15 Search Results for "Frankl, Peter"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.25
The Typical Algebraic Shifting of Graphs and Surfaces

Authors: Denys Bulavka, Eran Nevo, and Yuval Peled

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

Abstract
We initiate a statistical study of Kalai’s exterior algebraic shifting, focusing on concentration phenomena for random triangulations of a fixed space. First, for a uniform n-vertex refinement of any given graph G, we show that asymptotically almost-surely (a.a.s.) its exterior algebraic shifting is an explicit shifted graph depending only on n and the Betti numbers of G. Next, for any given compact connected Riemannian surface S, sample n points independently at random according to the volume measure, and consider the resulted a.a.s. unique Delaunay triangulation. We prove that a.a.s. its exterior algebraic shifting is an explicit shifted complex depending only on n and the Euler genus of S, and in particular is area-rigid. In both results the expected shifted complex is a homology lex-segment complex, a notion we define combinatorially and characterize numerically à la Björner-Kalai. As a tool to prove the result on surfaces, we prove a universality result on edge contractions: for every fixed surface triangulation K, every dense enough point set in the surface yields a Delaunay triangulation that edge contracts to K.
Cite as

Denys Bulavka, Eran Nevo, and Yuval Peled. The Typical Algebraic Shifting of Graphs and Surfaces. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bulavka_et_al:LIPIcs.SoCG.2026.25,
  author =	{Bulavka, Denys and Nevo, Eran and Peled, Yuval},
  title =	{{The Typical Algebraic Shifting of Graphs and Surfaces}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{25:1--25:15},
  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.2026.25},
  URN =		{urn:nbn:de:0030-drops-258312},
  doi =		{10.4230/LIPIcs.SoCG.2026.25},
  annote =	{Keywords: Algebraic shifting, Delaunay triangulation, surfaces, random triangulation, area rigidity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.112
Lower Bounds Beyond DNF of Parities

Authors: Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov

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

Abstract
We consider a subclass of AC⁰[2] circuits that simultaneously captures DNF∘Xor and depth-3 AC⁰ circuits. For this class we show a technique for proving lower bounds inspired by the top-down approach. We give lower bounds for the middle slice function, inner product function, and affine dispersers.
Cite as

Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov. Lower Bounds Beyond DNF of Parities. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{riazanov_et_al:LIPIcs.ITCS.2026.112,
  author =	{Riazanov, Artur and Sofronova, Anastasia and Sokolov, Dmitry},
  title =	{{Lower Bounds Beyond DNF of Parities}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{112:1--112:15},
  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.2026.112},
  URN =		{urn:nbn:de:0030-drops-253996},
  doi =		{10.4230/LIPIcs.ITCS.2026.112},
  annote =	{Keywords: boolean circuits, top-down, unpredictability}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.67
Query Lower Bounds for Correlation Clustering Under Memory Constraints

Authors: Sumegha Garg, Songhua He, and Periklis A. Papakonstantinou

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

Abstract
This work initiates the study of memory–query tradeoffs for graph problems, with a focus on correlation clustering. Correlation clustering asks for a partition of the vertices that minimizes disagreements: non‑edges inside clusters plus edges across clusters. Our first result is a tight query lower bound: to output a partition whose cost approximates the optimum up to an additive error of ε n², any algorithm requires Ω(n/ε²) adjacency-matrix queries. Under memory constraints, we show that even for the seemingly easier task of approximating the optimal clustering cost (without producing a partition), any algorithm in the random query model must make ≫ n/ε² adjacency-matrix queries. Finally, we prove the first general graph model query lower bound for correlation clustering, where algorithms are allowed adjacency-matrix, neighbor, and degree queries. The latter two bounds are not yet tight, leaving room for sharper results.
Cite as

Sumegha Garg, Songhua He, and Periklis A. Papakonstantinou. Query Lower Bounds for Correlation Clustering Under Memory Constraints. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 67:1-67:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{garg_et_al:LIPIcs.ITCS.2026.67,
  author =	{Garg, Sumegha and He, Songhua and Papakonstantinou, Periklis A.},
  title =	{{Query Lower Bounds for Correlation Clustering Under Memory Constraints}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{67:1--67:24},
  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.2026.67},
  URN =		{urn:nbn:de:0030-drops-253542},
  doi =		{10.4230/LIPIcs.ITCS.2026.67},
  annote =	{Keywords: correlation clustering, query-space complexity, information theory}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.110
Optimal Two-Round Communication Lower Bound for Graph Connectivity via Pointer Chasing

