37 Search Results for "Yannakakis, Mihalis"

Document
DOI: 10.4230/LIPIcs.CCC.2024.13
Hard Submatrices for Non-Negative Rank and Communication Complexity

Authors: Pavel Hrubeš

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

Abstract
Given a non-negative real matrix M of non-negative rank at least r, can we witness this fact by a small submatrix of M? While Moitra (SIAM J. Comput. 2013) proved that this cannot be achieved exactly, we show that such a witnessing is possible approximately: an m×n matrix of non-negative rank r always contains a submatrix with at most r³ rows and columns with non-negative rank at least Ω(r/(log n log m)). A similar result is proved for the 1-partition number of a Boolean matrix and, consequently, also for its two-player deterministic communication complexity. Tightness of the latter estimate is closely related to the log-rank conjecture of Lovász and Saks.
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Pavel Hrubeš. Hard Submatrices for Non-Negative Rank and Communication Complexity. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 13:1-13:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hrubes:LIPIcs.CCC.2024.13,
  author =	{Hrube\v{s}, Pavel},
  title =	{{Hard Submatrices for Non-Negative Rank and Communication Complexity}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{13:1--13:12},
  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.2024.13},
  URN =		{urn:nbn:de:0030-drops-204097},
  doi =		{10.4230/LIPIcs.CCC.2024.13},
  annote =	{Keywords: Non-negative rank, communication complexity, extension complexity}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.14
Complexity of Robust Orbit Problems for Torus Actions and the abc-Conjecture

Authors: Peter Bürgisser, Mahmut Levent Doğan, Visu Makam, Michael Walter, and Avi Wigderson

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

Abstract
When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer science, optimization, and more. Accordingly, it is of high interest to understand their computational complexity. Recently, Bürgisser et al. (2021) gave the first polynomial-time algorithms for orbit problems of torus actions, that is, actions of commutative continuous groups on Euclidean space. In this work, motivated by theoretical and practical applications, we study the computational complexity of robust generalizations of these orbit problems, which amount to approximating the distance of orbits in ℂⁿ up to a factor γ ≥ 1. In particular, this allows deciding whether two inputs are approximately in the same orbit or far from being so. On the one hand, we prove the NP-hardness of this problem for γ = n^Ω(1/log log n) by reducing the closest vector problem for lattices to it. On the other hand, we describe algorithms for solving this problem for an approximation factor γ = exp(poly(n)). Our algorithms combine tools from invariant theory and algorithmic lattice theory, and they also provide group elements witnessing the proximity of the given orbits (in contrast to the algebraic algorithms of prior work). We prove that they run in polynomial time if and only if a version of the famous number-theoretic abc-conjecture holds - establishing a new and surprising connection between computational complexity and number theory.
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Peter Bürgisser, Mahmut Levent Doğan, Visu Makam, Michael Walter, and Avi Wigderson. Complexity of Robust Orbit Problems for Torus Actions and the abc-Conjecture. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 14:1-14:48, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{burgisser_et_al:LIPIcs.CCC.2024.14,
  author =	{B\"{u}rgisser, Peter and Do\u{g}an, Mahmut Levent and Makam, Visu and Walter, Michael and Wigderson, Avi},
  title =	{{Complexity of Robust Orbit Problems for Torus Actions and the abc-Conjecture}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{14:1--14:48},
  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.2024.14},
  URN =		{urn:nbn:de:0030-drops-204100},
  doi =		{10.4230/LIPIcs.CCC.2024.14},
  annote =	{Keywords: computational invariant theory, geometric complexity theory, orbit problems, abc-conjecture, closest vector problem}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.27
Baby PIH: Parameterized Inapproximability of Min CSP

