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Documents authored by Hayes, Thomas P.

Document
DOI: 10.4230/LIPIcs.ITCS.2024.36
Fraud Detection for Random Walks

Authors: Varsha Dani, Thomas P. Hayes, Seth Pettie, and Jared Saia

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Traditional fraud detection is often based on finding statistical anomalies in data sets and transaction histories. A sophisticated fraudster, aware of the exact kinds of tests being deployed, might be difficult or impossible to catch. We are interested in paradigms for fraud detection that are provably robust against any adversary, no matter how sophisticated. In other words, the detection strategy should rely on signals in the data that are inherent in the goals the adversary is trying to achieve. Specifically, we consider a fraud detection game centered on a random walk on a graph. We assume this random walk is implemented by having a player at each vertex, who can be honest or not. In particular, when the random walk reaches a vertex owned by an honest player, it proceeds to a uniformly random neighbor at the next timestep. However, when the random walk reaches a dishonest player, it instead proceeds to an arbitrary neighbor chosen by an omniscient Adversary. The game is played between the Adversary and a Referee who sees the trajectory of the random walk. At any point during the random walk, if the Referee determines that a {specific} vertex is controlled by a dishonest player, the Referee accuses that player, and therefore wins the game. The Referee is allowed to make the occasional incorrect accusation, but must follow a policy that makes such mistakes with small probability of error. The goal of the adversary is to make the cover time large, ideally infinite, i.e., the walk should never reach at least one vertex. We consider the following basic question: how much can the omniscient Adversary delay the cover time without getting caught? Our main result is a tight upper bound on this delay factor. We also discuss possible applications of our results to settings such as Rotor Walks, Leader Election, and Sybil Defense.
Cite as

Varsha Dani, Thomas P. Hayes, Seth Pettie, and Jared Saia. Fraud Detection for Random Walks. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 36:1-36:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dani_et_al:LIPIcs.ITCS.2024.36,
  author =	{Dani, Varsha and Hayes, Thomas P. and Pettie, Seth and Saia, Jared},
  title =	{{Fraud Detection for Random Walks}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{36:1--36:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.36},
  URN =		{urn:nbn:de:0030-drops-195645},
  doi =		{10.4230/LIPIcs.ITCS.2024.36},
  annote =	{Keywords: Fraud detection, random processes, Markov chains}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.33
Optimal Mixing via Tensorization for Random Independent Sets on Arbitrary Trees

Authors: Charilaos Efthymiou, Thomas P. Hayes, Daniel Štefankovič, and Eric Vigoda

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We study the mixing time of the single-site update Markov chain, known as the Glauber dynamics, for generating a random independent set of a tree. Our focus is obtaining optimal convergence results for arbitrary trees. We consider the more general problem of sampling from the Gibbs distribution in the hard-core model where independent sets are weighted by a parameter λ > 0; the special case λ = 1 corresponds to the uniform distribution over all independent sets. Previous work of Martinelli, Sinclair and Weitz (2004) obtained optimal mixing time bounds for the complete Δ-regular tree for all λ. However, Restrepo et al. (2014) showed that for sufficiently large λ there are bounded-degree trees where optimal mixing does not hold. Recent work of Eppstein and Frishberg (2022) proved a polynomial mixing time bound for the Glauber dynamics for arbitrary trees, and more generally for graphs of bounded tree-width. We establish an optimal bound on the relaxation time (i.e., inverse spectral gap) of O(n) for the Glauber dynamics for unweighted independent sets on arbitrary trees. Moreover, for λ ≤ .44 we prove an optimal mixing time bound of O(n log n). We stress that our results hold for arbitrary trees and there is no dependence on the maximum degree Δ. Interestingly, our results extend (far) beyond the uniqueness threshold which is on the order λ = O(1/Δ). Our proof approach is inspired by recent work on spectral independence. In fact, we prove that spectral independence holds with a constant independent of the maximum degree for any tree, but this does not imply mixing for general trees as the optimal mixing results of Chen, Liu, and Vigoda (2021) only apply for bounded degree graphs. We instead utilize the combinatorial nature of independent sets to directly prove approximate tensorization of variance/entropy via a non-trivial inductive proof.
Cite as

Charilaos Efthymiou, Thomas P. Hayes, Daniel Štefankovič, and Eric Vigoda. Optimal Mixing via Tensorization for Random Independent Sets on Arbitrary Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{efthymiou_et_al:LIPIcs.APPROX/RANDOM.2023.33,
  author =	{Efthymiou, Charilaos and Hayes, Thomas P. and \v{S}tefankovi\v{c}, Daniel and Vigoda, Eric},
  title =	{{Optimal Mixing via Tensorization for Random Independent Sets on Arbitrary Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{33:1--33:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.33},
  URN =		{urn:nbn:de:0030-drops-188589},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.33},
  annote =	{Keywords: MCMC, Mixing Time, Independent Sets, Hard-Core Model, Approximate Counting Algorithms, Sampling Algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2022.16
How to Wake up Your Neighbors: Safe and Nearly Optimal Generic Energy Conservation in Radio Networks

