21 Search Results for "Mihajlin, Ivan"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.7
Computing L_∞ Hausdorff Distances Under Translations: The Interplay of Dimensionality, Symmetry and Discreteness

Authors: Sebastian Angrick, Kevin Buchin, Geri Gokaj, and Marvin Künnemann

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
To measure the similarity of the shape of point sets, rather than their mere closeness in space, various notions of a Hausdorff distance under translation have been investigated. Specifically, let P and Q denote point sets of n and m points, respectively, in ℝ^d. We consider the task of computing the minimum distance d(P,Q+τ) over an admissible set of translations τ ∈ T, where d(⋅, ⋅) denotes the Hausdorff distance under the L_∞-norm. As variants, we distinguish between continuous (T = ℝ^d) or discrete (T is a given finite set of t translations) as well as directed or undirected (choosing the directed or undirected Hausdorff distance for d(⋅, ⋅)). We seek to apply the paradigm of fine-grained complexity to understand the complexity of these variants, and in particular: How is the running time influenced by the dimension d, the relationship between n and m, and the specific choice of variant? As our main results, we obtain: - The asymmetric definition of the most studied variant, the continuous directed Hausdorff distance, results in an intrinsically asymmetric time complexity: While (Chan, SoCG'23) established a symmetric Õ((nm)^{d/2}) upper bound for all d ≥ 3 and proved it to be conditionally optimal for combinatorial algorithms whenever m ≤ n, we show that this lower bound does not hold for the case n ≪ m, by providing a combinatorial, almost-linear-time algorithm for d = 3 and n = m^{o(1)}. We further prove general, i.e., non-combinatorial, conditional lower bounds for d ≥ 3, in particular: (1) m^{⌊d/2⌋ - o(1)} for small n and (2) n^{d/2 - o(1)} for d = 3 and small m. - We observe that the directed and undirected case is closely related, in particular, all our lower bounds for d ≥ 3 hold for both the directed and undirected variant. A remarkable exception is the case of d = 1 for which we provide a conditional separation. Specifically, in contrast to the undirected variants being solvable in near-linear time (Rote, IPL'91), we show that the directed variants are at least as hard as the additive problem MaxConv LowerBound introduced in (Cygan, Mucha, Wegrzycki and Wlodarczyk, TALG'19). - We show that the discrete variants reduce to a variant of 3SUM for d ≤ 3. This gives a barrier in proving a tight lower bound of these variants under the Orthogonal Vectors Hypothesis (OVH); in contrast, the continuous variants admit a tight conditional lower bound under OVH in d = 2 (Bringmann, Nusser, JoCG'21). These results reveal an intricate interplay of dimensionality, symmetry and discreteness in determining the fine-grained complexity of computing Hausdorff distances under translation.
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Sebastian Angrick, Kevin Buchin, Geri Gokaj, and Marvin Künnemann. Computing L_∞ Hausdorff Distances Under Translations: The Interplay of Dimensionality, Symmetry and Discreteness. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{angrick_et_al:LIPIcs.SoCG.2026.7,
  author =	{Angrick, Sebastian and Buchin, Kevin and Gokaj, Geri and K\"{u}nnemann, Marvin},
  title =	{{Computing L\underline∞ Hausdorff Distances Under Translations: The Interplay of Dimensionality, Symmetry and Discreteness}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.7},
  URN =		{urn:nbn:de:0030-drops-258131},
  doi =		{10.4230/LIPIcs.SoCG.2026.7},
  annote =	{Keywords: Hausdorff Distance, Fine-Grained Complexity, Computational Geometry, Translation-Invariant Similarity Measures}
}
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.2026.113
Multi-Quadratic Sum-Of-Squares Lower Bounds Imply VNC ¹ ≠ VNP

Authors: Benjamin Rossman and Davidson Zhu

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

Abstract
The sum-of-squares (SoS) complexity of a d-multiquadratic polynomial f (quadratic in each of d blocks of n variables) is the minimum s such that f = ∑_{i = 1}^s g_i² with each g_i d-multilinear. In the case d = 2, Hrubeš, Wigderson and Yehudayoff [Hrubeš et al., 2011] showed that an n^{1+Ω(1)} lower bound on the SoS complexity of explicit biquadratic polynomials implies an exponential lower bound for non-commutative arithmetic circuits. In this paper, we establish an analogous connection between general multiquadratic sum-of-squares and commutative arithmetic formulas. Specifically, we show that an n^{d-o(log d)} lower bound on the SoS complexity of explicit d-multiquadratic polynomials, for any d = d(n) with ω(1) ≤ d(n) ≤ O((log n)/(log log n)), would separate the algebraic complexity classes VNC¹ and VNP.
Cite as

