74 Search Results for "Radhakrishnan, Jaikumar"


Volume

LIPIcs, Volume 18

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

FSTTCS 2012, December 15-17, 2012, Hyderabad, India

Editors: Deepak D'Souza, Jaikumar Radhakrishnan, and Kavitha Telikepalli

Document
Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy

Authors: Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)


Abstract
The following question arises naturally in the study of graph streaming algorithms: Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number n of vertices, and for which, nonetheless, any streaming algorithm with Õ(n) space (i.e., a semi-streaming algorithm) needs a polynomial n^Ω(1) number of passes? Assadi, Chen, and Khanna [STOC 2019] were the first to prove that this is indeed the case. However, the lower bounds that they obtained are for rather non-standard graph problems. Our first main contribution is to present the first polynomial-pass lower bounds for natural "not too hard" graph problems studied previously in the streaming model: k-cores and degeneracy. We devise a novel communication protocol for both problems with near-linear communication, thus showing that k-cores and degeneracy are natural examples of "not too hard" problems. Indeed, previous work have developed single-pass semi-streaming algorithms for approximating these problems. In contrast, we prove that any semi-streaming algorithm for exactly solving these problems requires (almost) Ω(n^{1/3}) passes. The lower bound follows by a reduction from a generalization of the hidden pointer chasing (HPC) problem of Assadi, Chen, and Khanna, which is also the basis of their earlier semi-streaming lower bounds. Our second main contribution is improved round-communication lower bounds for the underlying communication problems at the basis of these reductions: - We improve the previous lower bound of Assadi, Chen, and Khanna for HPC to achieve optimal bounds for this problem. - We further observe that all current reductions from HPC can also work with a generalized version of this problem that we call MultiHPC, and prove an even stronger and optimal lower bound for this generalization. These two results collectively allow us to improve the resulting pass lower bounds for semi-streaming algorithms by a polynomial factor, namely, from n^{1/5} to n^{1/3} passes.

Cite as

Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay. Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{assadi_et_al:LIPIcs.CCC.2024.7,
  author =	{Assadi, Sepehr and Ghosh, Prantar and Loff, Bruno and Mittal, Parth and Mukhopadhyay, Sagnik},
  title =	{{Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.7},
  URN =		{urn:nbn:de:0030-drops-204035},
  doi =		{10.4230/LIPIcs.CCC.2024.7},
  annote =	{Keywords: Graph streaming, Lower bounds, Communication complexity, k-Cores and degeneracy}
}
Document
Information Dissemination via Broadcasts in the Presence of Adversarial Noise

Authors: Klim Efremenko, Gillat Kol, Dmitry Paramonov, Ran Raz, and Raghuvansh R. Saxena

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)


Abstract
We initiate the study of error correcting codes over the multi-party adversarial broadcast channel. Specifically, we consider the classic information dissemination problem where n parties, each holding an input bit, wish to know each other’s input. For this, they communicate in rounds, where, in each round, one designated party sends a bit to all other parties over a channel governed by an adversary that may corrupt a constant fraction of the received communication. We mention that the dissemination problem was studied in the stochastic noise model since the 80’s. While stochastic noise in multi-party channels has received quite a bit of attention, the case of adversarial noise has largely been avoided, as such channels cannot handle more than a 1/n-fraction of errors. Indeed, this many errors allow an adversary to completely corrupt the incoming or outgoing communication for one of the parties and fail the protocol. Curiously, we show that by eliminating these "trivial" attacks, one can get a simple protocol resilient to a constant fraction of errors. Thus, a model that rules out such attacks is both necessary and sufficient to get a resilient protocol. The main shortcoming of our dissemination protocol is its length: it requires Θ(n²) communication rounds whereas n rounds suffice in the absence of noise. Our main result is a matching lower bound of Ω(n²) on the length of any dissemination protocol in our model. Our proof first "gets rid" of the channel noise by converting it to a form of "input noise", showing that a noisy dissemination protocol implies a (noiseless) protocol for a version of the direct sum gap-majority problem. We conclude the proof with a tight lower bound for the latter problem, which may be of independent interest.