Authors: Venkatesan Guruswami, Xuandi Ren, and Sai Sandeep

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

Abstract
The Parameterized Inapproximability Hypothesis (PIH) is the analog of the PCP theorem in the world of parameterized complexity. It asserts that no FPT algorithm can distinguish a satisfiable 2CSP instance from one which is only (1-ε)-satisfiable (where the parameter is the number of variables) for some constant 0 < ε < 1. We consider a minimization version of CSPs (Min-CSP), where one may assign r values to each variable, and the goal is to ensure that every constraint is satisfied by some choice among the r × r pairs of values assigned to its variables (call such a CSP instance r-list-satisfiable). We prove the following strong parameterized inapproximability for Min CSP: For every r ≥ 1, it is W[1]-hard to tell if a 2CSP instance is satisfiable or is not even r-list-satisfiable. We refer to this statement as "Baby PIH", following the recently proved Baby PCP Theorem (Barto and Kozik, 2021). Our proof adapts the combinatorial arguments underlying the Baby PCP theorem, overcoming some basic obstacles that arise in the parameterized setting. Furthermore, our reduction runs in time polynomially bounded in both the number of variables and the alphabet size, and thus implies the Baby PCP theorem as well.
Cite as

Venkatesan Guruswami, Xuandi Ren, and Sai Sandeep. Baby PIH: Parameterized Inapproximability of Min CSP. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{guruswami_et_al:LIPIcs.CCC.2024.27,
  author =	{Guruswami, Venkatesan and Ren, Xuandi and Sandeep, Sai},
  title =	{{Baby PIH: Parameterized Inapproximability of Min CSP}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{27:1--27:17},
  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.2024.27},
  URN =		{urn:nbn:de:0030-drops-204237},
  doi =		{10.4230/LIPIcs.CCC.2024.27},
  annote =	{Keywords: Parameterized Inapproximability Hypothesis, Constraint Satisfaction Problems}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.4
Separator Based Data Reduction for the Maximum Cut Problem

Authors: Jonas Charfreitag, Christine Dahn, Michael Kaibel, Philip Mayer, Petra Mutzel, and Lukas Schürmann

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Preprocessing is an important ingredient for solving the maximum cut problem to optimality on real-world graphs. In our work, we derive a new framework for data reduction rules based on vertex separators. Vertex separators are sets of vertices, whose removal increases the number of connected components of a graph. Certain small separators can be found in linear time, allowing for an efficient combination of our framework with existing data reduction rules. Additionally, we complement known data reduction rules for triangles with a new one. In our computational experiments on established benchmark instances, we clearly show the effectiveness and efficiency of our proposed data reduction techniques. The resulting graphs are significantly smaller than in earlier studies and sometimes no vertex is left, so preprocessing has fully solved the instance to optimality. The introduced techniques are also shown to offer significant speedup potential for an exact state-of-the-art solver and to help a state-of-the-art heuristic to produce solutions of higher quality.
Cite as

Jonas Charfreitag, Christine Dahn, Michael Kaibel, Philip Mayer, Petra Mutzel, and Lukas Schürmann. Separator Based Data Reduction for the Maximum Cut Problem. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 4:1-4:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{charfreitag_et_al:LIPIcs.SEA.2024.4,
  author =	{Charfreitag, Jonas and Dahn, Christine and Kaibel, Michael and Mayer, Philip and Mutzel, Petra and Sch\"{u}rmann, Lukas},
  title =	{{Separator Based Data Reduction for the Maximum Cut Problem}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{4:1--4:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.4},
  URN =		{urn:nbn:de:0030-drops-203698},
  doi =		{10.4230/LIPIcs.SEA.2024.4},
  annote =	{Keywords: Data Reduction, Maximum Cut, Vertex Separators}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.8
Practical Computation of Graph VC-Dimension