Benjamin Rossman and Davidson Zhu. Multi-Quadratic Sum-Of-Squares Lower Bounds Imply VNC ¹ ≠ VNP. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 113:1-113:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{rossman_et_al:LIPIcs.ITCS.2026.113,
  author =	{Rossman, Benjamin and Zhu, Davidson},
  title =	{{Multi-Quadratic Sum-Of-Squares Lower Bounds Imply VNC ¹ ≠ VNP}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{113:1--113:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.113},
  URN =		{urn:nbn:de:0030-drops-254006},
  doi =		{10.4230/LIPIcs.ITCS.2026.113},
  annote =	{Keywords: sum-of-squares, arithmetic formulas}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.115
Lower Bounds for Noncommutative Circuits with Low Syntactic Degree

Authors: Pratik Shastri

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

Abstract
Proving lower bounds on the size of noncommutative arithmetic circuits is an important problem in arithmetic circuit complexity. For explicit n variate polynomials of degree Θ(n), the best known general bound is Ω(n log n) [Strassen, 1973; Walter Baur and Volker Strassen, 1983]. Recent work of Chatterjee and Hrubeš [Chatterjee and Hrubeš, 2023] has provided stronger (Ω(n²)) bounds for the restricted class of homogeneous circuits. The present paper extends these results to a broader class of circuits by using syntactic degree as a complexity measure. The syntactic degree of a circuit is a well known parameter which measures the extent to which high degree computation is used in the circuit. A homogeneous circuit computing a degree d polynomial can be assumed, without loss of generality, to have syntactic degree exactly equal to d [Fournier et al., 2024]. We generalize this by considering circuits that are not necessarily homogeneous but have low syntactic degree. Specifically, for an explicit n variate, degree n polynomial f we show that any circuit with syntactic degree O(n) computing f must have size Ω(n^{1+c}) for some constant c > 0. We also show that any circuit with syntactic degree o(nlog n) computing the same f must have size ω(nlog n). We further analyze the circuit size required to compute f based on the number of distinct syntactic degrees appearing in the circuit. Our analysis yields an ω(nlog n) size lower bound for all but a narrow parameter regime where an improved bound is not obtained. Finally, we observe that low syntactic degree circuits are more powerful than homogeneous circuits in a fine grained sense: there exists an n variate, degree Θ(n) polynomial that has a circuit of size O(nlog ²n) and syntactic degree O(n) but any homogeneous circuit computing it requires size Ω(n²).
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Pratik Shastri. Lower Bounds for Noncommutative Circuits with Low Syntactic Degree. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 115:1-115:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{shastri:LIPIcs.ITCS.2026.115,
  author =	{Shastri, Pratik},
  title =	{{Lower Bounds for Noncommutative Circuits with Low Syntactic Degree}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{115:1--115:9},
  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.2026.115},
  URN =		{urn:nbn:de:0030-drops-254028},
  doi =		{10.4230/LIPIcs.ITCS.2026.115},
  annote =	{Keywords: Noncommutative Circuits, Lower Bounds, Circuit Complexity, Algebraic Complexity}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.9
An ETH-Tight FPT Algorithm for Rejection-Proof Set Packing with Applications to Kidney Exchange

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

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

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

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

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@InProceedings{jansen_et_al:LIPIcs.IPEC.2025.9,
  author =	{Jansen, Bart M. P. and Lamme, Jeroen S. K. and Verhaegh, Ruben F. A.},
  title =	{{An ETH-Tight FPT Algorithm for Rejection-Proof Set Packing with Applications to Kidney Exchange}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.9},
  URN =		{urn:nbn:de:0030-drops-251414},
  doi =		{10.4230/LIPIcs.IPEC.2025.9},
  annote =	{Keywords: Parameterized complexity, Multi-agent kidney exchange, Kernelization, Set packing}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.5
Kernelization for H-Coloring

