24 Search Results for "Bhangale, Amey"

Document
DOI: 10.4230/LIPIcs.LICS.2026.13
Towards Infinite PCSP: A Dichotomy for Monochromatic Cliques

Authors: Demian Banakh, Alexey Barsukov, and Tamio-Vesa Nakajima

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
The logic MMSNP is a well-studied fragment of Existential Second-Order logic that, from a computational perspective, captures finite-domain Constraint Satisfaction Problems (CSPs) modulo polynomial-time reductions. At the same time, MMSNP contains many problems that are expressible as ω-categorical CSPs but not as finite-domain ones. We initiate the study of Promise MMSNP (PMMSNP), a promise analogue of MMSNP. We show that every PMMSNP problem is poly-time equivalent to a (finite-domain) Promise CSP (PCSP), thereby extending the classical MMSNP-CSP correspondence to the promise setting. We then investigate the complexity of PMMSNPs arising from forbidding monochromatic cliques, a class encompassing promise graph colouring problems. For this class, we obtain a full complexity classification conditional on the Rich 2-to-1 Conjecture, a recently proposed perfect-completeness surrogate of the Unique Games Conjecture. As a key intermediate step which may be of independent interest, we prove that it is NP-hard, under the Rich 2-to-1 Conjecture, to properly colour a uniform hypergraph even if it is promised to admit a colouring satisfying a certain technical condition called reconfigurability. This proof is an extension of the recent work of Braverman, Khot, Lifshitz and Minzer (Adv. Math. 2025). To illustrate the broad applicability of this theorem, we show that it implies most of the linearly-ordered colouring conjecture of Barto, Battistelli, and Berg (STACS 2021).
Cite as

Demian Banakh, Alexey Barsukov, and Tamio-Vesa Nakajima. Towards Infinite PCSP: A Dichotomy for Monochromatic Cliques. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 13:1-13:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{banakh_et_al:LIPIcs.LICS.2026.13,
  author =	{Banakh, Demian and Barsukov, Alexey and Nakajima, Tamio-Vesa},
  title =	{{Towards Infinite PCSP: A Dichotomy for Monochromatic Cliques}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{13:1--13:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.13},
  URN =		{urn:nbn:de:0030-drops-268000},
  doi =		{10.4230/LIPIcs.LICS.2026.13},
  annote =	{Keywords: Promise Constraint Satisfaction Problem, MMSNP, Approximation Algorithms, Rainbow Colouring}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.29
A 4.509-Approximation Algorithm for Generalized Min Sum Set Cover

Authors: Amey Bhangale and Yezhou Zhang

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
We study the generalized min-sum set cover (GMSSC) problem, where given a collection of hyperedges E with arbitrary covering requirements {k_e ∈ ℤ^+ : e ∈ E}, the objective is to find an ordering of the vertices that minimizes the total cover time of the hyperedges. A hyperedge e is considered covered at the first time when k_e of its vertices appear in the ordering. We present a 4.509-approximation algorithm for GMSSC, improving upon the previous best-known guarantee of 4.642 [Nikhil Bansal et al., 2021]. Our approach retains the general LP-based framework of Bansal, Batra, Farhadi, and Tetali [Nikhil Bansal et al., 2021] but provides an improved analysis that narrows the gap toward the lower bound of 4-approximation assuming P≠NP. Our analysis takes advantage of the constraints of the linear program in a nontrivial way, along with new lower-tail bounds for the sums of independent Bernoulli random variables, which could be of independent interest.
Cite as

Amey Bhangale and Yezhou Zhang. A 4.509-Approximation Algorithm for Generalized Min Sum Set Cover. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 29:1-29:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhangale_et_al:LIPIcs.ICALP.2026.29,
  author =	{Bhangale, Amey and Zhang, Yezhou},
  title =	{{A 4.509-Approximation Algorithm for Generalized Min Sum Set Cover}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{29:1--29:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.29},
  URN =		{urn:nbn:de:0030-drops-264185},
  doi =		{10.4230/LIPIcs.ICALP.2026.29},
  annote =	{Keywords: Generalized Min Sum Set Cover, Approximation Algorithm, Min latency set cover, Linear programming, Knapsack cover inequalities}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.30
Optimal Inapproximability of Generalized Linear Equations over a Finite Group