Authors: Jaikumar Radhakrishnan, Chaitanya Reddy, and Rakesh Venkat

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

Abstract
We consider the communication complexity of the graph connectivity problem, where the edges of an n-vertex undirected graph G are distributed between two parties Alice and Bob, who are then required to communicate to determine if G is connected. We show that in any randomized protocol with two-rounds of communication, Alice and Bob must exchange Ω(nlog n) bits; such a lower bound for one-round protocols was shown by Sun and Woodruff (APPROX/RANDOM 2015). A one-round deterministic protocol, where Alice sends O(n log n) bits and Bob determines the answer, was observed by Hajnal, Maass and Turan (STOC 1988); they also showed a matching lower bound of Ω(n log n) bits for deterministic protocols with unbounded rounds of communication. For randomized protocols, a reduction from the set disjointness problem due to Babai, Frankl and Simon (FOCS 1986) implies a randomized lower bound of Ω(n) even with unbounded rounds of communication. Whether this lower bound can be improved to Ω(n log n) has been an outstanding open question, whose algorithmic implications were recently emphasized by Apers, Efron, Gawrychowski, Lee, Mukopadhyay and Nanongkai (FOCS 2022). Our lower bound for randomized two-round protocols is based on a reduction from a restricted version of the two-player pointer chasing problem originally studied by Papadimitriou and Sipser (JCSS 1984). Using this reduction, we show an ω(n) lower bounds on graph connectivity for any constant number of rounds by extending deterministic lower bounds shown by Ponzio, Radhakrishnan and Venkatesh (JCSS 2001) to the randomized setting.
Cite as

Jaikumar Radhakrishnan, Chaitanya Reddy, and Rakesh Venkat. Optimal Two-Round Communication Lower Bound for Graph Connectivity via Pointer Chasing. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 110:1-110:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{radhakrishnan_et_al:LIPIcs.ITCS.2026.110,
  author =	{Radhakrishnan, Jaikumar and Reddy, Chaitanya and Venkat, Rakesh},
  title =	{{Optimal Two-Round Communication Lower Bound for Graph Connectivity via Pointer Chasing}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{110:1--110:20},
  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.2026.110},
  URN =		{urn:nbn:de:0030-drops-253974},
  doi =		{10.4230/LIPIcs.ITCS.2026.110},
  annote =	{Keywords: Communication complexity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.39
Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules

Authors: Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou

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

Abstract
In reconfiguration problems, we are given two feasible solutions to a graph problem and asked whether one can be transformed into the other via a sequence of feasible intermediate solutions under a given reconfiguration rule. While earlier work focused on modifying a single element at a time, recent studies have started examining how different rules impact computational complexity. Motivated by recent progress, we study Independent Set Reconfiguration (ISR) and Vertex Cover Reconfiguration (VCR) under the k-Token Jumping (k-TJ) and k-Token Sliding (k-TS) models. In k-TJ, up to k vertices may be replaced, while k-TS additionally requires a perfect matching between removed and added vertices. It is known that the complexity of ISR crucially depends on k, ranging from PSPACE-complete and NP-complete to polynomial-time solvable. In this paper, we further explore the gradient of computational complexity of the problems. We first show that ISR under k-TJ with k = |I| - μ remains NP-hard when μ is any fixed positive integer and the input graph is restricted to graphs of maximum degree 3 or planar graphs of maximum degree 4, where |I| is the size of feasible solutions. In addition, we prove that the problem belongs to NP not only for μ = O(1) but also for μ = O(log |I|). In contrast, we show that VCR under k-TJ is in XP when parameterized by μ = |S| - k, where |S| is the size of feasible solutions. Furthermore, we establish the PSPACE-completeness of ISR and VCR under both k-TJ and k-TS on several graph classes, for fixed k as well as superconstant k relative to the size of feasible solutions.
Cite as