Cite as

Klim Efremenko, Gillat Kol, Dmitry Paramonov, Ran Raz, and Raghuvansh R. Saxena. Information Dissemination via Broadcasts in the Presence of Adversarial Noise. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 19:1-19:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{efremenko_et_al:LIPIcs.CCC.2024.19,
  author =	{Efremenko, Klim and Kol, Gillat and Paramonov, Dmitry and Raz, Ran and Saxena, Raghuvansh R.},
  title =	{{Information Dissemination via Broadcasts in the Presence of Adversarial Noise}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{19:1--19:33},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.19},
  URN =		{urn:nbn:de:0030-drops-204159},
  doi =		{10.4230/LIPIcs.CCC.2024.19},
  annote =	{Keywords: Radio Networks, Interactive Coding, Error Correcting Codes}
}
Document
Lower Bounds for Set-Multilinear Branching Programs

Authors: Prerona Chatterjee, Deepanshu Kush, Shubhangi Saraf, and Amir Shpilka

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)


Abstract
In this paper, we prove super-polynomial lower bounds for the model of sum of ordered set-multilinear algebraic branching programs, each with a possibly different ordering (∑smABP). Specifically, we give an explicit nd-variate polynomial of degree d such that any ∑smABP computing it must have size n^ω(1) for d as low as ω(log n). Notably, this constitutes the first such lower bound in the low degree regime. Moreover, for d = poly(n), we demonstrate an exponential lower bound. This result generalizes the seminal work of Nisan (STOC, 1991), which proved an exponential lower bound for a single ordered set-multilinear ABP. The significance of our lower bounds is underscored by the recent work of Bhargav, Dwivedi, and Saxena (TAMC, 2024), which showed that super-polynomial lower bounds against a sum of ordered set-multilinear branching programs - for a polynomial of sufficiently low degree - would imply super-polynomial lower bounds against general ABPs, thereby resolving Valiant’s longstanding conjecture that the permanent polynomial can not be computed efficiently by ABPs. More precisely, their work shows that if one could obtain such lower bounds when the degree is bounded by O(log n/ log log n), then it would imply super-polynomial lower bounds against general ABPs. Our results strengthen the works of Arvind & Raja (Chic. J. Theor. Comput. Sci., 2016) and Bhargav, Dwivedi & Saxena (TAMC, 2024), as well as the works of Ramya & Rao (Theor. Comput. Sci., 2020) and Ghoshal & Rao (International Computer Science Symposium in Russia, 2021), each of which established lower bounds for related or restricted versions of this model. They also strongly answer a question from the former two, which asked to prove super-polynomial lower bounds for general ∑smABP.

Cite as

Prerona Chatterjee, Deepanshu Kush, Shubhangi Saraf, and Amir Shpilka. Lower Bounds for Set-Multilinear Branching Programs. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{chatterjee_et_al:LIPIcs.CCC.2024.20,
  author =	{Chatterjee, Prerona and Kush, Deepanshu and Saraf, Shubhangi and Shpilka, Amir},
  title =	{{Lower Bounds for Set-Multilinear Branching Programs}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.20},
  URN =		{urn:nbn:de:0030-drops-204167},
  doi =		{10.4230/LIPIcs.CCC.2024.20},
  annote =	{Keywords: Lower Bounds, Algebraic Branching Programs, Set-multilinear polynomials}
}
Document
Track A: Algorithms, Complexity and Games
Simultaneously Approximating All 𝓁_p-Norms in Correlation Clustering

Authors: Sami Davies, Benjamin Moseley, and Heather Newman

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


Abstract
This paper considers correlation clustering on unweighted complete graphs. We give a combinatorial algorithm that returns a single clustering solution that is simultaneously O(1)-approximate for all 𝓁_p-norms of the disagreement vector; in other words, a combinatorial O(1)-approximation of the all-norms objective for correlation clustering. This is the first proof that minimal sacrifice is needed in order to optimize different norms of the disagreement vector. In addition, our algorithm is the first combinatorial approximation algorithm for the 𝓁₂-norm objective, and more generally the first combinatorial algorithm for the 𝓁_p-norm objective when 1 < p < ∞. It is also faster than all previous algorithms that minimize the 𝓁_p-norm of the disagreement vector, with run-time O(n^ω), where O(n^ω) is the time for matrix multiplication on n × n matrices. When the maximum positive degree in the graph is at most Δ, this can be improved to a run-time of O(nΔ² log n).