Authors: Amey Bhangale and Yezhou Zhang

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the fraction of satisfied constraints. In this work, we study the CSP where the constraints are generalized linear equations over a finite group G. More specifically, for a given S ⊆ G, the constraints in this CSP are of the form addition of the values to the variables (similarly, product for non-abelian groups) belongs to the set S. We give an approximation algorithm for this problem on satisfiable instances and show that it is optimal for certain S assuming 𝐏≠ NP. This natural predicate is one of the very few known predicates that are approximation resistant on almost satisfiable instances, assuming 𝐏≠ NP, but admits a non-trivial approximation algorithm on satisfiable instances.
Cite as

Amey Bhangale and Yezhou Zhang. Optimal Inapproximability of Generalized Linear Equations over a Finite Group. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 30:1-30:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bhangale_et_al:LIPIcs.ICALP.2026.30,
  author =	{Bhangale, Amey and Zhang, Yezhou},
  title =	{{Optimal Inapproximability of Generalized Linear Equations over a Finite Group}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{30:1--30:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael 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.2026.30},
  URN =		{urn:nbn:de:0030-drops-264193},
  doi =		{10.4230/LIPIcs.ICALP.2026.30},
  annote =	{Keywords: Constraint satisfaction problems, inapproximability, approximation algorithms, non-abelian groups, Fourier analysis}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.28
Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank

Authors: Nikolai Chukhin, Alexander S. Kulikov, Ivan Mihajlin, and Arina Smirnova

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

Abstract
Proving complexity lower bounds remains a challenging task: currently, we only know how to prove conditional uniform (algorithm) lower bounds and nonuniform (circuit) lower bounds in restricted circuit models. About a decade ago, Williams (STOC 2010) showed how to derive nonuniform lower bounds from uniform upper bounds: roughly, by designing a fast algorithm for checking satisfiability of circuits, one gets a lower bound for this circuit class. Since then, a number of results of this kind have been proved. For example, Jahanjou et al. (ICALP 2015) and Carmosino et al. (ITCS 2016) proved that if NSETH fails, then E^{NP} has series-parallel circuit size ω(n). One can also derive nonuniform lower bounds from nondeterministic uniform lower bounds. Perhaps the most well-known example is the Karp-Lipton theorem (STOC 1980): if Σ₂ ≠ Π₂, then NP ⊄ P/poly. Some recent examples include the following. Nederlof (STOC 2020) proved a lower bound on the matrix multiplication tensor rank under an assumption that TSP cannot be solved faster than in 2ⁿ time. Belova et al. (SODA 2024) proved that there exists an explicit polynomial family of arithmetic circuit size Ω(n^{δ}), for any δ > 0, assuming that MAX-3-SAT cannot be solved faster than in 2ⁿ nondeterministic time. Williams (FOCS 2024) proved an exponential lower bound for ETHR ∘ ETHR circuits under the Orthogonal Vectors conjecture. Whereas all the lower bounds above are proved under strong assumptions that might eventually be refuted, the revealed connections are of great interest and may still give further insights: one may be able to weaken the used assumptions or to construct generators from other fine-grained reductions. In this paper, we continue developing this line of research and show how uniform nondeterministic lower bounds can be used to construct generators of various types of combinatorial objects that are notoriously hard to analyze: Boolean functions of high circuit size, matrices of high rigidity, and tensors of high rank. Specifically, we prove the following. - If, for some ε and k, k-SAT cannot be solved in input-oblivious co-nondeterministic time O(2^{(1/2+ε)n}), then there exists a monotone Boolean function family in coNP of monotone circuit size 2^{Ω(n / log n)}. Combining this with the result above, we get win-win circuit lower bounds: either E^{NP{}} requires series-parallel circuits of size ω(n) or coNP requires monotone circuits of size 2^{Ω(n / log n)}. - If, for all ε > 0, MAX-3-SAT cannot be solved in co-nondeterministic time O(2^{(1 - ε)n}), then there exist small families of matrices with rigidity exceeding the best known constructions as well as small families of three-dimensional tensors of rank n^{1+Δ}, for some Δ > 0.
Cite as