Authors: David Coudert, Mónika Csikós, Guillaume Ducoffe, and Laurent Viennot

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
For any set system ℋ = (V,ℛ), ℛ ⊆ 2^V, a subset S ⊆ V is called shattered if every S' ⊆ S results from the intersection of S with some set in ℛ. The VC-dimension of ℋ is the size of a largest shattered set in V. In this paper, we focus on the problem of computing the VC-dimension of graphs. In particular, given a graph G = (V,E), the VC-dimension of G is defined as the VC-dimension of (V, N), where N contains each subset of V that can be obtained as the closed neighborhood of some vertex v ∈ V in G. Our main contribution is an algorithm for computing the VC-dimension of any graph, whose effectiveness is shown through experiments on various types of practical graphs, including graphs with millions of vertices. A key aspect of its efficiency resides in the fact that practical graphs have small VC-dimension, up to 8 in our experiments. As a side-product, we present several new bounds relating the graph VC-dimension to other classical graph theoretical notions. We also establish the W[1]-hardness of the graph VC-dimension problem by extending a previous result for arbitrary set systems.
Cite as

David Coudert, Mónika Csikós, Guillaume Ducoffe, and Laurent Viennot. Practical Computation of Graph VC-Dimension. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{coudert_et_al:LIPIcs.SEA.2024.8,
  author =	{Coudert, David and Csik\'{o}s, M\'{o}nika and Ducoffe, Guillaume and Viennot, Laurent},
  title =	{{Practical Computation of Graph VC-Dimension}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.8},
  URN =		{urn:nbn:de:0030-drops-203731},
  doi =		{10.4230/LIPIcs.SEA.2024.8},
  annote =	{Keywords: VC-dimension, graph, algorithm}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.15
Determining Fixed-Length Paths in Directed and Undirected Edge-Weighted Graphs

Authors: Daniel Hambly, Rhyd Lewis, and Padraig Corcoran

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
In this paper, we examine the NP-hard problem of identifying fixed-length s-t paths in edge-weighted graphs - that is, a path of a desired length k from a source vertex s to a target vertex t. Many existing strategies look at paths whose lengths are determined by the number of edges in the path. We, however, look at the length of the path as the sum of the edge weights. Here, three exact algorithms for this problem are proposed: the first based on an integer programming (IP) formulation, the second a backtracking algorithm, and the third based on an extension of Yen’s algorithm. Analysis of these algorithms on random graphs shows that the backtracking algorithm performs best on smaller values of k, whilst the IP is preferable for larger values of k.
Cite as

Daniel Hambly, Rhyd Lewis, and Padraig Corcoran. Determining Fixed-Length Paths in Directed and Undirected Edge-Weighted Graphs. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 15:1-15:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hambly_et_al:LIPIcs.SEA.2024.15,
  author =	{Hambly, Daniel and Lewis, Rhyd and Corcoran, Padraig},
  title =	{{Determining Fixed-Length Paths in Directed and Undirected Edge-Weighted Graphs}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{15:1--15:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.15},
  URN =		{urn:nbn:de:0030-drops-203805},
  doi =		{10.4230/LIPIcs.SEA.2024.15},
  annote =	{Keywords: Graphs, paths, backtracking, integer programming, Yen’s algorithm}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.17
Barcode Selection and Layout Optimization in Spatial Transcriptomics

Authors: Frederik L. Jatzkowski, Antonia Schmidt, Robert Mank, Steffen Schüler, and Matthias Müller-Hannemann

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
An important special case of the quadratic assignment problem arises in the synthesis of DNA microarrays for high-resolution spatial transcriptomics. The task is to select a suitable subset from a set of barcodes, i. e. short DNA strings that serve as unique identifiers, and to assign the selected barcodes to positions on a two-dimensional array in such a way that a position-dependent cost function is minimized. A typical microarray with dimensions of 768×1024 requires 786,432 many barcodes to be placed, leading to very challenging large-scale combinatorial optimization problems. The general quadratic assignment problem is well-known for its hardness, both in theory and in practice. It turns out that this also holds for the special case of the barcode layout problem. We show that the problem is even hard to approximate: It is MaxSNP-hard. An ILP formulation theoretically allows the computation of optimal results, but it is only applicable for tiny instances. Therefore, we have developed layout constructing and improving heuristics with the aim of computing near-optimal solutions for instances of realistic size. These include a sorting-based algorithm, a greedy algorithm, 2-OPT-based local search and a genetic algorithm. To assess the quality of the results, we compare the generated solutions with the expected cost of a random layout and with lower bounds. A combination of the greedy algorithm and 2-OPT local search produces the most promising results in terms of both quality and runtime. Solutions to large-scale instances with arrays of dimension 768×1024 show a 37% reduction in cost over a random solution and can be computed in about 3 minutes. Since the universe of suitable barcodes is much larger than the number of barcodes needed, this can be exploited. Experiments with different surpluses of barcodes show that a significant improvement in layout quality can be achieved at the cost of a reasonable increase in runtime. Another interesting finding is that the restriction of the barcode design space by biochemical constraints is actually beneficial for the overall layout cost.
Cite as