Shuichi Hirahara, Naoto Ohsaka, Tatsuhiro Suga, Akira Suzuki, Yuma Tamura, and Xiao Zhou. Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hirahara_et_al:LIPIcs.ISAAC.2025.39,
  author =	{Hirahara, Shuichi and Ohsaka, Naoto and Suga, Tatsuhiro and Suzuki, Akira and Tamura, Yuma and Zhou, Xiao},
  title =	{{Reachability of Independent Sets and Vertex Covers Under Extended Reconfiguration Rules}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{39:1--39:20},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-249474},
  doi =		{10.4230/LIPIcs.ISAAC.2025.39},
  annote =	{Keywords: combinatorial reconfiguration, extended reconfiguration rule, independent set reconfiguration, vertex cover reconfiguration, PSPACE-completeness, NP-completeness}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.34
Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice

Authors: Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro

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

Abstract
Radio Networks (RN) is one of the fundamental models for network communication where nodes can broadcast messages locally but their simultaneous transmissions can interfere with each other at their shared neighbors. This work focuses on performing the very fundamental primitive of Local Broadcast, in spite of the interferences. We investigate to what extent local knowledge, called advice, relating to the 2-local domination number γ₂ may speed up Local Broadcast. Specifically for each node and some dominating set, knowledge about some neighboring dominating node and the local number among the neighbors of that dominating node. We show that such advice is sufficient to build an efficient oblivious transmission schedule. Along those lines, we present three algorithms trading the level of adaptiveness (from oblivious to adaptive) for bits of advice per node (from O(log (Δγ₂)) to 1). All our algorithms complete Local Broadcast in Õ(Δγ₂²) rounds, where Δ is the maximum degree of the network. On the side of lower bounds, we show that, for each quasi-adaptive deterministic Local Broadcast algorithm, there is some RN that requires Ω(min{(min{Δ,γ₂}/log n)²,n}) communication rounds, where n is the number of network nodes. In quasi-adaptive protocols nodes may stop executing once its computational task is completed. To the best of our knowledge, this is the first (nearly) quadratic Local Broadcast (same message for all neighbors) lower bound in the RN model. Our lower bound is stronger than previous works in multiple ways: i) it is nearly quadratically better than the best known general lower bound for this class of algorithms, ii) it applies to a wider class of algorithms than previous work for fully oblivious, iii) it achieves similar time lower bound than previous work proved for a much more demanding Local Broadcast where each node sends a possibly different message to each neighbor, and iv) it takes into account the local domination parameter γ₂.
Cite as

Pawel Garncarek, Tomasz Jurdzinski, Dariusz R. Kowalski, Shay Kutten, and Miguel A. Mosteiro. Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 34:1-34:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garncarek_et_al:LIPIcs.ISAAC.2025.34,
  author =	{Garncarek, Pawel and Jurdzinski, Tomasz and Kowalski, Dariusz R. and Kutten, Shay and Mosteiro, Miguel A.},
  title =	{{Deterministic Local Problems in Radio Networks: On the Impact of Local Domination and a Bit of Advice}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{34:1--34:20},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-249426},
  doi =		{10.4230/LIPIcs.ISAAC.2025.34},
  annote =	{Keywords: Radio Networks, Local Broadcast, Distributed Deterministic Algorithms, Lower Bounds, Graph algorithms, Advice, Labeling Schemes, Local Domination}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.44
Density Frankl–Rödl on the Sphere

Authors: Venkatesan Guruswami and Shilun Li

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

Abstract
We establish a density variant of the Frankl–Rödl theorem on the sphere 𝕊^{n-1}, which concerns avoiding pairs of vectors with a specific distance, or equivalently, a prescribed inner product. In particular, we establish lower bounds on the probability that a randomly chosen pair of such vectors lies entirely within a measurable subset A ⊆ 𝕊^{n-1} of sufficiently large measure. Additionally, we prove a density version of spherical avoidance problems, which generalize from pairwise avoidance to broader configurations with prescribed pairwise inner products. Our framework encompasses a class of configurations we call inductive configurations, which include simplices with any prescribed inner product -1 < r < 1. As a consequence of our density statement, we show that all inductive configurations are sphere Ramsey.
Cite as

Venkatesan Guruswami and Shilun Li. Density Frankl–Rödl on the Sphere. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 44:1-44:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{guruswami_et_al:LIPIcs.APPROX/RANDOM.2025.44,
  author =	{Guruswami, Venkatesan and Li, Shilun},
  title =	{{Density Frankl–R\"{o}dl on the Sphere}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{44:1--44:18},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-244108},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.44},
  annote =	{Keywords: Frankl–R\"{o}dl, Sphere Ramsey, Sphere Avoidance, Reverse Hypercontractivity, Forbidden Angles}
}
Document
DOI: 10.4230/LIPIcs.SAT.2025.9
CNFs and DNFs with Exactly k Solutions

