13 Search Results for "Potukuchi, Aditya"

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.68
Rapid Mixing via Coupling Independence for Spin Systems with Unbounded Degree

Authors: Xiaoyu Chen and Weiming Feng

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We develop a new framework to prove the mixing or relaxation time for the Glauber dynamics on spin systems with unbounded degree. It works for general spin systems including both 2-spin and multi-spin systems. As applications for this approach: - We prove the optimal O(n) relaxation time for the Glauber dynamics of random q-list-coloring on an n-vertices triangle-tree graph with maximum degree Δ such that q/Δ > α^⋆, where α^⋆ ≈ 1.763 is the unique positive solution of the equation α = exp(1/α). This improves the n^{1+o(1)} relaxation time for Glauber dynamics obtained by the previous work of Jain, Pham, and Vuong (2022). Besides, our framework can also give a near-linear time sampling algorithm under the same condition. - We prove the optimal O(n) relaxation time and near-optimal Õ(n) mixing time for the Glauber dynamics on hardcore models with parameter λ in balanced bipartite graphs such that λ < λ_c(Δ_L) for the max degree Δ_L in left part and the max degree Δ_R of right part satisfies Δ_R = O(Δ_L). This improves the previous result by Chen, Liu, and Yin (2023). At the heart of our proof is the notion of coupling independence which allows us to consider multiple vertices as a huge single vertex with exponentially large domain and do a "coarse-grained" local-to-global argument on spin systems. The technique works for general (multi) spin systems and helps us obtain some new comparison results for Glauber dynamics.
Cite as

Xiaoyu Chen and Weiming Feng. Rapid Mixing via Coupling Independence for Spin Systems with Unbounded Degree. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 68:1-68:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2025.68,
  author =	{Chen, Xiaoyu and Feng, Weiming},
  title =	{{Rapid Mixing via Coupling Independence for Spin Systems with Unbounded Degree}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{68:1--68:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.68},
  URN =		{urn:nbn:de:0030-drops-244345},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.68},
  annote =	{Keywords: coupling independence, Glauber dynamics, mixing times, relaxation times, spin systems}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.57
List-Recovery of Random Linear Codes over Small Fields

Authors: Dean Doron, Jonathan Mosheiff, Nicolas Resch, and João Ribeiro

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study list-recoverability of random linear codes over small fields, both from errors and from erasures. We consider codes of rate ε-close to capacity, and aim to bound the dependence of the output list size L on ε, the input list size 𝓁, and the alphabet size q. Prior to our work, the best upper bound was L = q^O(𝓁/ε) (Zyablov and Pinsker, Prob. Per. Inf. 1981). Previous work has identified cases in which linear codes provably perform worse than non-linear codes with respect to list-recovery. While there exist non-linear codes that achieve L = O(𝓁/ε), we know that L ≥ 𝓁^Ω(1/ε) is necessary for list recovery from erasures over fields of small characteristic, and for list recovery from errors over large alphabets. We show that in other relevant regimes there is no significant price to pay for linearity, in the sense that we get the correct dependence on the gap-to-capacity ε and go beyond the Zyablov-Pinsker bound for the first time. Specifically, when q is constant and ε approaches zero, - For list-recovery from erasures over prime fields, we show that L ≤ C₁/ε. By prior work, such a result cannot be obtained for low-characteristic fields. - For list-recovery from errors over arbitrary fields, we prove that L ≤ C₂/ε. Above, C₁ and C₂ depend on the decoding radius, input list size, and field size. We provide concrete bounds on the constants above, and the upper bounds on L improve upon the Zyablov-Pinsker bound whenever q ≤ 2^{(1/ε)^c} for some small universal constant c > 0.
Cite as

Dean Doron, Jonathan Mosheiff, Nicolas Resch, and João Ribeiro. List-Recovery of Random Linear Codes over Small Fields. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 57:1-57:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.57,
  author =	{Doron, Dean and Mosheiff, Jonathan and Resch, Nicolas and Ribeiro, Jo\~{a}o},
  title =	{{List-Recovery of Random Linear Codes over Small Fields}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{57:1--57:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.57},
  URN =		{urn:nbn:de:0030-drops-244239},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.57},
  annote =	{Keywords: List recovery, random linear codes}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.53
Near-Optimal List-Recovery of Linear Code Families