Frederik L. Jatzkowski, Antonia Schmidt, Robert Mank, Steffen Schüler, and Matthias Müller-Hannemann. Barcode Selection and Layout Optimization in Spatial Transcriptomics. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 17:1-17:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jatzkowski_et_al:LIPIcs.SEA.2024.17,
  author =	{Jatzkowski, Frederik L. and Schmidt, Antonia and Mank, Robert and Sch\"{u}ler, Steffen and M\"{u}ller-Hannemann, Matthias},
  title =	{{Barcode Selection and Layout Optimization in Spatial Transcriptomics}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{17:1--17:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.17},
  URN =		{urn:nbn:de:0030-drops-203821},
  doi =		{10.4230/LIPIcs.SEA.2024.17},
  annote =	{Keywords: Spatial Transcriptomics, Array Layout, Optimization, Computational Complexity, GPU Computing, Integer Linear Programming, Metaheuristics}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.16
NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials

Authors: Omkar Baraskar, Agrim Dewan, Chandan Saha, and Pulkit Sinha

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

Abstract
An s-sparse polynomial has at most s monomials with nonzero coefficients. The Equivalence Testing problem for sparse polynomials (ETsparse) asks to decide if a given polynomial f is equivalent to (i.e., in the orbit of) some s-sparse polynomial. In other words, given f ∈ 𝔽[𝐱] and s ∈ ℕ, ETsparse asks to check if there exist A ∈ GL(|𝐱|, 𝔽) and 𝐛 ∈ 𝔽^|𝐱| such that f(A𝐱 + 𝐛) is s-sparse. We show that ETsparse is NP-hard over any field 𝔽, if f is given in the sparse representation, i.e., as a list of nonzero coefficients and exponent vectors. This answers a question posed by Gupta, Saha and Thankey (SODA 2023) and also, more explicitly, by Baraskar, Dewan and Saha (STACS 2024). The result implies that the Minimum Circuit Size Problem (MCSP) is NP-hard for a dense subclass of depth-3 arithmetic circuits if the input is given in sparse representation. We also show that approximating the smallest s₀ such that a given s-sparse polynomial f is in the orbit of some s₀-sparse polynomial to within a factor of s^{1/3 - ε} is NP-hard for any ε > 0; observe that s-factor approximation is trivial as the input is s-sparse. Finally, we show that for any constant σ ≥ 6, checking if a polynomial (given in sparse representation) is in the orbit of some support-σ polynomial is NP-hard. Support of a polynomial f is the maximum number of variables present in any monomial of f. These results are obtained via direct reductions from the 3-SAT problem.
Cite as

Omkar Baraskar, Agrim Dewan, Chandan Saha, and Pulkit Sinha. NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baraskar_et_al:LIPIcs.ICALP.2024.16,
  author =	{Baraskar, Omkar and Dewan, Agrim and Saha, Chandan and Sinha, Pulkit},
  title =	{{NP-Hardness of Testing Equivalence to Sparse Polynomials and to Constant-Support Polynomials}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{16:1--16:21},
  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.2024.16},
  URN =		{urn:nbn:de:0030-drops-201598},
  doi =		{10.4230/LIPIcs.ICALP.2024.16},
  annote =	{Keywords: Equivalence testing, MCSP, sparse polynomials, 3SAT}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.47
Lower Bounds on 0-Extension with Steiner Nodes