Authors: L. Sunil Chandran, Rishikesh Gajjala, and Kuldeep S. Meel

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
Model counting is a fundamental problem that consists of determining the number of satisfying assignments for a given Boolean formula. The weighted variant, which computes the weighted sum of satisfying assignments, has extensive applications in probabilistic reasoning, network reliability, statistical physics, and formal verification. A common approach for solving weighted model counting is to reduce it to unweighted model counting, which raises an important question: What is the minimum number of terms (or clauses) required to construct a DNF (or CNF) formula with exactly k satisfying assignments? In this paper, we establish both upper and lower bounds on this question. We prove that for any natural number k, one can construct a monotone DNF formula with exactly k satisfying assignments using at most O(√{log k}log log k) terms. This construction represents the first o(log k) upper bound for this problem. We complement this result by showing that there exist infinitely many values of k for which any DNF or CNF representation requires at least Ω(log log k) terms or clauses. These results have significant implications for the efficiency of model counting algorithms based on formula transformations.
Cite as

L. Sunil Chandran, Rishikesh Gajjala, and Kuldeep S. Meel. CNFs and DNFs with Exactly k Solutions. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chandran_et_al:LIPIcs.SAT.2025.9,
  author =	{Chandran, L. Sunil and Gajjala, Rishikesh and Meel, Kuldeep S.},
  title =	{{CNFs and DNFs with Exactly k Solutions}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.9},
  URN =		{urn:nbn:de:0030-drops-237433},
  doi =		{10.4230/LIPIcs.SAT.2025.9},
  annote =	{Keywords: Model counting, #SAT, Set Systems, Combinatorics}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.33
A Min-Entropy Approach to Multi-Party Communication Lower Bounds

Authors: Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang

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

Abstract
Information complexity is one of the most powerful techniques to prove information-theoretical lower bounds, in which Shannon entropy plays a central role. Though Shannon entropy has some convenient properties, such as the chain rule, it still has inherent limitations. One of the most notable barriers is the square-root loss, which appears in the square-root gap between entropy gaps and statistical distances, e.g., Pinsker’s inequality. To bypass this barrier, we introduce a new method based on min-entropy analysis. Building on this new method, we prove the following results. - An Ω(N^{∑_i α_i - max_i {α_i}}/k) randomized communication lower bound of the k-party set-intersection problem where the i-th party holds a random set of size ≈ N^{1-α_i}. - A tight Ω(n/k) randomized lower bound of the k-party Tree Pointer Jumping problems, improving an Ω(n/k²) lower bound by Chakrabarti, Cormode, and McGregor (STOC 08). - An Ω(n/k+√n) lower bound of the Chained Index problem, improving an Ω(n/k²) lower bound by Cormode, Dark, and Konrad (ICALP 19). Since these problems served as hard problems for numerous applications in streaming lower bounds and cryptography, our new lower bounds directly improve these streaming lower bounds and cryptography lower bounds. On the technical side, min-entropy does not have nice properties such as the chain rule. To address this issue, we enhance the structure-vs-pseudorandomness decomposition used by Göös, Pitassi, and Watson (FOCS 17) and Yang and Zhang (STOC 24); both papers used this decomposition to prove communication lower bounds. In this paper, we give a new breath to this method in the multi-party setting, presenting a new toolkit for proving multi-party communication lower bounds.
Cite as

Mi-Ying (Miryam) Huang, Xinyu Mao, Shuo Wang, Guangxu Yang, and Jiapeng Zhang. A Min-Entropy Approach to Multi-Party Communication Lower Bounds. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 33:1-33:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huang_et_al:LIPIcs.CCC.2025.33,
  author =	{Huang, Mi-Ying (Miryam) and Mao, Xinyu and Wang, Shuo and Yang, Guangxu and Zhang, Jiapeng},
  title =	{{A Min-Entropy Approach to Multi-Party Communication Lower Bounds}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{33:1--33:29},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-237273},
  doi =		{10.4230/LIPIcs.CCC.2025.33},
  annote =	{Keywords: communication complexity, lifting theorems, set intersection, chained index}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.16
Direct Sums for Parity Decision Trees