Nikolai Chukhin, Alexander S. Kulikov, Ivan Mihajlin, and Arina Smirnova. Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chukhin_et_al:LIPIcs.STACS.2026.28,
  author =	{Chukhin, Nikolai and Kulikov, Alexander S. and Mihajlin, Ivan and Smirnova, Arina},
  title =	{{Conditional Complexity Hardness: Monotone Circuit Size, Matrix Rigidity, and Tensor Rank}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{28:1--28:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.28},
  URN =		{urn:nbn:de:0030-drops-255177},
  doi =		{10.4230/LIPIcs.STACS.2026.28},
  annote =	{Keywords: computational complexity, circuit complexity, lower bounds, conditional lower bounds, monotone circuits, matrix rigidity, tensor rank, arithmetic circuits, fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.103
A General Framework for Low Soundness Homomorphism Testing

Authors: Tushant Mittal and Sourya Roy

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

Abstract
We introduce a general framework to design and analyze algorithms for the problem of testing homomorphisms between finite groups in the low-soundness regime. In this regime, we give the first constant-query tests for various families of groups. These include tests for: (i) homomorphisms between arbitrary cyclic groups, (ii) homomorphisms between any finite group and ℤ_p, (iii) automorphisms of dihedral and symmetric groups, (iv) inner automorphisms of non-abelian finite simple groups and extraspecial groups, and (v) testing linear characters of GL_n(F_q), and finite-dimensional Lie algebras over F_q. We also recover the result of Kiwi [TCS'03] for testing homomorphisms between F_qⁿ and F_q. Prior to this work, such tests were only known for abelian groups with a constant maximal order (such as F_qⁿ). No tests were known for non-abelian groups. As an additional corollary, our framework gives combinatorial list decoding bounds for cyclic groups with list size dependence of O(ε^{-2}) (for agreement parameter ε). This improves upon the currently best-known bound of O(ε^{-105}) due to Dinur, Grigorescu, Kopparty, and Sudan [STOC'08], and Guo and Sudan [RANDOM'14].
Cite as

Tushant Mittal and Sourya Roy. A General Framework for Low Soundness Homomorphism Testing. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 103:1-103:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{mittal_et_al:LIPIcs.ITCS.2026.103,
  author =	{Mittal, Tushant and Roy, Sourya},
  title =	{{A General Framework for Low Soundness Homomorphism Testing}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{103:1--103:18},
  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.2026.103},
  URN =		{urn:nbn:de:0030-drops-253901},
  doi =		{10.4230/LIPIcs.ITCS.2026.103},
  annote =	{Keywords: Property Testing, Coding Theory}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.13
Optimal Online Bipartite Matching in Degree-2 Graphs

Authors: Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Online bipartite matching is a classical problem in online algorithms and we know that both the deterministic fractional and randomized integral online matchings achieve the same competitive ratio of 1-1/e. In this work, we study classes of graphs where the online degree is restricted to 2. As expected, one can achieve a competitive ratio of better than 1-1/e in both the deterministic fractional and randomized integral cases, but surprisingly, these ratios are not the same. It was already known that for fractional matching, a 0.75 competitive ratio algorithm is optimal. We show that the folklore Half-Half algorithm achieves a competitive ratio of η ≈ 0.717772… and more surprisingly, show that this is optimal by giving a matching lower-bound. This yields a separation between the two problems: deterministic fractional and randomized integral, showing that it is impossible to obtain a perfect rounding scheme.
Cite as

Amey Bhangale, Arghya Chakraborty, and Prahladh Harsha. Optimal Online Bipartite Matching in Degree-2 Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhangale_et_al:LIPIcs.ISAAC.2025.13,
  author =	{Bhangale, Amey and Chakraborty, Arghya and Harsha, Prahladh},
  title =	{{Optimal Online Bipartite Matching in Degree-2 Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.13},
  URN =		{urn:nbn:de:0030-drops-249216},
  doi =		{10.4230/LIPIcs.ISAAC.2025.13},
  annote =	{Keywords: Online Algorithm, Bipartite matching}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.47
Time Lower Bounds for the Metropolis Process and Simulated Annealing