Cite as

Sami Davies, Benjamin Moseley, and Heather Newman. Simultaneously Approximating All 𝓁_p-Norms in Correlation Clustering. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 52:1-52:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{davies_et_al:LIPIcs.ICALP.2024.52,
  author =	{Davies, Sami and Moseley, Benjamin and Newman, Heather},
  title =	{{Simultaneously Approximating All 𝓁\underlinep-Norms in Correlation Clustering}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{52:1--52:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.52},
  URN =		{urn:nbn:de:0030-drops-201950},
  doi =		{10.4230/LIPIcs.ICALP.2024.52},
  annote =	{Keywords: Approximation algorithms, correlation clustering, all-norms, lp-norms}
}
Document
Track A: Algorithms, Complexity and Games
Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: A Complete Classification

Authors: Esther Galby, Sándor Kisfaludi-Bak, Dániel Marx, and Roohani Sharma

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


Abstract
In the Directed Steiner Network problem, the input is a directed graph G, a set T ⊆ V(G) of k terminals, and a demand graph D on T. The task is to find a subgraph H ⊆ G with the minimum number of edges such that for every (s,t) ∈ E(D), the solution H contains a directed s → t path. The goal of this paper is to investigate how the complexity of the problem depends on the demand pattern in planar graphs. Formally, if 𝒟 is a class of directed graphs, then the 𝒟-Steiner Network (𝒟-DSN) problem is the special case where the demand graph D is restricted to be from 𝒟. We give a complete characterization of the behavior of every 𝒟-DSN problem on planar graphs. We classify every class 𝒟 closed under transitive equivalence and identification of vertices into three cases: assuming ETH, either the problem is 1) solvable in time 2^O(k)⋅n^O(1), i.e., FPT parameterized by the number k of terminals, but not solvable in time 2^o(k)⋅n^O(1), 2) solvable in time f(k)⋅n^O(√k), but cannot be solved in time f(k)⋅n^o(√k), or 3) solvable in time f(k)⋅n^O(k), but cannot be solved in time f(k)⋅n^o(k). Our result is a far-reaching generalization and unification of earlier results on Directed Steiner Tree, Directed Steiner Network, and Strongly Connected Steiner Subgraph on planar graphs. As an important step of our lower bound proof, we discover a rare example of a genuinely planar problem (i.e., described by a planar graph and two sets of vertices) that cannot be solved in time f(k)⋅n^o(k): given two sets of terminals S and T with |S|+|T| = k, find a subgraph with minimum number of edges such that every vertex of T is reachable from every vertex of S.

Cite as

Esther Galby, Sándor Kisfaludi-Bak, Dániel Marx, and Roohani Sharma. Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: A Complete Classification. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 67:1-67:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{galby_et_al:LIPIcs.ICALP.2024.67,
  author =	{Galby, Esther and Kisfaludi-Bak, S\'{a}ndor and Marx, D\'{a}niel and Sharma, Roohani},
  title =	{{Subexponential Parameterized Directed Steiner Network Problems on Planar Graphs: A Complete Classification}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{67:1--67:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.67},
  URN =		{urn:nbn:de:0030-drops-202104},
  doi =		{10.4230/LIPIcs.ICALP.2024.67},
  annote =	{Keywords: Directed Steiner Network, Sub-exponential algorithm}
}
Document
Track A: Algorithms, Complexity and Games
Optimal Non-Adaptive Cell Probe Dictionaries and Hashing

Authors: Kasper Green Larsen, Rasmus Pagh, Giuseppe Persiano, Toniann Pitassi, Kevin Yeo, and Or Zamir