Authors: Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, and Weiqiang Yuan

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

Abstract
Direct sum theorems state that the cost of solving k instances of a problem is at least Ω(k) times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a direct sum theorem holds whenever (1) the lower bound for parity decision trees is proved using the discrepancy method; or (2) the lower bound is proved relative to a product distribution.
Cite as

Tyler Besselman, Mika Göös, Siyao Guo, Gilbert Maystre, and Weiqiang Yuan. Direct Sums for Parity Decision Trees. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 16:1-16:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{besselman_et_al:LIPIcs.CCC.2025.16,
  author =	{Besselman, Tyler and G\"{o}\"{o}s, Mika and Guo, Siyao and Maystre, Gilbert and Yuan, Weiqiang},
  title =	{{Direct Sums for Parity Decision Trees}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{16:1--16:38},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-237105},
  doi =		{10.4230/LIPIcs.CCC.2025.16},
  annote =	{Keywords: direct sum, parity decision trees, query complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.42
Local Enumeration: The Not-All-Equal Case

Authors: Mohit Gurumukhani, Ramamohan Paturi, Michael Saks, and Navid Talebanfard

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

Abstract
Gurumukhani et al. (CCC'24) proposed the local enumeration problem Enum(k, t) as an approach to break the Super Strong Exponential Time Hypothesis (SSETH): for a natural number k and a parameter t, given an n-variate k-CNF with no satisfying assignment of Hamming weight less than t(n), enumerate all satisfying assignments of Hamming weight exactly t(n). Furthermore, they gave a randomized algorithm for Enum(k, t) and employed new ideas to analyze the first non-trivial case, namely k = 3. In particular, they solved Enum(3, n/2) in expected 1.598ⁿ time. A simple construction shows a lower bound of 6^{n/4} ≈ 1.565ⁿ. In this paper, we show that to break SSETH, it is sufficient to consider a simpler local enumeration problem NAE-Enum(k, t): for a natural number k and a parameter t, given an n-variate k-CNF with no satisfying assignment of Hamming weight less than t(n), enumerate all Not-All-Equal (NAE) solutions of Hamming weight exactly t(n), i.e., those that satisfy and falsify some literal in every clause. We refine the algorithm of Gurumukhani et al. and show that it optimally solves NAE-Enum(3, n/2), namely, in expected time poly(n) ⋅ 6^{n/4}.
Cite as

Mohit Gurumukhani, Ramamohan Paturi, Michael Saks, and Navid Talebanfard. Local Enumeration: The Not-All-Equal Case. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 42:1-42:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gurumukhani_et_al:LIPIcs.STACS.2025.42,
  author =	{Gurumukhani, Mohit and Paturi, Ramamohan and Saks, Michael and Talebanfard, Navid},
  title =	{{Local Enumeration: The Not-All-Equal Case}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{42:1--42:19},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-228680},
  doi =		{10.4230/LIPIcs.STACS.2025.42},
  annote =	{Keywords: Depth 3 circuits, k-CNF satisfiability, Circuit lower bounds, Majority function}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.2
Improved Lower Bounds for 3-Query Matching Vector Codes

Authors: Divesh Aggarwal, Pranjal Dutta, Zeyong Li, Maciej Obremski, and Sidhant Saraogi

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

Abstract
A Matching Vector (MV) family modulo a positive integer m ≥ 2 is a pair of ordered lists U = (u_1, ⋯, u_K) and V = (v_1, ⋯, v_K) where u_i, v_j ∈ ℤ_m^n with the following property: for any i ∈ [K], the inner product ⟨u_i, v_i⟩ = 0 mod m, and for any i ≠ j, ⟨u_i, v_j⟩ ≠ 0 mod m. An MV family is called r-restricted if inner products ⟨u_i, v_j⟩, for all i,j, take at most r different values. The r-restricted MV families are extremely important since the only known construction of constant-query subexponential locally decodable codes (LDCs) are based on them. Such LDCs constructed via matching vector families are called matching vector codes. Let MV(m,n) (respectively MV(m, n, r)) denote the largest K such that there exists an MV family (respectively r-restricted MV family) of size K in ℤ_m^n. Such a MV family can be transformed in a black-box manner to a good r-query locally decodable code taking messages of length K to codewords of length N = m^n. For small prime m, an almost tight bound MV(m,n) ≤ O(m^{n/2}) was first shown by Dvir, Gopalan, Yekhanin (FOCS'10, SICOMP'11), while for general m, the same paper established an upper bound of O(m^{n-1+o_m(1)}), with o_m(1) denoting a function that goes to zero when m grows. For any arbitrary constant r ≥ 3 and composite m, the best upper bound till date on MV(m,n,r) is O(m^{n/2}), is due to Bhowmick, Dvir and Lovett (STOC'13, SICOMP'14).In a breakthrough work, Alrabiah, Guruswami, Kothari and Manohar (STOC'23) implicitly improve this bound for 3-restricted families to MV(m, n, 3) ≤ O(m^{n/3}). In this work, we present an upper bound for r = 3 where MV(m,n,3) ≤ m^{n/6 +O(log n)}, and as a result, any 3-query matching vector code must have codeword length of N ≥ K^{6-o(1)}.
Cite as

