100 Search Results for "Vassilevska Williams, Virginia"

Document
DOI: 10.4230/LIPIcs.ESA.2024.3
From Donkeys to Kings in Tournaments

Authors: Amir Abboud, Tomer Grossman, Moni Naor, and Tomer Solomon

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

Abstract
A tournament is an orientation of a complete graph. A vertex that can reach every other vertex within two steps is called a king. We study the complexity of finding k kings in a tournament graph. We show that the randomized query complexity of finding k ≤ 3 kings is O(n), and for the deterministic case it takes the same amount of queries (up to a constant) as finding a single king (the best known deterministic algorithm makes O(n^{3/2}) queries). On the other hand, we show that finding k ≥ 4 kings requires Ω(n²) queries, even in the randomized case. We consider the RAM model for k ≥ 4. We show an algorithm that finds k kings in time O(kn²), which is optimal for constant values of k. Alternatively, one can also find k ≥ 4 kings in time n^{ω} (the time for matrix multiplication). We provide evidence that this is optimal for large k by suggesting a fine-grained reduction from a variant of the triangle detection problem.
Cite as

Amir Abboud, Tomer Grossman, Moni Naor, and Tomer Solomon. From Donkeys to Kings in Tournaments. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abboud_et_al:LIPIcs.ESA.2024.3,
  author =	{Abboud, Amir and Grossman, Tomer and Naor, Moni and Solomon, Tomer},
  title =	{{From Donkeys to Kings in Tournaments}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.3},
  URN =		{urn:nbn:de:0030-drops-210740},
  doi =		{10.4230/LIPIcs.ESA.2024.3},
  annote =	{Keywords: Tournament Graphs, Kings, Query Complexity, Fine Grained Complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.4
Worst-Case to Expander-Case Reductions: Derandomized and Generalized

Authors: Amir Abboud and Nathan Wallheimer

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

Abstract
A recent paper by Abboud and Wallheimer [ITCS 2023] presents self-reductions for various fundamental graph problems, which transform worst-case instances to expanders, thus proving that the complexity remains unchanged if the input is assumed to be an expander. An interesting corollary of their self-reductions is that if some problem admits such reduction, then the popular algorithmic paradigm based on expander-decompositions is useless against it. In this paper, we improve their core gadget, which augments a graph to make it an expander while retaining its important structure. Our new core construction has the benefit of being simple to analyze and generalize while obtaining the following results: - A derandomization of the self-reductions, showing that the equivalence between worst-case and expander-case holds even for deterministic algorithms, and ruling out the use of expander-decompositions as a derandomization tool. - An extension of the results to other models of computation, such as the Fully Dynamic model and the Congested Clique model. In the former, we either improve or provide an alternative approach to some recent hardness results for dynamic expander graphs by Henzinger, Paz, and Sricharan [ESA 2022]. In addition, we continue this line of research by designing new self-reductions for more problems, such as Max-Cut and dynamic Densest Subgraph, and demonstrating that the core gadget can be utilized to lift lower bounds based on the OMv Conjecture to expanders.
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Amir Abboud and Nathan Wallheimer. Worst-Case to Expander-Case Reductions: Derandomized and Generalized. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abboud_et_al:LIPIcs.ESA.2024.4,
  author =	{Abboud, Amir and Wallheimer, Nathan},
  title =	{{Worst-Case to Expander-Case Reductions: Derandomized and Generalized}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.4},
  URN =		{urn:nbn:de:0030-drops-210751},
  doi =		{10.4230/LIPIcs.ESA.2024.4},
  annote =	{Keywords: Fine-grained complexity, expander graphs, self-reductions, worst-case to expander-case, expander decomposition, dynamic algorithms, exact and parameterized complexity, max-cut, maximum matching, k-clique detection, densest subgraph}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.9
On Connections Between k-Coloring and Euclidean k-Means