Authors: Zongchen Chen, Dan Mikulincer, Daniel Reichman, and Alexander S. Wein

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

Abstract
The Metropolis process (MP) and Simulated Annealing (SA) are stochastic local search heuristics that are often used in solving combinatorial optimization problems. Despite significant interest, there are very few theoretical results regarding the quality of approximation obtained by MP and SA (with polynomially many iterations) for NP-hard optimization problems. We provide rigorous lower bounds for MP and SA with respect to the classical maximum independent set problem when the algorithms are initialized from the empty set. We establish the existence of a family of graphs for which both MP and SA fail to find approximate solutions in polynomial time. More specifically, we show that for any ε ∈ (0,1) there are n-vertex graphs for which the probability SA (when limited to polynomially many iterations) will approximate the optimal solution within ratio Ω(1/n^{1-ε}) is exponentially small. Our lower bounds extend to graphs of constant average degree d, illustrating the failure of MP to achieve an approximation ratio of Ω(log(d)/d) in polynomial time. In some cases, our lower bounds apply even when the temperature is chosen adaptively. Finally, we prove exponential-time lower bounds when the inputs to these algorithms are bipartite graphs, and even trees, which are known to admit polynomial-time algorithms for the independent set problem.
Cite as

Zongchen Chen, Dan Mikulincer, Daniel Reichman, and Alexander S. Wein. Time Lower Bounds for the Metropolis Process and Simulated Annealing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 47:1-47:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2025.47,
  author =	{Chen, Zongchen and Mikulincer, Dan and Reichman, Daniel and Wein, Alexander S.},
  title =	{{Time Lower Bounds for the Metropolis Process and Simulated Annealing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{47:1--47:22},
  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.2025.47},
  URN =		{urn:nbn:de:0030-drops-244138},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.47},
  annote =	{Keywords: Metropolis Process, Simulated Annealing, Independent Set}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.10
Biased Linearity Testing in the 1% Regime

Authors: Subhash Khot and Kunal Mittal

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

Abstract
We study linearity testing over the p-biased hypercube ({0,1}ⁿ, μ_p^{⊗n}) in the 1% regime. For a distribution ν supported over {x ∈ {0,1}^k:∑_{i=1}^k x_i = 0 (mod 2)}, with marginal distribution μ_p in each coordinate, the corresponding k-query linearity test Lin(ν) proceeds as follows: Given query access to a function f:{0,1}ⁿ → {-1,1}, sample (x_1,… ,x_k)∼ ν^{⊗n}, query f on x_1,… ,x_k, and accept if and only if ∏_{i ∈ [k]} f(x_i) = 1. Building on the work of Bhangale, Khot, and Minzer (STOC '23), we show, for 0 < p ≤ 1/2, that if k ≥ 1+1/p, then there exists a distribution ν such that the test Lin(ν) works in the 1% regime; that is, any function f:{0,1}ⁿ → {-1,1} passing the test Lin(ν) with probability ≥ 1/2+ε, for some constant ε > 0, satisfies Pr_{x∼μ_p^{⊗n}}[f(x) = g(x)] ≥ 1/2+δ, for some linear function g, and a constant δ = δ(ε) > 0. Conversely, we show that if k < 1+1/p, then no such test Lin(ν) works in the 1% regime. Our key observation is that the linearity test Lin(ν) works if and only if the distribution ν satisfies a certain pairwise independence property.
Cite as

Subhash Khot and Kunal Mittal. Biased Linearity Testing in the 1% Regime. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khot_et_al:LIPIcs.CCC.2025.10,
  author =	{Khot, Subhash and Mittal, Kunal},
  title =	{{Biased Linearity Testing in the 1\% Regime}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{10:1--10:23},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-237046},
  doi =		{10.4230/LIPIcs.CCC.2025.10},
  annote =	{Keywords: Linearity test, 1\% regime, p-biased}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.38
Optimal Inapproximability of Promise Equations over Finite Groups

Authors: Silvia Butti, Alberto Larrauri, and Stanislav Živný

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

Abstract
A celebrated result of Håstad established that, for any constant ε > 0, it is NP-hard to find an assignment satisfying a (1/|G|+ε)-fraction of the constraints of a given 3-LIN instance over an Abelian group G even if one is promised that an assignment satisfying a (1-ε)-fraction of the constraints exists. Engebretsen, Holmerin, and Russell showed the same result for 3-LIN instances over any finite (not necessarily Abelian) group. In other words, for almost-satisfiable instances of 3-LIN the random assignment achieves an optimal approximation guarantee. We prove that the random assignment algorithm is still best possible under a stronger promise that the 3-LIN instance is almost satisfiable over an arbitrarily more restrictive group.
Cite as