Authors: Ray Li and Nikhil Shagrithaya

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We prove several results on linear codes achieving list-recovery capacity. We show that random linear codes achieve list-recovery capacity with constant output list size (independent of the alphabet size and length). That is, over alphabets of size at least 𝓁^Ω(1/ε), random linear codes of rate R are (1-R-ε, 𝓁, (𝓁/ε)^O(𝓁/ε))-list-recoverable for all R ∈ (0,1) and 𝓁. Together with a result of Levi, Mosheiff, and Shagrithaya, this implies that randomly punctured Reed-Solomon codes also achieve list-recovery capacity. We also prove that our output list size is near-optimal among all linear codes: all (1-R-ε, 𝓁, L)-list-recoverable linear codes must have L ≥ 𝓁^{Ω(R/ε)}. Our simple upper bound combines the Zyablov-Pinsker argument with recent bounds from Kopparty, Ron-Zewi, Saraf, Wootters, and Tamo on the maximum intersection of a "list-recovery ball" and a low-dimensional subspace with large distance. Our lower bound is inspired by a recent lower bound of Chen and Zhang.
Cite as

Ray Li and Nikhil Shagrithaya. Near-Optimal List-Recovery of Linear Code Families. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 53:1-53:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{li_et_al:LIPIcs.APPROX/RANDOM.2025.53,
  author =	{Li, Ray and Shagrithaya, Nikhil},
  title =	{{Near-Optimal List-Recovery of Linear Code Families}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{53:1--53:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.53},
  URN =		{urn:nbn:de:0030-drops-244199},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.53},
  annote =	{Keywords: Error-Correcting Codes, Randomness, List-Recovery, Reed-Solomon Codes, Random Linear Codes}
}
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)

Copy BibTex To Clipboard

@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.2025.125
Unbalanced Random Matching Markets with Partial Preferences

Authors: Aditya Potukuchi and Shikha Singh

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

Abstract
Properties of stable matchings in the popular random-matching-market model have been studied for over 50 years. In a random matching market, each agent has complete preferences drawn uniformly and independently at random. Wilson (1972), Knuth (1976) and Pittel (1989) proved that in balanced random matching markets, the proposers are matched to their ln nth choice on average. In this paper, we consider competitive markets with n jobs and n+k candidates, and partial lists where each agent only ranks their top d choices. Despite the long history of the problem, the following fundamental question remains unanswered for these generalized markets: what is the tight threshold on list length d that results in a perfect stable matching with high probability? In this paper, we answer this question exactly - we prove a sharp threshold d₀ = ln n ⋅ ln (n+k)/(k+1) on the existence of perfect stable matchings when k = o(n). That is, we show that if d < (1-ε) d₀, then no stable matching matches all jobs; moreover, if d > (1+ ε) d₀, then all jobs are matched in every stable matching with high probability. This bound improves and generalizes recent results by Kanoria, Min and Qian (2021). Furthermore, we extend the line of work studying the effect of imbalance on the expected rank of the proposers (termed the "stark effect of competition"). We establish the regime in unbalanced markets that forces this stark effect to take shape in markets with partial preferences.
Cite as

Aditya Potukuchi and Shikha Singh. Unbalanced Random Matching Markets with Partial Preferences. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 125:1-125:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{potukuchi_et_al:LIPIcs.ICALP.2025.125,
  author =	{Potukuchi, Aditya and Singh, Shikha},
  title =	{{Unbalanced Random Matching Markets with Partial Preferences}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{125:1--125:16},
  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.2025.125},
  URN =		{urn:nbn:de:0030-drops-235025},
  doi =		{10.4230/LIPIcs.ICALP.2025.125},
  annote =	{Keywords: stable matching, probabilistic method, Gale-Shapley algorithm}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2025.169
Complexity of Approximate Conflict-Free, Linearly-Ordered, and Nonmonochromatic Hypergraph Colourings

Authors: Tamio-Vesa Nakajima, Zephyr Verwimp, Marcin Wrochna, and Stanislav Živný

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

Abstract
Using the algebraic approach to promise constraint satisfaction problems, we establish complexity classifications of three natural variants of hypergraph colourings: standard nonmonochromatic colourings, conflict-free colourings, and linearly-ordered colourings. Firstly, we show that finding an 𝓁-colouring of a k-colourable r-uniform hypergraph is NP-hard for all constant 2 ≤ k ≤ 𝓁 and r ≥ 3. This provides a shorter proof of a celebrated result by Dinur et al. [FOCS'02/Combinatorica'05]. Secondly, we show that finding an 𝓁-conflict-free colouring of an r-uniform hypergraph that admits a k-conflict-free colouring is NP-hard for all constant 2 ≤ k ≤ 𝓁 and r ≥ 4, except for r = 4 and k = 2 (and any 𝓁); this case is solvable in polynomial time. The case of r = 3 is the standard nonmonochromatic colouring, and the case of r = 2 is the notoriously difficult open problem of approximate graph colouring. Thirdly, we show that finding an 𝓁-linearly-ordered colouring of an r-uniform hypergraph that admits a k-linearly-ordered colouring is NP-hard for all constant 3 ≤ k ≤ 𝓁 and r ≥ 4, thus improving on the results of Nakajima and Živný [ICALP'22/ACM TocT'23].
Cite as