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


Abstract
We present a simple and provably optimal non-adaptive cell probe data structure for the static dictionary problem. Our data structure supports storing a set of n key-value pairs from [u]× [u] using s words of space and answering key lookup queries in t = O(lg(u/n)/lg(s/n)) non-adaptive probes. This generalizes a solution to the membership problem (i.e., where no values are associated with keys) due to Buhrman et al. We also present matching lower bounds for the non-adaptive static membership problem in the deterministic setting. Our lower bound implies that both our dictionary algorithm and the preceding membership algorithm are optimal, and in particular that there is an inherent complexity gap in these problems between no adaptivity and one round of adaptivity (with which hashing-based algorithms solve these problems in constant time). Using the ideas underlying our data structure, we also obtain the first implementation of a n-wise independent family of hash functions with optimal evaluation time in the cell probe model.

Cite as

Kasper Green Larsen, Rasmus Pagh, Giuseppe Persiano, Toniann Pitassi, Kevin Yeo, and Or Zamir. Optimal Non-Adaptive Cell Probe Dictionaries and Hashing. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 104:1-104:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{larsen_et_al:LIPIcs.ICALP.2024.104,
  author =	{Larsen, Kasper Green and Pagh, Rasmus and Persiano, Giuseppe and Pitassi, Toniann and Yeo, Kevin and Zamir, Or},
  title =	{{Optimal Non-Adaptive Cell Probe Dictionaries and Hashing}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{104:1--104:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.104},
  URN =		{urn:nbn:de:0030-drops-202471},
  doi =		{10.4230/LIPIcs.ICALP.2024.104},
  annote =	{Keywords: non-adaptive, cell probe, dictionary, hashing}
}
Document
Track A: Algorithms, Complexity and Games
Alphabet Reduction for Reconfiguration Problems

Authors: Naoto Ohsaka

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


Abstract
We present a reconfiguration analogue of alphabet reduction à la Dinur (J. ACM, 2007) and its applications. Given a binary constraint graph G and its two satisfying assignments ψ^ini and ψ^tar, the Maxmin 2-CSP Reconfiguration problem requests to transform ψ^ini into ψ^tar by repeatedly changing the value of a single vertex so that the minimum fraction of satisfied edges is maximized. We demonstrate a polynomial-time reduction from Maxmin 2-CSP Reconfiguration with arbitrarily large alphabet size W ∈ ℕ to itself with universal alphabet size W₀ ∈ ℕ such that 1) the perfect completeness is preserved, and 2) if any reconfiguration for the former violates ε-fraction of edges, then Ω(ε)-fraction of edges must be unsatisfied during any reconfiguration for the latter. The crux of its construction is the reconfigurability of Hadamard codes, which enables to reconfigure between a pair of codewords, while avoiding getting too close to the other codewords. Combining this alphabet reduction with gap amplification due to Ohsaka (SODA 2024), we are able to amplify the 1 vs. 1-ε gap for arbitrarily small ε ∈ (0,1) up to the 1 vs. 1-ε₀ for some universal ε₀ ∈ (0,1) without blowing up the alphabet size. In particular, a 1 vs. 1-ε₀ gap version of Maxmin 2-CSP Reconfiguration with alphabet size W₀ is PSPACE-hard given a probabilistically checkable reconfiguration proof system having any soundness error 1-ε due to Hirahara and Ohsaka (STOC 2024) and Karthik C. S. and Manurangsi (2023). As an immediate corollary, we show that there exists a universal constant ε₀ ∈ (0,1) such that many popular reconfiguration problems are PSPACE-hard to approximate within a factor of 1-ε₀, including those of 3-SAT, Independent Set, Vertex Cover, Clique, Dominating Set, and Set Cover. This may not be achieved only by gap amplification of Ohsaka, which makes the alphabet size gigantic depending on ε^-1.