Silvia Butti, Alberto Larrauri, and Stanislav Živný. Optimal Inapproximability of Promise Equations over Finite Groups. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 38:1-38:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{butti_et_al:LIPIcs.ICALP.2025.38,
  author =	{Butti, Silvia and Larrauri, Alberto and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Optimal Inapproximability of Promise Equations over Finite Groups}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{38:1--38:14},
  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.2025.38},
  URN =		{urn:nbn:de:0030-drops-234150},
  doi =		{10.4230/LIPIcs.ICALP.2025.38},
  annote =	{Keywords: promise constraint satisfaction, approximation, linear equations}
}
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)

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@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
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.54
Parallel Repetition of k-Player Projection Games

Authors: Amey Bhangale, Mark Braverman, Subhash Khot, Yang P. Liu, and Dor Minzer

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We study parallel repetition of k-player games where the constraints satisfy the projection property. We prove exponential decay in the value of a parallel repetition of projection games with a value less than 1.
Cite as

Amey Bhangale, Mark Braverman, Subhash Khot, Yang P. Liu, and Dor Minzer. Parallel Repetition of k-Player Projection Games. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhangale_et_al:LIPIcs.APPROX/RANDOM.2024.54,
  author =	{Bhangale, Amey and Braverman, Mark and Khot, Subhash and Liu, Yang P. and Minzer, Dor},
  title =	{{Parallel Repetition of k-Player Projection Games}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.54},
  URN =		{urn:nbn:de:0030-drops-210475},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.54},
  annote =	{Keywords: Parallel Repetition, Multiplayer games, Projection games}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.20
Mixing of 3-Term Progressions in Quasirandom Groups

Authors: Amey Bhangale, Prahladh Harsha, and Sourya Roy

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
In this paper, we show the mixing of three-term progressions (x, xg, xg²) in every finite quasirandom group, fully answering a question of Gowers. More precisely, we show that for any D-quasirandom group G and any three sets A₁, A₂, A₃ ⊂ G, we have |Pr_{x,y∼ G}[x ∈ A₁, xy ∈ A₂, xy² ∈ A₃] - ∏_{i = 1}³ Pr_{x∼ G}[x ∈ A_i]| ≤ (2/(√{D)})^{1/4}. Prior to this, Tao answered this question when the underlying quasirandom group is SL_{d}(𝔽_q). Subsequently, Peluse extended the result to all non-abelian finite simple groups. In this work, we show that a slight modification of Peluse’s argument is sufficient to fully resolve Gowers' quasirandom conjecture for 3-term progressions. Surprisingly, unlike the proofs of Tao and Peluse, our proof is elementary and only uses basic facts from non-abelian Fourier analysis.
Cite as

Amey Bhangale, Prahladh Harsha, and Sourya Roy. Mixing of 3-Term Progressions in Quasirandom Groups. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 20:1-20:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bhangale_et_al:LIPIcs.ITCS.2022.20,
  author =	{Bhangale, Amey and Harsha, Prahladh and Roy, Sourya},
  title =	{{Mixing of 3-Term Progressions in Quasirandom Groups}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{20:1--20:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.20},
  URN =		{urn:nbn:de:0030-drops-156163},
  doi =		{10.4230/LIPIcs.ITCS.2022.20},
  annote =	{Keywords: Quasirandom groups, 3-term arithmetic progressions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.21
Max-3-Lin over Non-Abelian Groups with Universal Factor Graphs

Authors: Amey Bhangale and Aleksa Stanković

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
Factor graph of an instance of a constraint satisfaction problem with n variables and m constraints is the bipartite graph between [m] and [n] describing which variable appears in which constraints. Thus, an instance of a CSP is completely defined by its factor graph and the list of predicates. We show inapproximability of Max-3-LIN over non-abelian groups (both in the perfect completeness case and in the imperfect completeness case), with the same inapproximability factor as in the general case, even when the factor graph is fixed. Along the way, we also show that these optimal hardness results hold even when we restrict the linear equations in the Max-3-LIN instances to the form x⋅ y⋅ z = g, where x,y,z are the variables and g is a group element. We use representation theory and Fourier analysis over non-abelian groups to analyze the reductions.
Cite as

Amey Bhangale and Aleksa Stanković. Max-3-Lin over Non-Abelian Groups with Universal Factor Graphs. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 21:1-21:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bhangale_et_al:LIPIcs.ITCS.2022.21,
  author =	{Bhangale, Amey and Stankovi\'{c}, Aleksa},
  title =	{{Max-3-Lin over Non-Abelian Groups with Universal Factor Graphs}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{21:1--21:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.21},
  URN =		{urn:nbn:de:0030-drops-156177},
  doi =		{10.4230/LIPIcs.ITCS.2022.21},
  annote =	{Keywords: Universal factor graphs, linear equations, non-abelian groups, hardness of approximation}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.38
Hardness of Approximation of (Multi-)LCS over Small Alphabet