Tamio-Vesa Nakajima, Zephyr Verwimp, Marcin Wrochna, and Stanislav Živný. Complexity of Approximate Conflict-Free, Linearly-Ordered, and Nonmonochromatic Hypergraph Colourings. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 169:1-169:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{nakajima_et_al:LIPIcs.ICALP.2025.169,
  author =	{Nakajima, Tamio-Vesa and Verwimp, Zephyr and Wrochna, Marcin and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Complexity of Approximate Conflict-Free, Linearly-Ordered, and Nonmonochromatic Hypergraph Colourings}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{169:1--169:10},
  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.2025.169},
  URN =		{urn:nbn:de:0030-drops-235460},
  doi =		{10.4230/LIPIcs.ICALP.2025.169},
  annote =	{Keywords: hypergraph colourings, conflict-free colourings, unique-maximum colourings, linearly-ordered colourings}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.67
Error-Correcting Graph Codes

Authors: Swastik Kopparty, Aditya Potukuchi, and Harry Sha

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

Abstract
In this paper, we construct Error-Correcting Graph Codes. An error-correcting graph code of distance δ is a family C of graphs, on a common vertex set of size n, such that if we start with any graph in C, we would have to modify the neighborhoods of at least δ n vertices in order to obtain some other graph in C. This is a natural graph generalization of the standard Hamming distance error-correcting codes for binary strings. Yohananov and Yaakobi were the first to construct codes in this metric. We extend their work by showing 1) Combinatorial results determining the optimal rate vs distance trade-off nonconstructively. 2) Graph code analogues of Reed-Solomon codes and code concatenation, leading to positive distance codes for all rates and positive rate codes for all distances. 3) Graph code analogues of dual-BCH codes, yielding large codes with distance δ = 1-o(1). This gives an explicit "graph code of Ramsey graphs". Several recent works, starting with the paper of Alon, Gujgiczer, Körner, Milojević, and Simonyi, have studied more general graph codes; where the symmetric difference between any two graphs in the code is required to have some desired property. Error-correcting graph codes are a particularly interesting instantiation of this concept.
Cite as

Swastik Kopparty, Aditya Potukuchi, and Harry Sha. Error-Correcting Graph Codes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 67:1-67:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kopparty_et_al:LIPIcs.ITCS.2025.67,
  author =	{Kopparty, Swastik and Potukuchi, Aditya and Sha, Harry},
  title =	{{Error-Correcting Graph Codes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{67:1--67:20},
  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.2025.67},
  URN =		{urn:nbn:de:0030-drops-226950},
  doi =		{10.4230/LIPIcs.ITCS.2025.67},
  annote =	{Keywords: Graph codes, explicit construction, concatenation codes, tensor codes}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.35
A Spectral Approach to Approximately Counting Independent Sets in Dense Bipartite Graphs

Authors: Charlie Carlson, Ewan Davies, Alexandra Kolla, and Aditya Potukuchi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We give a randomized algorithm that approximates the number of independent sets in a dense, regular bipartite graph - in the language of approximate counting, we give an FPRAS for #BIS on the class of dense, regular bipartite graphs. Efficient counting algorithms typically apply to "high-temperature" problems on bounded-degree graphs, and our contribution is a notable exception as it applies to dense graphs in a low-temperature setting. Our methods give a counting-focused complement to the long line of work in combinatorial optimization showing that CSPs such as Max-Cut and Unique Games are easy on dense graphs via spectral arguments. Our contributions include a novel extension of the method of graph containers that differs considerably from other recent low-temperature algorithms. The additional key insights come from spectral graph theory and have previously been successful in approximation algorithms. As a result, we can overcome some limitations that seem inherent to the aforementioned class of algorithms. In particular, we exploit the fact that dense, regular graphs exhibit a kind of small-set expansion (i.e., bounded threshold rank), which, via subspace enumeration, lets us enumerate small cuts efficiently.
Cite as