Cite as

Naoto Ohsaka. Alphabet Reduction for Reconfiguration Problems. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 113:1-113:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{ohsaka:LIPIcs.ICALP.2024.113,
  author =	{Ohsaka, Naoto},
  title =	{{Alphabet Reduction for Reconfiguration Problems}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{113:1--113:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.113},
  URN =		{urn:nbn:de:0030-drops-202560},
  doi =		{10.4230/LIPIcs.ICALP.2024.113},
  annote =	{Keywords: reconfiguration problems, hardness of approximation, Hadamard codes, alphabet reduction}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
The Structure of Trees in the Pushdown Hierarchy

Authors: Arnaud Carayol and Lucien Charamond

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


Abstract
In this article, we investigate the structure of the trees in the pushdown hierarchy, a hierarchy of infinite graphs having a decidable MSO-theory. We show that a binary complete tree in the pushdown hierarchy must contain at least two different subtrees which are isomorphic. We extend this property to any tree with no leaves and with chains of unary vertices of bounded length. We provided two applications of this result. A first application in formal language theory, gives a simple argument to show that some languages are not deterministic higher-order indexed languages. A second application in number theory shows that the real numbers defined by deterministic higher-order pushdown automata are either rational or transcendental.

Cite as

Arnaud Carayol and Lucien Charamond. The Structure of Trees in the Pushdown Hierarchy. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 131:1-131:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{carayol_et_al:LIPIcs.ICALP.2024.131,
  author =	{Carayol, Arnaud and Charamond, Lucien},
  title =	{{The Structure of Trees in the Pushdown Hierarchy}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{131:1--131:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.131},
  URN =		{urn:nbn:de:0030-drops-202749},
  doi =		{10.4230/LIPIcs.ICALP.2024.131},
  annote =	{Keywords: Pushdown hierarchy, Monadic second-order logic, Automatic numbers}
}
Document
Online Facility Location with Weights and Congestion

Authors: Arghya Chakraborty and Rahul Vaze

Published in: LIPIcs, Volume 284, 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)


Abstract
The classic online facility location problem deals with finding the optimal set of facilities in an online fashion when demand requests arrive one at a time and facilities need to be opened to service these requests. In this work, we study two variants of the online facility location problem; (1) weighted requests and (2) congestion. Both of these variants are motivated by their applications to real life scenarios and the previously known results on online facility location cannot be directly adapted to analyse them. - Weighted requests: In this variant, each demand request is a pair (x,w) where x is the standard location of the demand while w is the corresponding weight of the request. The cost of servicing request (x,w) at facility F is w⋅ d(x,F). For this variant, given n requests, we present an online algorithm attaining a competitive ratio of 𝒪(log n) in the secretarial model for the weighted requests and show that it is optimal. -Congestion: The congestion variant considers the case when there is a congestion cost that grows with the number of requests served by each facility. For this variant, when the congestion cost is a monomial, we show that there exists an algorithm attaining a constant competitive ratio. This constant is a function of the exponent of the monomial and the facility opening cost but independent of the number of requests.

Cite as

Arghya Chakraborty and Rahul Vaze. Online Facility Location with Weights and Congestion. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{chakraborty_et_al:LIPIcs.FSTTCS.2023.6,
  author =	{Chakraborty, Arghya and Vaze, Rahul},
  title =	{{Online Facility Location with Weights and Congestion}},
  booktitle =	{43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-304-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{284},
  editor =	{Bouyer, Patricia and Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2023.6},
  URN =		{urn:nbn:de:0030-drops-193797},
  doi =		{10.4230/LIPIcs.FSTTCS.2023.6},
  annote =	{Keywords: online algorithms, online facility location, probabilistic method, weighted-requests, congestion}
}
Document
Criticality of AC⁰-Formulae

Authors: Prahladh Harsha, Tulasimohan Molli, and Ashutosh Shankar

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)