Authors: Amey Bhangale, Diptarka Chakraborty, and Rajendra Kumar

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

Abstract
The problem of finding longest common subsequence (LCS) is one of the fundamental problems in computer science, which finds application in fields such as computational biology, text processing, information retrieval, data compression etc. It is well known that (decision version of) the problem of finding the length of a LCS of an arbitrary number of input sequences (which we refer to as Multi-LCS problem) is NP-complete. Jiang and Li [SICOMP'95] showed that if Max-Clique is hard to approximate within a factor of s then Multi-LCS is also hard to approximate within a factor of Θ(s). By the NP-hardness of the problem of approximating Max-Clique by Zuckerman [ToC'07], for any constant δ > 0, the length of a LCS of arbitrary number of input sequences of length n each, cannot be approximated within an n^{1-δ}-factor in polynomial time unless {P}={NP}. However, the reduction of Jiang and Li assumes the alphabet size to be Ω(n). So far no hardness result is known for the problem of approximating Multi-LCS over sub-linear sized alphabet. On the other hand, it is easy to get 1/|Σ|-factor approximation for strings of alphabet Σ. In this paper, we make a significant progress towards proving hardness of approximation over small alphabet by showing a polynomial-time reduction from the well-studied densest k-subgraph problem with perfect completeness to approximating Multi-LCS over alphabet of size poly(n/k). As a consequence, from the known hardness result of densest k-subgraph problem (e.g. [Manurangsi, STOC'17]) we get that no polynomial-time algorithm can give an n^{-o(1)}-factor approximation of Multi-LCS over an alphabet of size n^{o(1)}, unless the Exponential Time Hypothesis is false.
Cite as

Amey Bhangale, Diptarka Chakraborty, and Rajendra Kumar. Hardness of Approximation of (Multi-)LCS over Small Alphabet. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 38:1-38:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bhangale_et_al:LIPIcs.APPROX/RANDOM.2020.38,
  author =	{Bhangale, Amey and Chakraborty, Diptarka and Kumar, Rajendra},
  title =	{{Hardness of Approximation of (Multi-)LCS over Small Alphabet}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{38:1--38:16},
  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.2020.38},
  URN =		{urn:nbn:de:0030-drops-126418},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.38},
  annote =	{Keywords: Longest common subsequence, Hardness of approximation, ETH-hardness, Densest k-subgraph problem}
}
Document
DOI: 10.4230/LIPIcs.CCC.2020.9
Simultaneous Max-Cut Is Harder to Approximate Than Max-Cut

Authors: Amey Bhangale and Subhash Khot

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

Abstract
A systematic study of simultaneous optimization of constraint satisfaction problems was initiated by Bhangale et al. [ICALP, 2015]. The simplest such problem is the simultaneous Max-Cut. Bhangale et al. [SODA, 2018] gave a .878-minimum approximation algorithm for simultaneous Max-Cut which is almost optimal assuming the Unique Games Conjecture (UGC). For single instance Max-Cut, Goemans-Williamson [JACM, 1995] gave an α_GW-approximation algorithm where α_GW ≈ .87856720... which is optimal assuming the UGC. It was left open whether one can achieve an α_GW-minimum approximation algorithm for simultaneous Max-Cut. We answer the question by showing that there exists an absolute constant ε₀ ≥ 10^{-5} such that it is NP-hard to get an (α_GW- ε₀)-minimum approximation for simultaneous Max-Cut assuming the Unique Games Conjecture.
Cite as

Amey Bhangale and Subhash Khot. Simultaneous Max-Cut Is Harder to Approximate Than Max-Cut. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bhangale_et_al:LIPIcs.CCC.2020.9,
  author =	{Bhangale, Amey and Khot, Subhash},
  title =	{{Simultaneous Max-Cut Is Harder to Approximate Than Max-Cut}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{9:1--9:15},
  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.2020.9},
  URN =		{urn:nbn:de:0030-drops-125610},
  doi =		{10.4230/LIPIcs.CCC.2020.9},
  annote =	{Keywords: Simultaneous CSPs, Unique Games hardness, Max-Cut}
}
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