Divesh Aggarwal, Pranjal Dutta, Zeyong Li, Maciej Obremski, and Sidhant Saraogi. Improved Lower Bounds for 3-Query Matching Vector Codes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 2:1-2:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aggarwal_et_al:LIPIcs.ITCS.2025.2,
  author =	{Aggarwal, Divesh and Dutta, Pranjal and Li, Zeyong and Obremski, Maciej and Saraogi, Sidhant},
  title =	{{Improved Lower Bounds for 3-Query Matching Vector Codes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{2:1--2:19},
  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.2025.2},
  URN =		{urn:nbn:de:0030-drops-226308},
  doi =		{10.4230/LIPIcs.ITCS.2025.2},
  annote =	{Keywords: Locally Decodable Codes, Matching Vector Families}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.11
Rank Lower Bounds on Non-Local Quantum Computation

Authors: Vahid R. Asadi, Eric Culf, and Alex May

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

Abstract
A non-local quantum computation (NLQC) replaces an interaction between two quantum systems with a single simultaneous round of communication and shared entanglement. We study two classes of NLQC, f-routing and f-BB84, which are of relevance to classical information theoretic cryptography and quantum position-verification. We give the first non-trivial lower bounds on entanglement in both settings, but are restricted to lower bounding protocols with perfect correctness. Within this setting, we give a lower bound on the Schmidt rank of any entangled state that completes these tasks for a given function f(x,y) in terms of the rank of a matrix g(x,y) whose entries are zero when f(x,y) = 0, and strictly positive otherwise. This also leads to a lower bound on the Schmidt rank in terms of the non-deterministic quantum communication complexity of f(x,y). Because of a relationship between f-routing and the conditional disclosure of secrets (CDS) primitive studied in information theoretic cryptography, we obtain a new technique for lower bounding the randomness complexity of CDS.
Cite as

Vahid R. Asadi, Eric Culf, and Alex May. Rank Lower Bounds on Non-Local Quantum Computation. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{asadi_et_al:LIPIcs.ITCS.2025.11,
  author =	{Asadi, Vahid R. and Culf, Eric and May, Alex},
  title =	{{Rank Lower Bounds on Non-Local Quantum Computation}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{11:1--11:18},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-226399},
  doi =		{10.4230/LIPIcs.ITCS.2025.11},
  annote =	{Keywords: Non-local quantum computation, quantum position-verification, conditional disclosure of secrets}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.49
One-Way Communication Complexity and Non-Adaptive Decision Trees