Authors: Yu Chen and Zihan Tan

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

Abstract
In the 0-Extension problem, we are given an edge-weighted graph G = (V,E,c), a set T ⊆ V of its vertices called terminals, and a semi-metric D over T, and the goal is to find an assignment f of each non-terminal vertex to a terminal, minimizing the sum, over all edges (u,v) ∈ E, the product of the edge weight c(u,v) and the distance D(f(u),f(v)) between the terminals that u,v are mapped to. Current best approximation algorithms on 0-Extension are based on rounding a linear programming relaxation called the semi-metric LP relaxation. The integrality gap of this LP, is upper bounded by O(log|T|/log log|T|) and lower bounded by Ω((log|T|)^{2/3}), has been shown to be closely related to the quality of cut and flow vertex sparsifiers. We study a variant of the 0-Extension problem where Steiner vertices are allowed. Specifically, we focus on the integrality gap of the same semi-metric LP relaxation to this new problem. Following from previous work, this new integrality gap turns out to be closely related to the quality achievable by cut/flow vertex sparsifiers with Steiner nodes, a major open problem in graph compression. We show that the new integrality gap stays superconstant Ω(log log |T|) even if we allow a super-linear O(|T|log^{1-ε}|T|) number of Steiner nodes.
Cite as

Yu Chen and Zihan Tan. Lower Bounds on 0-Extension with Steiner Nodes. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 47:1-47:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2024.47,
  author =	{Chen, Yu and Tan, Zihan},
  title =	{{Lower Bounds on 0-Extension with Steiner Nodes}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{47:1--47:18},
  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.2024.47},
  URN =		{urn:nbn:de:0030-drops-201905},
  doi =		{10.4230/LIPIcs.ICALP.2024.47},
  annote =	{Keywords: Graph Algorithms, Zero Extension, Integrality Gap}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.19
Sublinear Algorithms for TSP via Path Covers

Authors: Soheil Behnezhad, Mohammad Roghani, Aviad Rubinstein, and Amin Saberi

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

Abstract
We study sublinear time algorithms for the traveling salesman problem (TSP). First, we focus on the closely related maximum path cover problem, which asks for a collection of vertex disjoint paths that include the maximum number of edges. We show that for any fixed ε > 0, there is an algorithm that (1/2 - ε)-approximates the maximum path cover size of an n-vertex graph in Õ(n) time. This improves upon a (3/8-ε)-approximate Õ(n √n)-time algorithm of Chen, Kannan, and Khanna [ICALP'20]. Equipped with our path cover algorithm, we give an Õ(n) time algorithm that estimates the cost of (1,2)-TSP within a factor of (1.5+ε) which is an improvement over a folklore (1.75 + ε)-approximate Õ(n)-time algorithm, as well as a (1.625+ε)-approximate Õ(n√n)-time algorithm of [CHK ICALP'20]. For graphic TSP, we present an Õ(n) algorithm that estimates the cost of graphic TSP within a factor of 1.83 which is an improvement over a 1.92-approximate Õ(n) time algorithm due to [CHK ICALP'20, Behnezhad FOCS'21]. We show that the approximation can be further improved to 1.66 using n^{2-Ω(1)} time. All of our Õ(n) time algorithms are information-theoretically time-optimal up to polylog n factors. Additionally, we show that our approximation guarantees for path cover and (1,2)-TSP hit a natural barrier: We show better approximations require better sublinear time algorithms for the well-studied maximum matching problem.
Cite as

Soheil Behnezhad, Mohammad Roghani, Aviad Rubinstein, and Amin Saberi. Sublinear Algorithms for TSP via Path Covers. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{behnezhad_et_al:LIPIcs.ICALP.2024.19,
  author =	{Behnezhad, Soheil and Roghani, Mohammad and Rubinstein, Aviad and Saberi, Amin},
  title =	{{Sublinear Algorithms for TSP via Path Covers}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{19:1--19:16},
  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.2024.19},
  URN =		{urn:nbn:de:0030-drops-201623},
  doi =		{10.4230/LIPIcs.ICALP.2024.19},
  annote =	{Keywords: Sublinear Algorithms, Traveling Salesman Problem, Approximation Algorithm, (1, 2)-TSP, Graphic TSP}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.22
Two-Sets Cut-Uncut on Planar Graphs

Authors: Matthias Bentert, Pål Grønås Drange, Fedor V. Fomin, Petr A. Golovach, and Tuukka Korhonen

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

Abstract
We study Two-Sets Cut-Uncut on planar graphs. Therein, one is given an undirected planar graph G and two disjoint sets S and T of vertices as input. The question is, what is the minimum number of edges to remove from G, such that all vertices in S are separated from all vertices in T, while maintaining that every vertex in S, and respectively in T, stays in the same connected component. We show that this problem can be solved in 2^{|S|+|T|} n^𝒪(1) time with a one-sided-error randomized algorithm. Our algorithm implies a polynomial-time algorithm for the network diversion problem on planar graphs, which resolves an open question from the literature. More generally, we show that Two-Sets Cut-Uncut is fixed-parameter tractable when parameterized by the number r of faces in a planar embedding covering the terminals S ∪ T, by providing a 2^𝒪(r) n^𝒪(1)-time algorithm.
Cite as

Matthias Bentert, Pål Grønås Drange, Fedor V. Fomin, Petr A. Golovach, and Tuukka Korhonen. Two-Sets Cut-Uncut on Planar Graphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bentert_et_al:LIPIcs.ICALP.2024.22,
  author =	{Bentert, Matthias and Drange, P\r{a}l Gr{\o}n\r{a}s and Fomin, Fedor V. and Golovach, Petr A. and Korhonen, Tuukka},
  title =	{{Two-Sets Cut-Uncut on Planar Graphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{22:1--22:18},
  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.2024.22},
  URN =		{urn:nbn:de:0030-drops-201654},
  doi =		{10.4230/LIPIcs.ICALP.2024.22},
  annote =	{Keywords: planar graphs, cut-uncut, group-constrained paths}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.33
Kernelization Dichotomies for Hitting Subgraphs Under Structural Parameterizations

Authors: Marin Bougeret, Bart M. P. Jansen, and Ignasi Sau

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

Abstract
For a fixed graph H, the H-Subgraph Hitting problem consists in deleting the minimum number of vertices from an input graph to obtain a graph without any occurrence of H as a subgraph. This problem can be seen as a generalization of Vertex Cover, which corresponds to the case H = K₂. We initiate a study of H-Subgraph Hitting from the point of view of characterizing structural parameterizations that allow for polynomial kernels, within the recently active framework of taking as the parameter the number of vertex deletions to obtain a graph in a "simple" class 𝒞. Our main contribution is to identify graph parameters that, when H-Subgraph Hitting is parameterized by the vertex-deletion distance to a class 𝒞 where any of these parameters is bounded, and assuming standard complexity assumptions and that H is biconnected, allow us to prove the following sharp dichotomy: the problem admits a polynomial kernel if and only if H is a clique. These new graph parameters are inspired by the notion of 𝒞-elimination distance introduced by Bulian and Dawar [Algorithmica 2016], and generalize it in two directions. Our results also apply to the version of the problem where one wants to hit H as an induced subgraph, and imply in particular, that the problems of hitting minors and hitting (induced) subgraphs have a substantially different behavior with respect to the existence of polynomial kernels under structural parameterizations.
Cite as

Marin Bougeret, Bart M. P. Jansen, and Ignasi Sau. Kernelization Dichotomies for Hitting Subgraphs Under Structural Parameterizations. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bougeret_et_al:LIPIcs.ICALP.2024.33,
  author =	{Bougeret, Marin and Jansen, Bart M. P. and Sau, Ignasi},
  title =	{{Kernelization Dichotomies for Hitting Subgraphs Under Structural Parameterizations}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{33:1--33:20},
  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.2024.33},
  URN =		{urn:nbn:de:0030-drops-201766},
  doi =		{10.4230/LIPIcs.ICALP.2024.33},
  annote =	{Keywords: hitting subgraphs, hitting induced subgraphs, parameterized complexity, polynomial kernel, complexity dichotomy, elimination distance}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.57
Non-Linear Paging

Authors: Ilan Doron-Arad and Joseph (Seffi) Naor

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

Abstract
We formulate and study non-linear paging - a broad model of online paging where the size of subsets of pages is determined by a monotone non-linear set function of the pages. This model captures the well-studied classic weighted paging and generalized paging problems, and also submodular and supermodular paging, studied here for the first time, that have a range of applications from virtual memory to machine learning. Unlike classic paging, the cache threshold parameter k does not yield good competitive ratios for non-linear paging. Instead, we introduce a novel parameter 𝓁 that generalizes the notion of cache size to the non-linear setting. We obtain a tight deterministic 𝓁-competitive algorithm for general non-linear paging and a o(log²𝓁)-competitive lower bound for randomized algorithms. Our algorithm is based on a new generic LP for the problem that captures both submodular and supermodular paging, in contrast to LPs used for submodular cover settings. We finally focus on the supermodular paging problem, which is a variant of online set cover and online submodular cover, where sets are repeatedly requested to be removed from the cover. We obtain polylogarithmic lower and upper bounds and an offline approximation algorithm.
Cite as

Ilan Doron-Arad and Joseph (Seffi) Naor. Non-Linear Paging. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 57:1-57:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doronarad_et_al:LIPIcs.ICALP.2024.57,
  author =	{Doron-Arad, Ilan and Naor, Joseph (Seffi)},
  title =	{{Non-Linear Paging}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{57:1--57:19},
  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.2024.57},
  URN =		{urn:nbn:de:0030-drops-202000},
  doi =		{10.4230/LIPIcs.ICALP.2024.57},
  annote =	{Keywords: paging, competitive analysis, non-linear paging, submodular and supermodular functions}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.68
A Tight Subexponential-Time Algorithm for Two-Page Book Embedding

Authors: Robert Ganian, Haiko Müller, Sebastian Ordyniak, Giacomo Paesani, and Mateusz Rychlicki

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

Abstract
A book embedding of a graph is a drawing that maps vertices onto a line and edges to simple pairwise non-crossing curves drawn into "pages", which are half-planes bounded by that line. Two-page book embeddings, i.e., book embeddings into 2 pages, are of special importance as they are both NP-hard to compute and have specific applications. We obtain a 2^𝒪(√n) algorithm for computing a book embedding of an n-vertex graph on two pages - a result which is asymptotically tight under the Exponential Time Hypothesis. As a key tool in our approach, we obtain a single-exponential fixed-parameter algorithm for the same problem when parameterized by the treewidth of the input graph. We conclude by establishing the fixed-parameter tractability of computing minimum-page book embeddings when parameterized by the feedback edge number, settling an open question arising from previous work on the problem.
Cite as

Robert Ganian, Haiko Müller, Sebastian Ordyniak, Giacomo Paesani, and Mateusz Rychlicki. A Tight Subexponential-Time Algorithm for Two-Page Book Embedding. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 68:1-68:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ganian_et_al:LIPIcs.ICALP.2024.68,
  author =	{Ganian, Robert and M\"{u}ller, Haiko and Ordyniak, Sebastian and Paesani, Giacomo and Rychlicki, Mateusz},
  title =	{{A Tight Subexponential-Time Algorithm for Two-Page Book Embedding}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{68:1--68:18},
  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.2024.68},
  URN =		{urn:nbn:de:0030-drops-202114},
  doi =		{10.4230/LIPIcs.ICALP.2024.68},
  annote =	{Keywords: book embedding, page number, subexponential algorithms, subhamiltonicity, feedback edge number}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.69
Quantum Algorithms for Graph Coloring and Other Partitioning, Covering, and Packing Problems

Authors: Serge Gaspers and Jerry Zirui Li

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

Abstract
Let U be a universe on n elements, let k be a positive integer, and let ℱ be a family of (implicitly defined) subsets of U. We consider the problems of partitioning U into k sets from ℱ, covering U with k sets from ℱ, and packing k non-intersecting sets from ℱ into U. Classically, these problems can be solved via inclusion-exclusion in 2ⁿ n^O(1) time [Andreas Björklund et al., 2009]. Quantumly, there are faster algorithms for graph coloring with running time O(1.9140ⁿ) [Kazuya Shimizu and Ryuhei Mori, 2022] and for Set Cover with a small number of sets with running time O(1.7274ⁿ |ℱ|^O(1)) [Andris Ambainis et al., 2019]. In this paper, we give a quantum speedup for Set Partition, Set Cover, and Set Packing whenever there is a classical enumeration algorithm that lends itself to a quadratic quantum speedup, which, for any subinstance on a set X ⊆ U, enumerates at least one member of a k-partition, k-cover, or k-packing (if one exists) restricted to (or projected onto, in the case of k-cover) the set X in c^|X| n^O(1) time with c < 2. Our bounded-error quantum algorithm runs in time (2+c)^{n/2} n^O(1) for Set Partition, Set Cover, and Set Packing. It is obtained by combining three algorithms that have the best running time for some values of c. When c ≤ 1.147899, our algorithm is slightly faster than (2+c)^{n/2} n^O(1); when c approaches 1, it matches the O(1.7274ⁿ |ℱ|^O(1)) running time of [Andris Ambainis et al., 2019] for Set Cover when |ℱ| is subexponential in n. For covering, packing, and partitioning into maximal independent sets, maximal cliques, maximal bicliques, maximal cluster graphs, maximal triangle-free graphs, maximal cographs, maximal claw-free graphs, maximal trivially-perfect graphs, maximal threshold graphs, maximal split graphs, maximal line graphs, and maximal induced forests, we obtain bounded-error quantum algorithms with running times ranging from O(1.8554ⁿ) to O(1.9629ⁿ). Packing and covering by maximal induced matchings can be done quantumly in O(1.8934ⁿ) time. For Graph Coloring (covering with k maximal independent sets), we further improve the running time to O(1.7956ⁿ) by leveraging faster algorithms for coloring with a small number of colors to better balance our divide-and-conquer steps. For Domatic Number (packing k minimal dominating sets), we obtain a O((2-ε)ⁿ) running time for some ε > 0. Several of our results should be of interest to proponents of classical computing: - We present an inclusion-exclusion algorithm with running time O^*(∑_{i=0}^⌊αn⌋ binom(n,i)), which determines, for each X ⊆ U of size at most α n, 0 ≤ α ≤ 1, whether (X,ℱ) has a k-cover, k-partition, or k-packing. This running time is best-possible, up to polynomial factors. - We prove that for any linear-sized vertex subset X ⊆ V of a graph G = (V,E), the number of minimal dominating sets of G that are subsets of X is O((2-ε)^|X|) for some ε > 0.
Cite as

Serge Gaspers and Jerry Zirui Li. Quantum Algorithms for Graph Coloring and Other Partitioning, Covering, and Packing Problems. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 69:1-69:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gaspers_et_al:LIPIcs.ICALP.2024.69,
  author =	{Gaspers, Serge and Li, Jerry Zirui},
  title =	{{Quantum Algorithms for Graph Coloring and Other Partitioning, Covering, and Packing Problems}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{69:1--69:20},
  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.2024.69},
  URN =		{urn:nbn:de:0030-drops-202124},
  doi =		{10.4230/LIPIcs.ICALP.2024.69},
  annote =	{Keywords: Graph algorithms, quantum algorithms, graph coloring, domatic number, set cover, set partition, set packing}
}
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