Abstract
Rossman [In Proc. 34th Comput. Complexity Conf., 2019] introduced the notion of criticality. The criticality of a Boolean function f : {0,1}ⁿ → {0,1} is the minimum λ ≥ 1 such that for all positive integers t and all p ∈ [0,1], Pr_{ρ∼ℛ_p}[DT_{depth}(f|_ρ) ≥ t] ≤ (pλ)^t, where ℛ_p refers to the distribution of p-random restrictions. Håstad’s celebrated switching lemma shows that the criticality of any k-DNF is at most O(k). Subsequent improvements to correlation bounds of AC⁰-circuits against parity showed that the criticality of any AC⁰-circuit of size S and depth d+1 is at most O(log S)^d and any regular AC⁰-formula of size S and depth d+1 is at most O((1/d)⋅log S)^d. We strengthen these results by showing that the criticality of any AC⁰-formula (not necessarily regular) of size S and depth d+1 is at most O((log S)/d)^d, resolving a conjecture due to Rossman. This result also implies Rossman’s optimal lower bound on the size of any depth-d AC⁰-formula computing parity [Comput. Complexity, 27(2):209-223, 2018.]. Our result implies tight correlation bounds against parity, tight Fourier concentration results and improved #SAT algorithm for AC⁰-formulae.

Cite as

Prahladh Harsha, Tulasimohan Molli, and Ashutosh Shankar. Criticality of AC⁰-Formulae. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{harsha_et_al:LIPIcs.CCC.2023.19,
  author =	{Harsha, Prahladh and Molli, Tulasimohan and Shankar, Ashutosh},
  title =	{{Criticality of AC⁰-Formulae}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{19:1--19:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.19},
  URN =		{urn:nbn:de:0030-drops-182898},
  doi =		{10.4230/LIPIcs.CCC.2023.19},
  annote =	{Keywords: AC⁰ circuits, AC⁰ formulae, criticality, switching lemma, correlation bounds}
}
Document
An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions

Authors: Florian Barth, Stefan Funke, and Claudius Proissl

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)


Abstract
Graphs with multiple edge costs arise naturally in the route planning domain when apart from travel time other criteria like fuel consumption or positive height difference are also objectives to be minimized. In such a scenario, this paper investigates the number of extreme shortest paths between a given source-target pair s, t. We show that for a fixed but arbitrary number of cost types d ≥ 1 the number of extreme shortest paths is in n^O(log^{d-1}n) in graphs G with n nodes. This is a generalization of known upper bounds for d = 2 and d = 3.

Cite as

Florian Barth, Stefan Funke, and Claudius Proissl. An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 14:1-14:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{barth_et_al:LIPIcs.ESA.2022.14,
  author =	{Barth, Florian and Funke, Stefan and Proissl, Claudius},
  title =	{{An Upper Bound on the Number of Extreme Shortest Paths in Arbitrary Dimensions}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{14:1--14:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.14},
  URN =		{urn:nbn:de:0030-drops-169525},
  doi =		{10.4230/LIPIcs.ESA.2022.14},
  annote =	{Keywords: Parametric Shortest Paths, Extreme Shortest Paths}
}
Document
Track A: Algorithms, Complexity and Games
Set Membership with Two Classical and Quantum Bit Probes