Authors: Varsha Dani and Thomas P. Hayes

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
Recent work [Chang et al., 2018; Chang et al., 2020; Varsha Dani et al., 2021] has shown that it is sometimes feasible to significantly reduce the energy usage of some radio-network algorithms by adaptively powering down the radio receiver when it is not needed. Although past work has focused on modifying specific network algorithms in this way, we now ask the question of whether this problem can be solved in a generic way, treating the algorithm as a kind of black box. We are able to answer this question in the affirmative, presenting a new general way to modify arbitrary radio-network algorithms in an attempt to save energy. At the expense of a small increase in the time complexity, we can provably reduce the energy usage to an extent that is provably nearly optimal within a certain class of general-purpose algorithms. As an application, we show that our algorithm reduces the energy cost of breadth-first search in radio networks from the previous best bound of 2^O(√{log n}) to polylog(n), where n is the number of nodes in the network A key ingredient in our algorithm is hierarchical clustering based on additive Voronoi decomposition done at multiple scales. Similar clustering algorithms have been used in other recent work on energy-aware computation in radio networks, but we believe the specific approach presented here may be of independent interest.
Cite as

Varsha Dani and Thomas P. Hayes. How to Wake up Your Neighbors: Safe and Nearly Optimal Generic Energy Conservation in Radio Networks. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 16:1-16:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dani_et_al:LIPIcs.DISC.2022.16,
  author =	{Dani, Varsha and Hayes, Thomas P.},
  title =	{{How to Wake up Your Neighbors: Safe and Nearly Optimal Generic Energy Conservation in Radio Networks}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{16:1--16:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.16},
  URN =		{urn:nbn:de:0030-drops-172071},
  doi =		{10.4230/LIPIcs.DISC.2022.16},
  annote =	{Keywords: Radio Networks, Low Energy Computation, Clustering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.48
Improved Reconstruction of Random Geometric Graphs

Authors: Varsha Dani, Josep Díaz, Thomas P. Hayes, and Cristopher Moore

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

Abstract
Embedding graphs in a geographical or latent space, i.e. inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We consider the classic model of random geometric graphs where n points are scattered uniformly in a square of area n, and two points have an edge between them if and only if their Euclidean distance is less than r. The reconstruction problem then consists of inferring the vertex positions, up to the symmetries of the square, given only the adjacency matrix of the resulting graph. We give an algorithm that, if r = n^α for α > 0, with high probability reconstructs the vertex positions with a maximum error of O(n^β) where β = 1/2-(4/3)α, until α ≥ 3/8 where β = 0 and the error becomes O(√{log n}). This improves over earlier results, which were unable to reconstruct with error less than r. Our method estimates Euclidean distances using a hybrid of graph distances and short-range estimates based on the number of common neighbors. We extend our results to the surface of the sphere in ℝ³ and to hypercubes in any constant dimension.
Cite as

Varsha Dani, Josep Díaz, Thomas P. Hayes, and Cristopher Moore. Improved Reconstruction of Random Geometric Graphs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 48:1-48:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dani_et_al:LIPIcs.ICALP.2022.48,
  author =	{Dani, Varsha and D{\'\i}az, Josep and Hayes, Thomas P. and Moore, Cristopher},
  title =	{{Improved Reconstruction of Random Geometric Graphs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{48:1--48:17},
  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.2022.48},
  URN =		{urn:nbn:de:0030-drops-163897},
  doi =		{10.4230/LIPIcs.ICALP.2022.48},
  annote =	{Keywords: Reconstruction algorithm, distances in RGG, d-dimensional hypercube, 3 dimensional sphere}
}
Document
DOI: 10.4230/LIPIcs.DISC.2021.19
Wake up and Join Me! an Energy-Efficient Algorithm for Maximal Matching in Radio Networks

Authors: Varsha Dani, Aayush Gupta, Thomas P. Hayes, and Seth Pettie

Published in: LIPIcs, Volume 209, 35th International Symposium on Distributed Computing (DISC 2021)