Charlie Carlson, Ewan Davies, Alexandra Kolla, and Aditya Potukuchi. A Spectral Approach to Approximately Counting Independent Sets in Dense Bipartite Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 35:1-35:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{carlson_et_al:LIPIcs.ICALP.2024.35,
  author =	{Carlson, Charlie and Davies, Ewan and Kolla, Alexandra and Potukuchi, Aditya},
  title =	{{A Spectral Approach to Approximately Counting Independent Sets in Dense Bipartite Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{35:1--35:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.35},
  URN =		{urn:nbn:de:0030-drops-201782},
  doi =		{10.4230/LIPIcs.ICALP.2024.35},
  annote =	{Keywords: approximate counting, independent sets, bipartite graphs, graph containers}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.30
On the List Recoverability of Randomly Punctured Codes

Authors: Ben Lund and Aditya Potukuchi

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
We show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound. In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound. It was previously known that there are Reed-Solomon codes that do not have this property. As an immediate corollary to our main theorem, we obtain better degree bounds on unbalanced expanders that come from Reed-Solomon codes.
Cite as

Ben Lund and Aditya Potukuchi. On the List Recoverability of Randomly Punctured Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 30:1-30:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{lund_et_al:LIPIcs.APPROX/RANDOM.2020.30,
  author =	{Lund, Ben and Potukuchi, Aditya},
  title =	{{On the List Recoverability of Randomly Punctured Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{30:1--30:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.30},
  URN =		{urn:nbn:de:0030-drops-126330},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.30},
  annote =	{Keywords: List recovery, randomly punctured codes, Reed-Solomon codes}
}
Document
DOI: 10.4230/LIPIcs.CCC.2020.31
Connecting Perebor Conjectures: Towards a Search to Decision Reduction for Minimizing Formulas

Authors: Rahul Ilango

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)

Abstract
A longstanding open question is whether there is an equivalence between the computational task of determining the minimum size of any circuit computing a given function and the task of producing a minimum-sized circuit for a given function. While it is widely conjectured that both tasks require "perebor," or brute-force search, researchers have not yet ruled out the possibility that the search problem requires exponential time but the decision problem has a linear time algorithm. In this paper, we make progress in connecting the search and decision complexity of minimizing formulas. Let MFSP denote the problem that takes as input the truth table of a Boolean function f and an integer size parameter s and decides whether there is a formula for f of size at most s. Let Search- denote the corresponding search problem where one has to output some optimal formula for computing f. Our main result is that given an oracle to MFSP, one can solve Search-MFSP in time polynomial in the length N of the truth table of f and the number t of "near-optimal" formulas for f, in particular O(N⁶t²)-time. While the quantity t is not well understood, we use this result (and some extensions) to prove that given an oracle to MFSP: - there is a deterministic 2^O(N/(log log N))-time oracle algorithm for solving Search-MFSP on all but a o(1)-fraction of instances, and - there is a randomized O(2^.67N)-time oracle algorithm for solving Search-MFSP on all instances. Intriguingly, the main idea behind our algorithms is in some sense a "reverse application" of the gate elimination technique.
Cite as

Rahul Ilango. Connecting Perebor Conjectures: Towards a Search to Decision Reduction for Minimizing Formulas. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 31:1-31:35, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{ilango:LIPIcs.CCC.2020.31,
  author =	{Ilango, Rahul},
  title =	{{Connecting Perebor Conjectures: Towards a Search to Decision Reduction for Minimizing Formulas}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{31:1--31:35},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  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.CCC.2020.31},
  URN =		{urn:nbn:de:0030-drops-125834},
  doi =		{10.4230/LIPIcs.CCC.2020.31},
  annote =	{Keywords: minimum circuit size problem, minimum formula size problem, gate elimination, search to decision reduction, self-reducibility}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.93
A Spectral Bound on Hypergraph Discrepancy

Authors: Aditya Potukuchi

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Let ℋ be a t-regular hypergraph on n vertices and m edges. Let M be the m × n incidence matrix of ℋ and let us denote λ = max_{v ∈ 𝟏^⟂} 1/‖v‖ ‖Mv‖. We show that the discrepancy of ℋ is O(√t + λ). As a corollary, this gives us that for every t, the discrepancy of a random t-regular hypergraph with n vertices and m ≥ n edges is almost surely O(√t) as n grows. The proof also gives a polynomial time algorithm that takes a hypergraph as input and outputs a coloring with the above guarantee.
Cite as

Aditya Potukuchi. A Spectral Bound on Hypergraph Discrepancy. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 93:1-93:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{potukuchi:LIPIcs.ICALP.2020.93,
  author =	{Potukuchi, Aditya},
  title =	{{A Spectral Bound on Hypergraph Discrepancy}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{93:1--93:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.93},
  URN =		{urn:nbn:de:0030-drops-125002},
  doi =		{10.4230/LIPIcs.ICALP.2020.93},
  annote =	{Keywords: Hypergraph discrepancy, Spectral methods, Beck-Fiala conjecture}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.34
Approaching MCSP from Above and Below: Hardness for a Conditional Variant and AC^0[p]