Authors: Enver Aman, Karthik C. S., and Sharath Punna

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

Abstract
In the Euclidean k-means problems we are given as input a set of n points in ℝ^d and the goal is to find a set of k points C ⊆ ℝ^d, so as to minimize the sum of the squared Euclidean distances from each point in P to its closest center in C. In this paper, we formally explore connections between the k-coloring problem on graphs and the Euclidean k-means problem. Our results are as follows: - For all k ≥ 3, we provide a simple reduction from the k-coloring problem on regular graphs to the Euclidean k-means problem. Moreover, our technique extends to enable a reduction from a structured max-cut problem (which may be considered as a partial 2-coloring problem) to the Euclidean 2-means problem. Thus, we have a simple and alternate proof of the NP-hardness of Euclidean 2-means problem. - In the other direction, we mimic the O(1.7297ⁿ) time algorithm of Williams [TCS'05] for the max-cut of problem on n vertices to obtain an algorithm for the Euclidean 2-means problem with the same runtime, improving on the naive exhaustive search running in 2ⁿ⋅ poly(n,d) time. - We prove similar results and connections as above for the Euclidean k-min-sum problem.
Cite as

Enver Aman, Karthik C. S., and Sharath Punna. On Connections Between k-Coloring and Euclidean k-Means. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{aman_et_al:LIPIcs.ESA.2024.9,
  author =	{Aman, Enver and Karthik C. S. and Punna, Sharath},
  title =	{{On Connections Between k-Coloring and Euclidean k-Means}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.9},
  URN =		{urn:nbn:de:0030-drops-210808},
  doi =		{10.4230/LIPIcs.ESA.2024.9},
  annote =	{Keywords: k-means, k-minsum, Euclidean space, fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.16
Longest Common Substring with Gaps and Related Problems

Authors: Aranya Banerjee, Daniel Gibney, and Sharma V. Thankachan

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

Abstract
The longest common substring (also known as longest common factor) and longest common subsequence problems are two well-studied classical string problems. The former is solvable in optimal 𝒪(n) time for two strings of length m and n with m ≤ n, and the latter is solvable in 𝒪(nm) time, which is conditionally optimal under the Strong Exponential Time Hypothesis. In this work, we study the problem of longest common factor with gaps, that is, finding a set of at most k matching substrings obeying precedence conditions with maximum total length. For k = 1, this is equivalent to the longest common factor problem, and for k = m, this is equivalent to the longest common subsequence problem. Our work demonstrates that, for constant k, this problem can be solved in strongly subquadratic time, i.e., nm^{1 - Θ(1)}. Motivated by co-linear chaining applications in Computational Biology, we further demonstrate that the longest common factor with gaps results can be extended to the case where the matches are restricted to maximal exact matches (MEMs). To further demonstrate the applicability of our techniques, we show that a similar approach can be used for a restricted version of the episode matching problem where one seeks an ordered set of at most k matches whose concatenation equals a query pattern P and the length of the substring of T containing the matches is minimized. These solutions all run in strongly subquadratic time for constant k.
Cite as

Aranya Banerjee, Daniel Gibney, and Sharma V. Thankachan. Longest Common Substring with Gaps and Related Problems. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{banerjee_et_al:LIPIcs.ESA.2024.16,
  author =	{Banerjee, Aranya and Gibney, Daniel and Thankachan, Sharma V.},
  title =	{{Longest Common Substring with Gaps and Related Problems}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.16},
  URN =		{urn:nbn:de:0030-drops-210877},
  doi =		{10.4230/LIPIcs.ESA.2024.16},
  annote =	{Keywords: Pattern Matching, Longest Common Subsequence, Episode Matching}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.19
Longest Common Extensions with Wildcards: Trade-Off and Applications

Authors: Gabriel Bathie, Panagiotis Charalampopoulos, and Tatiana Starikovskaya

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

Abstract
We study the Longest Common Extension (LCE) problem in a string containing wildcards. Wildcards (also called "don't cares" or "holes") are special characters that match any other character in the alphabet, similar to the character "?" in Unix commands or "." in regular expression engines. We consider the problem parametrized by G, the number of maximal contiguous groups of wildcards in the input string. Our main contribution is a simple data structure for this problem that can be built in O(n (G/t) log n) time, occupies O(nG/t) space, and answers queries in O(t) time, for any t ∈ [1 .. G]. Up to the O(log n) factor, this interpolates smoothly between the data structure of Crochemore et al. [JDA 2015], which has O(nG) preprocessing time and space, and O(1) query time, and a simple solution based on the "kangaroo jumping" technique [Landau and Vishkin, STOC 1986], which has O(n) preprocessing time and space, and O(G) query time. By establishing a connection between this problem and Boolean matrix multiplication, we show that our solution is optimal up to subpolynomial factors when G = Ω(n) under a widely believed hypothesis. In addition, we develop a new simple, deterministic and combinatorial algorithm for sparse Boolean matrix multiplication. Finally, we show that our data structure can be used to obtain efficient algorithms for approximate pattern matching and structural analysis of strings with wildcards. First, we consider the problem of pattern matching with k errors (i.e., edit operations) in the setting where both the pattern and the text may contain wildcards. The "kangaroo jumping" technique can be adapted to yield an algorithm for this problem with runtime O(n(k+G)), where G is the total number of maximal contiguous groups of wildcards in the text and the pattern and n is the length of the text. By combining "kangaroo jumping" with a tailor-made data structure for LCE queries, Akutsu [IPL 1995] devised an O(n√{km} polylog m)-time algorithm. We improve on both algorithms when k ≪ G ≪ m by giving an algorithm with runtime O(n(k + √{Gk log n})). Secondly, we give O(n√G log n)-time and O(n)-space algorithms for computing the prefix array, as well as the quantum/deterministic border and period arrays of a string with wildcards. This is an improvement over the O(n√{nlog n})-time algorithms of Iliopoulos and Radoszewski [CPM 2016] when G = O(n / log n).
Cite as

Gabriel Bathie, Panagiotis Charalampopoulos, and Tatiana Starikovskaya. Longest Common Extensions with Wildcards: Trade-Off and Applications. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bathie_et_al:LIPIcs.ESA.2024.19,
  author =	{Bathie, Gabriel and Charalampopoulos, Panagiotis and Starikovskaya, Tatiana},
  title =	{{Longest Common Extensions with Wildcards: Trade-Off and Applications}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{19:1--19:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.19},
  URN =		{urn:nbn:de:0030-drops-210904},
  doi =		{10.4230/LIPIcs.ESA.2024.19},
  annote =	{Keywords: Longest common prefix, longest common extension, wildcards, Boolean matrix multiplication, approximate pattern matching, periodicity arrays}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.20
Pattern Matching with Mismatches and Wildcards

Authors: Gabriel Bathie, Panagiotis Charalampopoulos, and Tatiana Starikovskaya

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

Abstract
In this work, we address the problem of approximate pattern matching with wildcards. Given a pattern P of length m containing D wildcards, a text T of length n, and an integer k, our objective is to identify all fragments of T within Hamming distance k from P. Our primary contribution is an algorithm with runtime 𝒪(n + (D+k)(G+k)⋅ n/m) for this problem. Here, G ≤ D represents the number of maximal wildcard fragments in P. We derive this algorithm by elaborating in a non-trivial way on the ideas presented by [Charalampopoulos, Kociumaka, and Wellnitz, FOCS'20] for pattern matching with mismatches (without wildcards). Our algorithm improves over the state of the art when D, G, and k are small relative to n. For instance, if m = n/2, k = G = n^{2/5}, and D = n^{3/5}, our algorithm operates in 𝒪(n) time, surpassing the Ω(n^{6/5}) time requirement of all previously known algorithms. In the case of exact pattern matching with wildcards (k = 0), we present a much simpler algorithm with runtime 𝒪(n + DG ⋅ n/m) that clearly illustrates our main technical innovation: the utilisation of positions of P that do not belong to any fragment of P with a density of wildcards much larger than D/m as anchors for the sought (approximate) occurrences. Notably, our algorithm outperforms the best-known 𝒪(n log m)-time FFT-based algorithms of [Cole and Hariharan, STOC'02] and [Clifford and Clifford, IPL'04] if DG = o(m log m). We complement our algorithmic results with a structural characterization of the k-mismatch occurrences of P. We demonstrate that in a text of length 𝒪(m), these occurrences can be partitioned into 𝒪((D+k)(G+k)) arithmetic progressions. Additionally, we construct an infinite family of examples with Ω((D+k)k) arithmetic progressions of occurrences, leveraging a combinatorial result on progression-free sets [Elkin, SODA'10].
Cite as

Gabriel Bathie, Panagiotis Charalampopoulos, and Tatiana Starikovskaya. Pattern Matching with Mismatches and Wildcards. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 20:1-20:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bathie_et_al:LIPIcs.ESA.2024.20,
  author =	{Bathie, Gabriel and Charalampopoulos, Panagiotis and Starikovskaya, Tatiana},
  title =	{{Pattern Matching with Mismatches and Wildcards}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.20},
  URN =		{urn:nbn:de:0030-drops-210910},
  doi =		{10.4230/LIPIcs.ESA.2024.20},
  annote =	{Keywords: pattern matching, wildcards, mismatches, Hamming distance}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.21
Improved Space Bounds for Subset Sum

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

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

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

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

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@InProceedings{belova_et_al:LIPIcs.ESA.2024.21,
  author =	{Belova, Tatiana and Chukhin, Nikolai and Kulikov, Alexander S. and Mihajlin, Ivan},
  title =	{{Improved Space Bounds for Subset Sum}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.21},
  URN =		{urn:nbn:de:0030-drops-210925},
  doi =		{10.4230/LIPIcs.ESA.2024.21},
  annote =	{Keywords: algorithms, subset sum, complexity, space, upper bounds}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.25
Graph Spanners for Group Steiner Distances

Authors: Davide Bilò, Luciano Gualà, Stefano Leucci, and Alessandro Straziota

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

Abstract
A spanner is a sparse subgraph of a given graph G which preserves distances, measured w.r.t. some distance metric, up to a multiplicative stretch factor. This paper addresses the problem of constructing graph spanners w.r.t. the group Steiner metric, which generalizes the recently introduced beer distance metric. In such a metric we are given a collection of groups of required vertices, and we measure the distance between two vertices as the length of the shortest path between them that traverses at least one required vertex from each group. We discuss the relation between group Steiner spanners and classic spanners and we show that they exhibit strong ties with sourcewise spanners w.r.t. the shortest path metric. Nevertheless, group Steiner spanners capture several interesting scenarios that are not encompassed by existing spanners. This happens, e.g., for the singleton case, in which each group consists of a single required vertex, thus modeling the setting in which routes need to traverse certain points of interests (in any order). We provide several constructions of group Steiner spanners for both the all-pairs and single-source case, which exhibit various size-stretch trade-offs. Notably, we provide spanners with almost-optimal trade-offs for the singleton case. Moreover, some of our spanners also yield novel trade-offs for classical sourcewise spanners. Finally, we also investigate the query times that can be achieved when our spanners are turned into group Steiner distance oracles with the same size, stretch, and building time.
Cite as

Davide Bilò, Luciano Gualà, Stefano Leucci, and Alessandro Straziota. Graph Spanners for Group Steiner Distances. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bilo_et_al:LIPIcs.ESA.2024.25,
  author =	{Bil\`{o}, Davide and Gual\`{a}, Luciano and Leucci, Stefano and Straziota, Alessandro},
  title =	{{Graph Spanners for Group Steiner Distances}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.25},
  URN =		{urn:nbn:de:0030-drops-210968},
  doi =		{10.4230/LIPIcs.ESA.2024.25},
  annote =	{Keywords: Network sparsification, Graph spanners, Group Steiner tree, Distance oracles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.34
Exploring the Approximability Landscape of 3SUM

Authors: Karl Bringmann, Ahmed Ghazy, and Marvin Künnemann

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

Abstract
Since an increasing number of problems in P have conditional lower bounds against exact algorithms, it is natural to study which of these problems can be efficiently approximated. Often, however, there are many potential ways to formulate an approximate version of a problem. We ask: How sensitive is the (in-)approximability of a problem in P to its precise formulation? To this end, we perform a case study using the popular 3SUM problem. Its many equivalent formulations give rise to a wide range of potential approximate relaxations. Specifically, to obtain an approximate relaxation in our framework, one can choose among the options: (a) 3SUM or Convolution 3SUM, (b) monochromatic or trichromatic, (c) allowing under-approximation, over-approximation, or both, (d) approximate decision or approximate optimization, (e) single output or multiple outputs and (f) implicit or explicit target (given as input). We show general reduction principles between some variants and find that we can classify the remaining problems (over polynomially bounded positive integers) into three regimes: 1) (1+ε)-approximable in near-linear time Õ(n + 1/ε), 2) (1+ε)-approximable in near-quadratic time Õ(n/ε) or Õ(n+1/ε²), or 3) non-approximable, i.e., requiring time n^{2± o(1)} even for any approximation factor. In each of these three regimes, we provide matching upper and conditional lower bounds. To prove our results, we establish two results that may be of independent interest: Over polynomially bounded integers, we show subquadratic equivalence of (min,+)-convolution and polyhedral 3SUM, and we prove equivalence of the Strong 3SUM conjecture and the Strong Convolution 3SUM conjecture.
Cite as

Karl Bringmann, Ahmed Ghazy, and Marvin Künnemann. Exploring the Approximability Landscape of 3SUM. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bringmann_et_al:LIPIcs.ESA.2024.34,
  author =	{Bringmann, Karl and Ghazy, Ahmed and K\"{u}nnemann, Marvin},
  title =	{{Exploring the Approximability Landscape of 3SUM}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{34:1--34:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.34},
  URN =		{urn:nbn:de:0030-drops-211057},
  doi =		{10.4230/LIPIcs.ESA.2024.34},
  annote =	{Keywords: Fine-grained Complexity, Conditional Lower Bounds, Approximation Schemes, Min-Plus Convolution}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.35
On Finding Longest Palindromic Subsequences Using Longest Common Subsequences

Authors: Gerth Stølting Brodal, Rolf Fagerberg, and Casper Moldrup Rysgaard

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

Abstract
Two standard textbook problems illustrating dynamic programming are to find the longest common subsequence (LCS) between two strings and to find the longest palindromic subsequence (LPS) of a single string. A popular claim is that the longest palindromic subsequence in a string can be computed as the longest common subsequence between the string and the reversed string. We prove that the correctness of this claim depends on how the longest common subsequence is computed. In particular, we prove that the classical dynamic programming solution by Wagner and Fischer [JACM 1974] for finding an LCS in fact does find an LPS, while a slightly different LCS backtracking strategy makes the algorithm fail to always report a palindrome.
Cite as

Gerth Stølting Brodal, Rolf Fagerberg, and Casper Moldrup Rysgaard. On Finding Longest Palindromic Subsequences Using Longest Common Subsequences. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{brodal_et_al:LIPIcs.ESA.2024.35,
  author =	{Brodal, Gerth St{\o}lting and Fagerberg, Rolf and Rysgaard, Casper Moldrup},
  title =	{{On Finding Longest Palindromic Subsequences Using Longest Common Subsequences}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{35:1--35:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.35},
  URN =		{urn:nbn:de:0030-drops-211068},
  doi =		{10.4230/LIPIcs.ESA.2024.35},
  annote =	{Keywords: Palindromic subsequence, longest common subsequence, dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.45
Near Optimal Dual Fault Tolerant Distance Oracle

Authors: Dipan Dey and Manoj Gupta

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

Abstract
We present a dual fault-tolerant distance oracle for undirected and unweighted graphs. Given a set F of two edges, as well as a source node s and a destination node t, our oracle returns the length of the shortest path from s to t that avoids F in O(1) time with a high probability. The space complexity of our oracle is Õ(n²) , making it nearly optimal in terms of both space and query time. Prior to our work, Pettie and Duan [SODA 2009] designed a dual fault-tolerant distance oracle that required Õ(n²) space and O(log n) query time. In addition to improving the query time, our oracle is much simpler than the previous approach.
Cite as

Dipan Dey and Manoj Gupta. Near Optimal Dual Fault Tolerant Distance Oracle. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 45:1-45:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dey_et_al:LIPIcs.ESA.2024.45,
  author =	{Dey, Dipan and Gupta, Manoj},
  title =	{{Near Optimal Dual Fault Tolerant Distance Oracle}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{45:1--45:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.45},
  URN =		{urn:nbn:de:0030-drops-211164},
  doi =		{10.4230/LIPIcs.ESA.2024.45},
  annote =	{Keywords: Distance Sensitive Oracle, Dual Fault Distance Oracle}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.51
Better Diameter Algorithms for Bounded VC-Dimension Graphs and Geometric Intersection Graphs

Authors: Lech Duraj, Filip Konieczny, and Krzysztof Potępa

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

Abstract
We develop a framework for algorithms finding the diameter in graphs of bounded distance Vapnik-Chervonenkis dimension, in (parameterized) subquadratic time complexity. The class of bounded distance VC-dimension graphs is wide, including, e.g. all minor-free graphs. We build on the work of Ducoffe et al. [SODA'20, SIGCOMP'22], improving their technique. With our approach the algorithms become simpler and faster, working in 𝒪{(k ⋅ n^{1-1/d} ⋅ m ⋅ polylog(n))} time complexity for the graph on n vertices and m edges, where k is the diameter and d is the distance VC-dimension of the graph. Furthermore, it allows us to use the improved technique in more general setting. In particular, we use this framework for geometric intersection graphs, i.e. graphs where vertices are identical geometric objects on a plane and the adjacency is defined by intersection. Applying our approach for these graphs, we partially answer a question posed by Bringmann et al. [SoCG'22], finding an 𝒪{(n^{7/4} ⋅ polylog(n))} parameterized diameter algorithm for unit square intersection graph of size n, as well as a more general algorithm for convex polygon intersection graphs.
Cite as

Lech Duraj, Filip Konieczny, and Krzysztof Potępa. Better Diameter Algorithms for Bounded VC-Dimension Graphs and Geometric Intersection Graphs. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 51:1-51:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{duraj_et_al:LIPIcs.ESA.2024.51,
  author =	{Duraj, Lech and Konieczny, Filip and Pot\k{e}pa, Krzysztof},
  title =	{{Better Diameter Algorithms for Bounded VC-Dimension Graphs and Geometric Intersection Graphs}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{51:1--51:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.51},
  URN =		{urn:nbn:de:0030-drops-211229},
  doi =		{10.4230/LIPIcs.ESA.2024.51},
  annote =	{Keywords: Graph Diameter, Geometric Intersection Graphs, Vapnik-Chervonenkis Dimension}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.57
Removing the log Factor from (min,+)-Products on Bounded Range Integer Matrices

Authors: Dvir Fried, Tsvi Kopelowitz, and Ely Porat

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

Abstract
We revisit the problem of multiplying two square matrices over the (min, +) semi-ring, where all entries are integers from a bounded range [-M : M] ∪ {∞}. The current state of the art for this problem is a simple O(M n^{ω} log M) time algorithm by Alon, Galil and Margalit [JCSS'97], where ω is the exponent in the runtime of the fastest matrix multiplication (FMM) algorithm. We design a new simple algorithm whose runtime is O(M n^ω + M n² log M), thereby removing the logM factor in the runtime if ω > 2 or if n^ω = Ω (n²log n).
Cite as

Dvir Fried, Tsvi Kopelowitz, and Ely Porat. Removing the log Factor from (min,+)-Products on Bounded Range Integer Matrices. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 57:1-57:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fried_et_al:LIPIcs.ESA.2024.57,
  author =	{Fried, Dvir and Kopelowitz, Tsvi and Porat, Ely},
  title =	{{Removing the log Factor from (min,+)-Products on Bounded Range Integer Matrices}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{57:1--57:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.57},
  URN =		{urn:nbn:de:0030-drops-211283},
  doi =		{10.4230/LIPIcs.ESA.2024.57},
  annote =	{Keywords: FMM, (min , +)-product, FFT}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.65
A Nearly Linear Time Construction of Approximate Single-Source Distance Sensitivity Oracles

Authors: Kaito Harada, Naoki Kitamura, Taisuke Izumi, and Toshimitsu Masuzawa

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

Abstract
An α-approximate vertex fault-tolerant distance sensitivity oracle (α-VSDO) for a weighted input graph G = (V, E, w) and a source vertex s ∈ V is the data structure answering an α-approximate distance from s to t in G-x for any given query (x, t) ∈ V × V. It is a data structure version of the so-called single-source replacement path problem (SSRP). In this paper, we present a new nearly linear-time algorithm of constructing a (1 + ε)-VSDO for any directed input graph with polynomially bounded integer edge weights. More precisely, the presented oracle attains Õ(m log (nW)/ ε + n log² (nW)/ε²) construction time, Õ(n log (nW) / ε) size, and Õ(1/ε) query time, where n is the number of vertices, m is the number of edges, and W is the maximum edge weight. These bounds are all optimal up to polylogarithmic factors. To the best of our knowledge, this is the first non-trivial algorithm for SSRP/VSDO beating Õ(mn) computation time for directed graphs with general edge weight functions, and also the first nearly linear-time construction breaking approximation factor 3. Such a construction has been unknown even for undirected and unweighted graphs. In addition, our result implies that the known conditional lower bounds for the exact SSRP computation does not apply to the case of approximation.
Cite as

Kaito Harada, Naoki Kitamura, Taisuke Izumi, and Toshimitsu Masuzawa. A Nearly Linear Time Construction of Approximate Single-Source Distance Sensitivity Oracles. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 65:1-65:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{harada_et_al:LIPIcs.ESA.2024.65,
  author =	{Harada, Kaito and Kitamura, Naoki and Izumi, Taisuke and Masuzawa, Toshimitsu},
  title =	{{A Nearly Linear Time Construction of Approximate Single-Source Distance Sensitivity Oracles}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{65:1--65:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.65},
  URN =		{urn:nbn:de:0030-drops-211367},
  doi =		{10.4230/LIPIcs.ESA.2024.65},
  annote =	{Keywords: data structure, distance sensitivity oracle, replacement path problem, graph algorithm}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.72
Connectivity Oracles for Predictable Vertex Failures

Authors: Bingbing Hu, Evangelos Kosinas, and Adam Polak

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

Abstract
The problem of designing connectivity oracles supporting vertex failures is one of the basic data structures problems for undirected graphs. It is already well understood: previous works [Duan-Pettie STOC'10; Long-Saranurak FOCS'22] achieve query time linear in the number of failed vertices, and it is conditionally optimal as long as we require preprocessing time polynomial in the size of the graph and update time polynomial in the number of failed vertices. We revisit this problem in the paradigm of algorithms with predictions: we ask if the query time can be improved if the set of failed vertices can be predicted beforehand up to a small number of errors. More specifically, we design a data structure that, given a graph G = (V,E) and a set of vertices predicted to fail D̂ ⊆ V of size d = |D̂|, preprocesses it in time Õ(d|E|) and then can receive an update given as the symmetric difference between the predicted and the actual set of failed vertices D̂△D = (D̂ ⧵ D) ∪ (D ⧵ D̂) of size η = |D̂△D|, process it in time Õ(η⁴), and after that answer connectivity queries in G ⧵ D in time O(η). Viewed from another perspective, our data structure provides an improvement over the state of the art for the fully dynamic subgraph connectivity problem in the sensitivity setting [Henzinger-Neumann ESA'16]. We argue that the preprocessing time and query time of our data structure are conditionally optimal under standard fine-grained complexity assumptions.
Cite as

Bingbing Hu, Evangelos Kosinas, and Adam Polak. Connectivity Oracles for Predictable Vertex Failures. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 72:1-72:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hu_et_al:LIPIcs.ESA.2024.72,
  author =	{Hu, Bingbing and Kosinas, Evangelos and Polak, Adam},
  title =	{{Connectivity Oracles for Predictable Vertex Failures}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{72:1--72:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.72},
  URN =		{urn:nbn:de:0030-drops-211437},
  doi =		{10.4230/LIPIcs.ESA.2024.72},
  annote =	{Keywords: Data structures, graph connectivity, algorithms with predictions}
}
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