Abstract
We consider networks of small, autonomous devices that communicate with each other wirelessly. Minimizing energy usage is an important consideration in designing algorithms for such networks, as battery life is a crucial and limited resource. Working in a model where both sending and listening for messages deplete energy, we consider the problem of finding a maximal matching of the nodes in a radio network of arbitrary and unknown topology. We present a distributed randomized algorithm that produces, with high probability, a maximal matching. The maximum energy cost per node is O(log² n), and the time complexity is O(Δ log n). Here n is any upper bound on the number of nodes, and Δ is any upper bound on the maximum degree; n and Δ are parameters of our algorithm that we assume are known a priori to all the processors. We note that there exist families of graphs for which our bounds on energy cost and time complexity are simultaneously optimal up to polylog factors, so any significant improvement would need additional assumptions about the network topology. We also consider the related problem of assigning, for each node in the network, a neighbor to back up its data in case of eventual node failure. Here, a key goal is to minimize the maximum load, defined as the number of nodes assigned to a single node. We present an efficient decentralized low-energy algorithm that finds a neighbor assignment whose maximum load is at most a polylog(n) factor bigger that the optimum.
Cite as

Varsha Dani, Aayush Gupta, Thomas P. Hayes, and Seth Pettie. Wake up and Join Me! an Energy-Efficient Algorithm for Maximal Matching in Radio Networks. In 35th International Symposium on Distributed Computing (DISC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 209, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dani_et_al:LIPIcs.DISC.2021.19,
  author =	{Dani, Varsha and Gupta, Aayush and Hayes, Thomas P. and Pettie, Seth},
  title =	{{Wake up and Join Me! an Energy-Efficient Algorithm for Maximal Matching in Radio Networks}},
  booktitle =	{35th International Symposium on Distributed Computing (DISC 2021)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-210-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{209},
  editor =	{Gilbert, Seth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2021.19},
  URN =		{urn:nbn:de:0030-drops-148219},
  doi =		{10.4230/LIPIcs.DISC.2021.19},
  annote =	{Keywords: Distributed Algorithms, Energy-Aware Computation, Radio Networks, Maximal Matching, Sensor Networks}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.59
On the Power of Choice for k-Colorability of Random Graphs

Authors: Varsha Dani, Diksha Gupta, and Thomas P. Hayes

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
In an r-choice Achlioptas process, random edges are generated r at a time, and an online strategy is used to select one of them for inclusion in a graph. We investigate the problem of whether such a selection strategy can shift the k-colorability transition; that is, the number of edges at which the graph goes from being k-colorable to non-k-colorable. We show that, for k ≥ 9, two choices suffice to delay the k-colorability threshold, and that for every k ≥ 2, six choices suffice.
Cite as

Varsha Dani, Diksha Gupta, and Thomas P. Hayes. On the Power of Choice for k-Colorability of Random Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 59:1-59:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{dani_et_al:LIPIcs.APPROX/RANDOM.2021.59,
  author =	{Dani, Varsha and Gupta, Diksha and Hayes, Thomas P.},
  title =	{{On the Power of Choice for k-Colorability of Random Graphs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{59:1--59:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.59},
  URN =		{urn:nbn:de:0030-drops-147527},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.59},
  annote =	{Keywords: Random graphs, Achlioptas Processes, Phase Transition, Graph Colorability}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.48
Improved Strong Spatial Mixing for Colorings on Trees

Authors: Charilaos Efthymiou, Andreas Galanis, Thomas P. Hayes, Daniel Štefankovič, and Eric Vigoda

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
Strong spatial mixing (SSM) is a form of correlation decay that has played an essential role in the design of approximate counting algorithms for spin systems. A notable example is the algorithm of Weitz (2006) for the hard-core model on weighted independent sets. We study SSM for the q-colorings problem on the infinite (d+1)-regular tree. Weak spatial mixing (WSM) captures whether the influence of the leaves on the root vanishes as the height of the tree grows. Jonasson (2002) established WSM when q>d+1. In contrast, in SSM, we first fix a coloring on a subset of internal vertices, and we again ask if the influence of the leaves on the root is vanishing. It was known that SSM holds on the (d+1)-regular tree when q>alpha d where alpha ~~ 1.763... is a constant that has arisen in a variety of results concerning random colorings. Here we improve on this bound by showing SSM for q>1.59d. Our proof establishes an L^2 contraction for the BP operator. For the contraction we bound the norm of the BP Jacobian by exploiting combinatorial properties of the coloring of the tree.
Cite as

Charilaos Efthymiou, Andreas Galanis, Thomas P. Hayes, Daniel Štefankovič, and Eric Vigoda. Improved Strong Spatial Mixing for Colorings on Trees. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{efthymiou_et_al:LIPIcs.APPROX-RANDOM.2019.48,
  author =	{Efthymiou, Charilaos and Galanis, Andreas and Hayes, Thomas P. and \v{S}tefankovi\v{c}, Daniel and Vigoda, Eric},
  title =	{{Improved Strong Spatial Mixing for Colorings on Trees}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.48},
  URN =		{urn:nbn:de:0030-drops-112630},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.48},
  annote =	{Keywords: colorings, regular tree, spatial mixing, phase transitions}
}
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