Authors: Yael Berkman and Ishay Haviv

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

Abstract
For a fixed graph H, the H-Coloring problem asks whether a given graph admits an edge-preserving function from its vertex set to that of H. A seminal theorem of Hell and Nešetřil asserts that the H-Coloring problem is NP-hard whenever H is loopless and non-bipartite. A result of Jansen and Pieterse implies that for every graph H, the H-Coloring problem parameterized by the vertex cover number k admits a kernel with O(k^Δ(H)) vertices and bit-size bounded by O(k^Δ(H)⋅log k), where Δ(H) denotes the maximum degree in H. For the case where H is a complete graph on at least three vertices, this kernel size nearly matches conditional lower bounds established by Jansen and Kratsch and by Jansen and Pieterse. This paper presents new upper and lower bounds on the kernel size of H-Coloring problems parameterized by the vertex cover number. The upper bounds arise from two kernelization algorithms. The first is purely combinatorial, and its size is governed by a structural quantity of the graph H, called the non-adjacency witness number. As applications, we obtain kernels whose size is bounded by a fixed polynomial for natural classes of graphs H with unbounded maximum degree, such as planar graphs and, more broadly, graphs with bounded degeneracy. More strikingly, we show that for almost every graph H, the degree of the polynomial that bounds the size of our combinatorial kernel grows only logarithmically in Δ(H). Our second kernel leverages linear-algebraic tools and involves the notion of faithful independent representations of graphs. It strengthens the general bound from prior work and, among other applications, yields near-optimal kernels for problems concerning the dimension of orthogonal graph representations over finite fields. We complement our kernelization results with conditional lower bounds, thereby nearly settling the kernel complexity of the problem for various target graphs H.
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Yael Berkman and Ishay Haviv. Kernelization for H-Coloring. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berkman_et_al:LIPIcs.IPEC.2025.5,
  author =	{Berkman, Yael and Haviv, Ishay},
  title =	{{Kernelization for H-Coloring}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.5},
  URN =		{urn:nbn:de:0030-drops-251376},
  doi =		{10.4230/LIPIcs.IPEC.2025.5},
  annote =	{Keywords: Kernelization, Graph coloring, Graph homomorphism}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.43
A Finer View of the Parameterized Landscape of Labeled Graph Contractions

Authors: Yashaswini Mathur and Prafullkumar Tale

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We study the Labeled Contractibility problem, where the input consists of two vertex-labeled graphs G and H, and the goal is to determine whether H can be obtained from G via a sequence of edge contractions. Lafond and Marchand [WADS 2025] initiated the parameterized complexity study of this problem, showing it to be W[1]-hard when parameterized by the number k of allowed contractions. They also proved that the problem is fixed-parameter tractable when parameterized by the tree-width tw of G, via an application of Courcelle’s theorem resulting in a non-constructive algorithm. In this work, we present a constructive fixed-parameter algorithm for Labeled Contractibility with running time 2^{𝒪(tw²)} ⋅ |V(G)|^{𝒪(1)}. We also prove that unless the Exponential Time Hypothesis ({ETH}) fails, it does not admit an algorithm running in time 2^{o(tw²)} ⋅ |V(G)|^{𝒪(1)}. This result adds Labeled Contractibility to a small list of problems that admit such a lower bound and matching algorithm. We further strengthen existing hardness results by showing that the problem remains NP-complete even when both input graphs have bounded maximum degree. We also investigate parameterizations by (k + δ(G)) where δ(G) denotes the degeneracy of G, and rule out the existence of subexponential-time algorithms. This answers question raised in Lafond and Marchand [WADS 2025]. We additionally provide an improved FPT algorithm with better dependence on (k + δ(G)) than previously known. Finally, we analyze a brute-force algorithm for Labeled Contractibility with running time |V(H)|^{𝒪(|V(G)|)}, and show that this running time is optimal under {ETH}.
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Yashaswini Mathur and Prafullkumar Tale. A Finer View of the Parameterized Landscape of Labeled Graph Contractions. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 43:1-43:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mathur_et_al:LIPIcs.FSTTCS.2025.43,
  author =	{Mathur, Yashaswini and Tale, Prafullkumar},
  title =	{{A Finer View of the Parameterized Landscape of Labeled Graph Contractions}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{43:1--43:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.43},
  URN =		{urn:nbn:de:0030-drops-251237},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.43},
  annote =	{Keywords: Labeled Contraction, ETH Lower-bound, Treewidth, NP-hard}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.111
Hardness of Median and Center in the Ulam Metric

Authors: Nick Fischer, Elazar Goldenberg, Mursalin Habib, and Karthik C. S.