Authors: Nikhil S. Mande, Swagato Sanyal, and Suhail Sherif

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the Inner Product on a constant number of inputs. More generally, we show the following when the gadget is Inner Product on 2b input bits for all b ≥ 2, denoted IP. - If f is a total Boolean function that depends on all of its n input bits, then the bounded-error one-way quantum communication complexity of f∘IP equals Ω(n(b-1)). - If f is a partial Boolean function, then the deterministic one-way communication complexity of f∘IP is at least Ω(b ⋅ 𝖣_{dt}^ → (f)), where 𝖣_{dt}^ → (f) denotes non-adaptive decision tree complexity of f. To prove our quantum lower bound, we first show a lower bound on the VC-dimension of f∘IP. We then appeal to a result of Klauck [STOC'00], which immediately yields our quantum lower bound. Our deterministic lower bound relies on a combinatorial result independently proven by Ahlswede and Khachatrian [Adv. Appl. Math.'98], and Frankl and Tokushige [Comb.'99]. It is known due to a result of Montanaro and Osborne [arXiv'09] that the deterministic one-way communication complexity of f∘XOR equals the non-adaptive parity decision tree complexity of f. In contrast, we show the following when the inner gadget is the AND function on 2 input bits. - There exists a function for which even the quantum non-adaptive AND decision tree complexity of f is exponentially large in the deterministic one-way communication complexity of f∘AND. - However, for symmetric functions f, the non-adaptive AND decision tree complexity of f is at most quadratic in the (even two-way) communication complexity of f∘AND. In view of the first bullet, a lower bound on non-adaptive AND decision tree complexity of f does not lift to a lower bound on one-way communication complexity of f∘AND. The proof of the first bullet above uses the well-studied Odd-Max-Bit function. For the second bullet, we first observe a connection between the one-way communication complexity of f and the Möbius sparsity of f, and then give a lower bound on the Möbius sparsity of symmetric functions. An upper bound on the non-adaptive AND decision tree complexity of symmetric functions follows implicitly from prior work on combinatorial group testing; for the sake of completeness, we include a proof of this result. It is well known that the rank of the communication matrix of a function F is an upper bound on its deterministic one-way communication complexity. This bound is known to be tight for some F. However, in our final result we show that this is not the case when F = f∘AND. More precisely we show that for all f, the deterministic one-way communication complexity of F = f∘AND is at most (rank(M_{F}))(1 - Ω(1)), where M_{F} denotes the communication matrix of F.
Cite as

Nikhil S. Mande, Swagato Sanyal, and Suhail Sherif. One-Way Communication Complexity and Non-Adaptive Decision Trees. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 49:1-49:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{mande_et_al:LIPIcs.STACS.2022.49,
  author =	{Mande, Nikhil S. and Sanyal, Swagato and Sherif, Suhail},
  title =	{{One-Way Communication Complexity and Non-Adaptive Decision Trees}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{49:1--49:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.49},
  URN =		{urn:nbn:de:0030-drops-158598},
  doi =		{10.4230/LIPIcs.STACS.2022.49},
  annote =	{Keywords: Decision trees, communication complexity, composed Boolean functions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.72
A Variant of the VC-Dimension with Applications to Depth-3 Circuits

Authors: Peter Frankl, Svyatoslav Gryaznov, and Navid Talebanfard

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

Abstract
We introduce the following variant of the VC-dimension. Given S ⊆ {0,1}ⁿ and a positive integer d, we define 𝕌_d(S) to be the size of the largest subset I ⊆ [n] such that the projection of S on every subset of I of size d is the d-dimensional cube. We show that determining the largest cardinality of a set with a given 𝕌_d dimension is equivalent to a Turán-type problem related to the total number of cliques in a d-uniform hypergraph. This allows us to beat the Sauer-Shelah lemma for this notion of dimension. We use this to obtain several results on Σ₃^k-circuits, i.e., depth-3 circuits with top gate OR and bottom fan-in at most k: - Tight relationship between the number of satisfying assignments of a 2-CNF and the dimension of the largest projection accepted by it, thus improving Paturi, Saks, and Zane (Comput. Complex. '00). - Improved Σ₃³-circuit lower bounds for affine dispersers for sublinear dimension. Moreover, we pose a purely hypergraph-theoretic conjecture under which we get further improvement. - We make progress towards settling the Σ₃² complexity of the inner product function and all degree-2 polynomials over 𝔽₂ in general. The question of determining the Σ₃³ complexity of IP was recently posed by Golovnev, Kulikov, and Williams (ITCS'21).
Cite as

Peter Frankl, Svyatoslav Gryaznov, and Navid Talebanfard. A Variant of the VC-Dimension with Applications to Depth-3 Circuits. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 72:1-72:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{frankl_et_al:LIPIcs.ITCS.2022.72,
  author =	{Frankl, Peter and Gryaznov, Svyatoslav and Talebanfard, Navid},
  title =	{{A Variant of the VC-Dimension with Applications to Depth-3 Circuits}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{72:1--72:19},
  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.2022.72},
  URN =		{urn:nbn:de:0030-drops-156680},
  doi =		{10.4230/LIPIcs.ITCS.2022.72},
  annote =	{Keywords: VC-dimension, Hypergraph, Clique, Affine Disperser, Circuit}
}
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