Authors: Shyam S. Dhamapurkar, Shubham Vivek Pawar, and Jaikumar Radhakrishnan

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


Abstract
We study the classical and quantum bit-probe versions of the static set membership problem : Given a subset, S (|S| ≤ n) of a universe, 𝒰 (|𝒰| = m ≫ n), represent it as a binary string in memory so that the query "Is x in S?" (x ∈ 𝒰) can be answered by making at most t probes into the string. Let s_{A}(m,n,t) denote the minimum length of the bit string in any scheme that solves this static set membership problem. We show that for n ≥ 4 s_A(m,n,t = 2) = 𝒪(m^{1-1/(n-1)}) (if n = 0 (mod 3)); 𝒪(m^{1-1/n}) (if n = 1,2 (mod 3)); 𝒪(m^{6/7}) (if n = 8,9). These bounds are shown using a common scheme that is based on a graph-theoretic observation on orienting the edges of a graph of high girth. For all n ≥ 4, these bounds substantially improve on the previous best bounds known for this problem, some of which required elaborate constructions [Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2020]. Our schemes are explicit. A lower bound of the form s_A(m,n,2) = Ω(m^{1-1/⌊{n/4}⌋}) was known for this problem. We show an improved lower bound of s_A(m,n,2) = Ω(m^{1-2/(n+3)}); this bound was previously known only for n = 3,5 [Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2020; Mirza Galib Anwarul Husain Baig et al., 2019; Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2018; Mirza Galib Anwarul Husain Baig et al., 2019; Mirza Galib Anwarul Husain Baig and Deepanjan Kesh, 2020]. We consider the quantum version of the problem, where access to the bit-string b ∈ {0,1}^s is provided in the form of a quantum oracle that performs the transformation 𝒪_b: |i⟩ ↦ (-1)^{b_i} |i⟩. Let s_Q(m,n,2) denote the minimum length of the bit string that solves the above set membership problem in the quantum model (with adaptive queries but no error). We show that for all n ≤ m^{1/8}, we have s_{QA}(m,n,2) = 𝒪(m^{7/8}). This upper bound makes crucial use of Nash-William’s theorem [Diestel, 2005] for decomposing a graph into forests. This result is significant because, prior to this work, it was not known if quantum schemes yield any advantage over classical schemes. We also consider schemes that make a small number of quantum non-adaptive probes. In particular, we show that the space required in this case, s_{QN}(m,n = 2,t = 2) = O(√m) and s_{QN}(m,n = 2,t = 3) = O(m^{1/3}); in contrast, it is known that two non-adaptive classical probes yield no savings. Our quantum schemes are simple and use only the fact that the XOR of two bits of memory can be computed using just one quantum query to the oracle.

Cite as

Shyam S. Dhamapurkar, Shubham Vivek Pawar, and Jaikumar Radhakrishnan. Set Membership with Two Classical and Quantum Bit Probes. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 52:1-52:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{dhamapurkar_et_al:LIPIcs.ICALP.2022.52,
  author =	{Dhamapurkar, Shyam S. and Pawar, Shubham Vivek and Radhakrishnan, Jaikumar},
  title =	{{Set Membership with Two Classical and Quantum Bit Probes}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{52:1--52:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.52},
  URN =		{urn:nbn:de:0030-drops-163932},
  doi =		{10.4230/LIPIcs.ICALP.2022.52},
  annote =	{Keywords: set membership problem, bit probe complexity, graphs with high girth, quantum data structure}
}
Document
Fairly Popular Matchings and Optimality

Authors: Telikepalli Kavitha

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


Abstract
We consider a matching problem in a bipartite graph G = (A ∪ B, E) where vertices have strict preferences over their neighbors. A matching M is popular if for any matching N, the number of vertices that prefer M is at least the number that prefer N; thus M does not lose a head-to-head election against any matching where vertices are voters. It is easy to find popular matchings; however when there are edge costs, it is NP-hard to find (or even approximate) a min-cost popular matching. This hardness motivates relaxations of popularity. Here we introduce fairly popular matchings. A fairly popular matching may lose elections but there is no good matching (wrt popularity) that defeats a fairly popular matching. In particular, any matching that defeats a fairly popular matching does not occur in the support of any popular mixed matching. We show that a min-cost fairly popular matching can be computed in polynomial time and the fairly popular matching polytope has a compact extended formulation. We also show the following hardness result: given a matching M, it is NP-complete to decide if there exists a popular matching that defeats M. Interestingly, there exists a set K of at most m popular matchings in G (where |E| = m) such that if a matching is defeated by some popular matching in G then it has to be defeated by one of the matchings in K.

Cite as

Telikepalli Kavitha. Fairly Popular Matchings and Optimality. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 41:1-41:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{kavitha:LIPIcs.STACS.2022.41,
  author =	{Kavitha, Telikepalli},
  title =	{{Fairly Popular Matchings and Optimality}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{41:1--41:22},
  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.2022.41},
  URN =		{urn:nbn:de:0030-drops-158516},
  doi =		{10.4230/LIPIcs.STACS.2022.41},
  annote =	{Keywords: Bipartite graphs, Stable matchings, Mixed matchings, Polytopes}
}
Document
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}
}
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