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The classical rank aggregation problem seeks to combine a set X of n permutations into a single representative "consensus" permutation. In this paper, we investigate two fundamental rank aggregation tasks under the well-studied Ulam metric: computing a median permutation (which minimizes the sum of Ulam distances to X) and computing a center permutation (which minimizes the maximum Ulam distance to X) in two settings. - Continuous Setting: In the continuous setting, the median/center is allowed to be any permutation. It is known that computing a center in the Ulam metric is NP-hard and we add to this by showing that computing a median is NP-hard as well via a simple reduction from the Max-Cut problem. While this result may not be unexpected, it had remained elusive until now and confirms a speculation by Chakraborty, Das, and Krauthgamer [SODA '21]. - Discrete Setting: In the discrete setting, the median/center must be a permutation from the input set. We fully resolve the fine-grained complexity of the discrete median and discrete center problems under the Ulam metric, proving that the naive Õ(n² L)-time algorithm (where L is the length of the permutation) is conditionally optimal. This resolves an open problem raised by Abboud, Bateni, Cohen-Addad, Karthik C. S., and Seddighin [APPROX '23]. Our reductions are inspired by the known fine-grained lower bounds for similarity measures, but we face and overcome several new highly technical challenges.
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Nick Fischer, Elazar Goldenberg, Mursalin Habib, and Karthik C. S.. Hardness of Median and Center in the Ulam Metric. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 111:1-111:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fischer_et_al:LIPIcs.ESA.2025.111,
  author =	{Fischer, Nick and Goldenberg, Elazar and Habib, Mursalin and Karthik C. S.},
  title =	{{Hardness of Median and Center in the Ulam Metric}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{111:1--111:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.111},
  URN =		{urn:nbn:de:0030-drops-245809},
  doi =		{10.4230/LIPIcs.ESA.2025.111},
  annote =	{Keywords: Ulam distance, median, center, rank aggregation, fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.31
Towards Free Lunch Derandomization from Necessary Assumptions (And OWFs)

Authors: Marshall Ball, Lijie Chen, and Roei Tell

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

Abstract
The question of optimal derandomization, introduced by Doron et. al (JACM 2022), garnered significant recent attention. Works in recent years showed conditional superfast derandomization algorithms, as well as conditional impossibility results, and barriers for obtaining superfast derandomization using certain black-box techniques. Of particular interest is the extreme high-end, which focuses on "free lunch" derandomization, as suggested by Chen and Tell (FOCS 2021). This is derandomization that incurs essentially no time overhead, and errs only on inputs that are infeasible to find. Constructing such algorithms is challenging, and so far there have not been any results following the one in their initial work. In their result, their algorithm is essentially the classical Nisan-Wigderson generator, and they relied on an ad-hoc assumption asserting the existence of a function that is non-batch-computable over all polynomial-time samplable distributions. In this work we deduce free lunch derandomization from a variety of natural hardness assumptions. In particular, we do not resort to non-batch-computability, and the common denominator for all of our assumptions is hardness over all polynomial-time samplable distributions, which is necessary for the conclusion. The main technical components in our proofs are constructions of new and superfast targeted generators, which completely eliminate the time overheads that are inherent to all previously known constructions. In particular, we present an alternative construction for the targeted generator by Chen and Tell (FOCS 2021), which is faster than the original construction, and also more natural and technically intuitive. These contributions significantly strengthen the evidence for the possibility of free lunch derandomization, distill the required assumptions for such a result, and provide the first set of dedicated technical tools that are useful for studying the question.
Cite as

Marshall Ball, Lijie Chen, and Roei Tell. Towards Free Lunch Derandomization from Necessary Assumptions (And OWFs). In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ball_et_al:LIPIcs.CCC.2025.31,
  author =	{Ball, Marshall and Chen, Lijie and Tell, Roei},
  title =	{{Towards Free Lunch Derandomization from Necessary Assumptions (And OWFs)}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{31:1--31:20},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-237259},
  doi =		{10.4230/LIPIcs.CCC.2025.31},
  annote =	{Keywords: Pseudorandomness, Derandomization}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.7
Faster Edge Coloring by Partition Sieving