Authors: Rahul Ilango

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
The Minimum Circuit Size Problem (MCSP) asks whether a given Boolean function has a circuit of at most a given size. MCSP has been studied for over a half-century and has deep connections throughout theoretical computer science including to cryptography, computational learning theory, and proof complexity. For example, we know (informally) that if MCSP is easy to compute, then most cryptography can be broken. Despite this cryptographic hardness connection and extensive research, we still know relatively little about the hardness of MCSP unconditionally. Indeed, until very recently it was unknown whether MCSP can be computed in AC^0[2] (Golovnev et al., ICALP 2019). Our main contribution in this paper is to formulate a new "oracle" variant of circuit complexity and prove that this problem is NP-complete under randomized reductions. In more detail, we define the Minimum Oracle Circuit Size Problem (MOCSP) that takes as input the truth table of a Boolean function f, a size threshold s, and the truth table of an oracle Boolean function O, and determines whether there is a circuit with O-oracle gates and at most s wires that computes f. We prove that MOCSP is NP-complete under randomized polynomial-time reductions. We also extend the recent AC^0[p] lower bound against MCSP by Golovnev et al. to a lower bound against the circuit minimization problem for depth-d formulas, (AC^0_d)-MCSP. We view this result as primarily a technical contribution. In particular, our proof takes a radically different approach from prior MCSP-related hardness results.
Cite as

Rahul Ilango. Approaching MCSP from Above and Below: Hardness for a Conditional Variant and AC^0[p]. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 34:1-34:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{ilango:LIPIcs.ITCS.2020.34,
  author =	{Ilango, Rahul},
  title =	{{Approaching MCSP from Above and Below: Hardness for a Conditional Variant and AC^0\lbrackp\rbrack}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{34:1--34:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.34},
  URN =		{urn:nbn:de:0030-drops-117191},
  doi =		{10.4230/LIPIcs.ITCS.2020.34},
  annote =	{Keywords: Minimum Circuit Size Problem, reductions, NP-completeness, circuit lower bounds}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2019.25
On the AC^0[oplus] Complexity of Andreev’s Problem

Authors: Aditya Potukuchi

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

Abstract
Andreev’s Problem is the following: Given an integer d and a subset of S subset F_q x F_q, is there a polynomial y = p(x) of degree at most d such that for every a in F_q, (a,p(a)) in S? We show an AC^0[oplus] lower bound for this problem. This problem appears to be similar to the list recovery problem for degree-d Reed-Solomon codes over F_q which states the following: Given subsets A_1,...,A_q of F_q, output all (if any) the Reed-Solomon codewords contained in A_1 x *s x A_q. In particular, we study this problem when the lists A_1, ..., A_q are randomly chosen, and are of a certain size. This may be of independent interest.
Cite as

Aditya Potukuchi. On the AC^0[oplus] Complexity of Andreev’s Problem. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{potukuchi:LIPIcs.FSTTCS.2019.25,
  author =	{Potukuchi, Aditya},
  title =	{{On the AC^0\lbrackoplus\rbrack Complexity of Andreev’s Problem}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{25:1--25:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.25},
  URN =		{urn:nbn:de:0030-drops-115879},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.25},
  annote =	{Keywords: List Recovery, Sharp Threshold, Fourier Analysis}
}
  • Refine by Type
  • 13 Document/PDF
  • 7 Document/HTML

  • Refine by Publication Year
  • 7 2025
  • 1 2024
  • 4 2020
  • 1 2019

  • Refine by Author
  • 6 Potukuchi, Aditya
  • 2 Ilango, Rahul
  • 1 Carlson, Charlie
  • 1 Chen, Xiaoyu
  • 1 Davies, Ewan
  • Show More...

  • Refine by Series/Journal
  • 13 LIPIcs

  • Refine by Classification
  • 3 Theory of computation → Circuit complexity
  • 3 Theory of computation → Problems, reductions and completeness
  • 2 Mathematics of computing → Coding theory
  • 2 Theory of computation → Error-correcting codes
  • 1 Mathematics of computing → Approximation algorithms
  • Show More...

  • Refine by Keyword
  • 2 Glauber dynamics
  • 2 List recovery
  • 2 approximate counting
  • 1 Beck-Fiala conjecture
  • 1 Erdős-Rényi Graphs
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact