertices.
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Úrsula Hébert-Johnson, Daniel Lokshtanov, and Eric Vigoda. Counting and Sampling Labeled Chordal Graphs in Polynomial Time. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 58:1-58:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hebertjohnson_et_al:LIPIcs.ESA.2023.58,
  author =	{H\'{e}bert-Johnson, \'{U}rsula and Lokshtanov, Daniel and Vigoda, Eric},
  title =	{{Counting and Sampling Labeled Chordal Graphs in Polynomial Time}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{58:1--58:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.58},
  URN =		{urn:nbn:de:0030-drops-187119},
  doi =		{10.4230/LIPIcs.ESA.2023.58},
  annote =	{Keywords: Counting algorithms, graph sampling, chordal graphs}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.32
Anonymity-Preserving Space Partitions

Authors: Úrsula Hébert-Johnson, Chinmay Sonar, Subhash Suri, and Vaishali Surianarayanan

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We consider a multidimensional space partitioning problem, which we call Anonymity-Preserving Partition. Given a set P of n points in ℝ^d and a collection H of m axis-parallel hyperplanes, the hyperplanes of H partition the space into an arrangement A(H) of rectangular cells. Given an integer parameter t > 0, we call a cell C in this arrangement deficient if 0 < |C ∩ P| < t; that is, the cell contains at least one but fewer than t data points of P. Our problem is to remove the minimum number of hyperplanes from H so that there are no deficient cells. We show that the problem is NP-complete for all dimensions d ≥ 2. We present a polynomial-time d-approximation algorithm, for any fixed d, and we also show that the problem can be solved exactly in time (2d-0.924)^k m^O(1) + O(n), where k is the solution size. The one-dimensional case of the problem, where all hyperplanes are parallel, can be solved optimally in polynomial time, but we show that a related Interval Anonymity problem is NP-complete even in one dimension.
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Úrsula Hébert-Johnson, Chinmay Sonar, Subhash Suri, and Vaishali Surianarayanan. Anonymity-Preserving Space Partitions. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hebertjohnson_et_al:LIPIcs.ISAAC.2021.32,
  author =	{H\'{e}bert-Johnson, \'{U}rsula and Sonar, Chinmay and Suri, Subhash and Surianarayanan, Vaishali},
  title =	{{Anonymity-Preserving Space Partitions}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.32},
  URN =		{urn:nbn:de:0030-drops-154654},
  doi =		{10.4230/LIPIcs.ISAAC.2021.32},
  annote =	{Keywords: Anonymity, Hitting Set, LP, Constant Approximation, Fixed-Parameter Tractable, Space Partitions, Parameterized Complexity}
}
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