Authors: Shyan Akmal and Tomohiro Koana

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

Abstract
In the Edge Coloring problem, we are given an undirected graph G with n vertices and m edges, and are tasked with finding the smallest positive integer k so that the edges of G can be assigned k colors in such a way that no two edges incident to the same vertex are assigned the same color. Edge Coloring is a classic NP-hard problem, and so significant research has gone into designing fast exponential-time algorithms for solving Edge Coloring and its variants exactly. Prior work showed that Edge Coloring can be solved in 2^mpoly(n) time and polynomial space, and in graphs with average degree d in 2^{(1-ε_d)m}⋅poly(n) time and exponential space, where ε_d = (1/d)^Θ(d³). We present an algorithm that solves Edge Coloring in 2^{m-3n/5}⋅poly(n) time and polynomial space. Our result is the first algorithm for this problem which simultaneously runs in faster than 2^m⋅poly(m) time and uses only polynomial space. In graphs of average degree d, our algorithm runs in 2^{(1-6/(5d))m}⋅poly(n) time, which has far better dependence in d than previous results. We also consider a generalization of Edge Coloring called List Edge Coloring, where each edge e in the input graph comes with a list L_e ⊆ {1, …, k} of colors, and we must determine whether we can assign each edge a color from its list so that no two edges incident to the same vertex receive the same color. We show that this problem can be solved in 2^{(1-6/(5k))m}⋅poly(n) time and polynomial space. The previous best algorithm for List Edge Coloring took 2^m⋅poly(n) time and space. Our algorithms are algebraic, and work by constructing a special polynomial P based off the input graph that contains a multilinear monomial (i.e., a monomial where every variable has degree at most one) if and only if the answer to the List Edge Coloring problem on the input graph is YES. We then solve the problem by detecting multilinear monomials in P. Previous work also employed such monomial detection techniques to solve Edge Coloring. We obtain faster algorithms both by carefully constructing our polynomial P, and by improving the runtimes for certain structured monomial detection problems using a technique we call partition sieving.
Cite as

Shyan Akmal and Tomohiro Koana. Faster Edge Coloring by Partition Sieving. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{akmal_et_al:LIPIcs.STACS.2025.7,
  author =	{Akmal, Shyan and Koana, Tomohiro},
  title =	{{Faster Edge Coloring by Partition Sieving}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.7},
  URN =		{urn:nbn:de:0030-drops-228328},
  doi =		{10.4230/LIPIcs.STACS.2025.7},
  annote =	{Keywords: Coloring, Edge coloring, Chromatic index, Matroid, Pfaffian, Algebraic algorithm}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.26
Toward Better Depth Lower Bounds: Strong Composition of XOR and a Random Function

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

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

Abstract
Proving formula depth lower bounds is a fundamental challenge in complexity theory, with the strongest known bound of (3 - o(1))log n established by Håstad over 25 years ago. The Karchmer-Raz-Wigderson (KRW) conjecture offers a promising approach to advance these bounds and separate P from NC¹. It suggests that the depth complexity of a function composition f ⋄ g approximates the sum of the depth complexities of f and g. The Karchmer-Wigderson (KW) relation framework translates formula depth into communication complexity, restating the KRW conjecture as CC(KW_f ⋄ KW_g) ≈ CC(KW_f) + CC(KW_g). Prior work has confirmed the conjecture under various relaxations, often replacing one or both KW relations with the universal relation or constraining the communication game through strong composition. In this paper, we examine the strong composition KW_XOR ⊛ KW_f of the parity function and a random Boolean function f. We prove that with probability 1-o(1), any protocol solving this composition requires at least n^{3 - o(1)} leaves. This result establishes a depth lower bound of (3 - o(1))log n, matching Håstad’s bound, but is applicable to a broader class of inner functions, even when the outer function is simple. Though bounds for the strong composition do not translate directly to formula depth bounds, they usually help to analyze the standard composition (of the corresponding two functions) which is directly related to formula depth. Our proof utilizes formal complexity measures. First, we apply Khrapchenko’s method to show that numerous instances of f remain unsolved after several communication steps. Subsequently, we transition to a different formal complexity measure to demonstrate that the remaining communication problem is at least as hard as KW_OR ⊛ KW_f. This hybrid approach not only achieves the desired lower bound, but also introduces a novel technique for analyzing formula depth, potentially informing future research in complexity theory.
Cite as

Nikolai Chukhin, Alexander S. Kulikov, and Ivan Mihajlin. Toward Better Depth Lower Bounds: Strong Composition of XOR and a Random Function. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chukhin_et_al:LIPIcs.STACS.2025.26,
  author =	{Chukhin, Nikolai and Kulikov, Alexander S. and Mihajlin, Ivan},
  title =	{{Toward Better Depth Lower Bounds: Strong Composition of XOR and a Random Function}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.26},
  URN =		{urn:nbn:de:0030-drops-228513},
  doi =		{10.4230/LIPIcs.STACS.2025.26},
  annote =	{Keywords: complexity, formula complexity, lower bounds, Boolean functions, depth}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.21
Improved Space Bounds for Subset Sum

Authors: Tatiana Belova, Nikolai Chukhin, Alexander S. Kulikov, and Ivan Mihajlin

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
More than 40 years ago, Schroeppel and Shamir presented an algorithm that solves the Subset Sum problem for n integers in time O^*(2^{0.5n}) and space O^*(2^{0.25n}). The time upper bound remains unbeaten, but the space upper bound has been improved to O^*(2^{0.249999n}) in a recent breakthrough paper by Nederlof and Węgrzycki (STOC 2021). Their algorithm is a clever combination of a number of previously known techniques with a new reduction and a new algorithm for the Orthogonal Vectors problem. In this paper, we give two new algorithms for Subset Sum. We start by presenting an Arthur-Merlin algorithm: upon receiving the verifier’s randomness, the prover sends an n/4-bit long proof to the verifier who checks it in (deterministic) time and space O^*(2^{n/4}). An interesting consequence of this result is the following fine-grained lower bound: assuming that 4-SUM cannot be solved in time O(n^{2-ε}) for all ε > 0, Circuit SAT cannot be solved in time O(g2^{(1-ε)n}), for all ε > 0 (where n and g denote the number of inputs and the number of gates, respectively). Then, we improve the space bound by Nederlof and Węgrzycki to O^*(2^{0.246n}) and also simplify their algorithm and its analysis. We achieve this space bound by further filtering sets of subsets using a random prime number. This allows us to reduce an instance of Subset Sum to a larger number of instances of smaller size.
Cite as

Tatiana Belova, Nikolai Chukhin, Alexander S. Kulikov, and Ivan Mihajlin. Improved Space Bounds for Subset Sum. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{belova_et_al:LIPIcs.ESA.2024.21,
  author =	{Belova, Tatiana and Chukhin, Nikolai and Kulikov, Alexander S. and Mihajlin, Ivan},
  title =	{{Improved Space Bounds for Subset Sum}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.21},
  URN =		{urn:nbn:de:0030-drops-210925},
  doi =		{10.4230/LIPIcs.ESA.2024.21},
  annote =	{Keywords: algorithms, subset sum, complexity, space, upper bounds}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.66
Super-Cubic Lower Bound for Generalized Karchmer-Wigderson Games

Authors: Artur Ignatiev, Ivan Mihajlin, and Alexander Smal

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
In this paper, we prove a super-cubic lower bound on the size of a communication protocol for generalized Karchmer-Wigderson game for an explicit function f: {0,1}ⁿ → {0,1}^{log n}. Lower bounds for original Karchmer-Wigderson games correspond to De Morgan formula lower bounds, thus the best known size lower bound is cubic. The generalized Karchmer-Wigderson games are similar to the original ones, so we hope that our approach can provide an insight for proving better lower bounds on the original Karchmer-Wigderson games, and hence for proving new lower bounds on De Morgan formula size. To achieve super-cubic lower bound we adapt several techniques used in formula complexity to communication protocols, prove communication complexity lower bound for a composition of several functions with a multiplexer relation, and use a technique from [Ivan Mihajlin and Alexander Smal, 2021] to extract the "hardest" function from it. As a result, in this setting we are able to show that there is a relatively small set of functions such that at least one of them does not have a small protocol. The resulting lower bound of Ω̃(n^3.156) is significantly better than the bound obtained from the counting argument.
Cite as

Artur Ignatiev, Ivan Mihajlin, and Alexander Smal. Super-Cubic Lower Bound for Generalized Karchmer-Wigderson Games. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 66:1-66:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ignatiev_et_al:LIPIcs.ISAAC.2022.66,
  author =	{Ignatiev, Artur and Mihajlin, Ivan and Smal, Alexander},
  title =	{{Super-Cubic Lower Bound for Generalized Karchmer-Wigderson Games}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{66:1--66:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.66},
  URN =		{urn:nbn:de:0030-drops-173510},
  doi =		{10.4230/LIPIcs.ISAAC.2022.66},
  annote =	{Keywords: communication complexity, circuit complexity, Karchmer-Wigderson games}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.47
CNF Encodings of Parity

Authors: Gregory Emdin, Alexander S. Kulikov, Ivan Mihajlin, and Nikita Slezkin

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

Abstract
The minimum number of clauses in a CNF representation of the parity function x₁ ⊕ x₂ ⊕ … ⊕ x_n is 2^{n-1}. One can obtain a more compact CNF encoding by using non-deterministic variables (also known as guess or auxiliary variables). In this paper, we prove the following lower bounds, that almost match known upper bounds, on the number m of clauses and the maximum width k of clauses: 1) if there are at most s auxiliary variables, then m ≥ Ω(2^{n/(s+1)}/n) and k ≥ n/(s+1); 2) the minimum number of clauses is at least 3n. We derive the first two bounds from the Satisfiability Coding Lemma due to Paturi, Pudlák, and Zane using a tight connection between CNF encodings and depth-3 circuits. In particular, we show that lower bounds on the size of a CNF encoding of a Boolean function imply depth-3 circuit lower bounds for this function.
Cite as

Gregory Emdin, Alexander S. Kulikov, Ivan Mihajlin, and Nikita Slezkin. CNF Encodings of Parity. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 47:1-47:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{emdin_et_al:LIPIcs.MFCS.2022.47,
  author =	{Emdin, Gregory and Kulikov, Alexander S. and Mihajlin, Ivan and Slezkin, Nikita},
  title =	{{CNF Encodings of Parity}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{47:1--47:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.47},
  URN =		{urn:nbn:de:0030-drops-168455},
  doi =		{10.4230/LIPIcs.MFCS.2022.47},
  annote =	{Keywords: encoding, parity, lower bounds, circuits, CNF}
}
Document
DOI: 10.4230/LIPIcs.CCC.2022.13
A Better-Than-3log(n) Depth Lower Bound for De Morgan Formulas with Restrictions on Top Gates

Authors: Ivan Mihajlin and Anastasia Sofronova

Published in: LIPIcs, Volume 234, 37th Computational Complexity Conference (CCC 2022)

Abstract
We prove that a modification of Andreev’s function is not computable by (3 + α - ε) log(n) depth De Morgan formula with (2α - ε)log{n} layers of AND gates at the top for any 0 < α < 1/5 and any constant ε > 0. In order to do this, we prove a weak variant of Karchmer-Raz-Wigderson conjecture. To be more precise, we prove the existence of two functions f : {0,1}ⁿ → {0,1} and g : {0,1}ⁿ → {0,1}ⁿ such that f(g(x) ⊕ y) is not computable by depth (1 + α - ε) n formulas with (2 α - ε) n layers of AND gates at the top. We do this by a top-down approach, which was only used before for depth-3 model. Our technical contribution includes combinatorial insights into structure of composition with random boolean function, which led us to introducing a notion of well-mixed sets. A set of functions is well-mixed if, when composed with a random function, it does not have subsets that agree on large fractions of inputs. We use probabilistic method to prove the existence of well-mixed sets.
Cite as

Ivan Mihajlin and Anastasia Sofronova. A Better-Than-3log(n) Depth Lower Bound for De Morgan Formulas with Restrictions on Top Gates. In 37th Computational Complexity Conference (CCC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 234, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mihajlin_et_al:LIPIcs.CCC.2022.13,
  author =	{Mihajlin, Ivan and Sofronova, Anastasia},
  title =	{{A Better-Than-3log(n) Depth Lower Bound for De Morgan Formulas with Restrictions on Top Gates}},
  booktitle =	{37th Computational Complexity Conference (CCC 2022)},
  pages =	{13:1--13:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-241-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{234},
  editor =	{Lovett, Shachar},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2022.13},
  URN =		{urn:nbn:de:0030-drops-165755},
  doi =		{10.4230/LIPIcs.CCC.2022.13},
  annote =	{Keywords: formula complexity, communication complexity, Karchmer-Raz-Wigderson conjecture, De Morgan formulas}
}
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