21 Search Results for "Iacono, John"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.38
The Group Access Bounds for Binary Search Trees

Authors: Parinya Chalermsook, Manoj Gupta, Wanchote Jiamjitrak, Akash Pareek, and Sorrachai Yingchareonthawornchai

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

Abstract
The access lemma (Sleator and Tarjan, JACM 1985) is a property of binary search trees (BSTs) that implies interesting consequences such as static optimality, static finger, and working set property on any access sequence X = (x_1,x_2,… ,x_m). However, there are known corollaries of the dynamic optimality that cannot be derived via the access lemma, such as the dynamic finger, and any o(log n)-competitive ratio to the optimal BST where n is the number of keys. In this paper, we introduce the group access bound that can be defined with respect to a reference group access tree. Group access bounds generalize the access lemma and imply properties that are far stronger than those implied by the classical access lemma. For each of the following results, there is a group access tree whose group access bound 1) Is O(√{log n})-competitive to the optimal BST. 2) Achieves the k-finger bound with an additive term of O(m log k log log n) (randomized) when the reference tree is an almost complete binary tree. 3) Satisfies the unified bound with an additive term of O(m log log n). 4) Matches the unified bound with a time window k with an additive term of O(m log k log log n) (randomized). Furthermore, we prove the simulation theorem: For every group access tree, there is an online BST algorithm that is O(1)-competitive with its group access bound. In particular, any new group access bound will automatically imply a new BST algorithm achieving the same bound. Thereby, we obtain an improved k-finger bound (reference tree is an almost complete binary tree), an improved unified bound with a time window k, and matching the best-known bound for Unified bound in the BST model. Since any dynamically optimal BST must achieve the group access bounds, we believe our results provide a new direction towards proving o(log n)-competitiveness of the Splay tree and Greedy, two prime candidates for the dynamic optimality conjecture.
Cite as

Parinya Chalermsook, Manoj Gupta, Wanchote Jiamjitrak, Akash Pareek, and Sorrachai Yingchareonthawornchai. The Group Access Bounds for Binary Search Trees. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chalermsook_et_al:LIPIcs.ICALP.2024.38,
  author =	{Chalermsook, Parinya and Gupta, Manoj and Jiamjitrak, Wanchote and Pareek, Akash and Yingchareonthawornchai, Sorrachai},
  title =	{{The Group Access Bounds for Binary Search Trees}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{38:1--38:18},
  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.2024.38},
  URN =		{urn:nbn:de:0030-drops-201817},
  doi =		{10.4230/LIPIcs.ICALP.2024.38},
  annote =	{Keywords: Dynamic Optimality, Binary Search Tree, Online Algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.64
Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time

Authors: Nick Fischer and Leo Wennmann

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

Abstract
In this work we revisit the elementary scheduling problem 1||∑ p_j U_j. The goal is to select, among n jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence without violating their due dates. This problem is NP-hard, but a classical algorithm by Lawler and Moore from the 60s solves this problem in pseudo-polynomial time O(nP), where P is the total processing time of all jobs. With the aim to develop best-possible pseudo-polynomial-time algorithms, a recent wave of results has improved Lawler and Moore’s algorithm for 1||∑ p_j U_j: First to time Õ(P^{7/4}) [Bringmann, Fischer, Hermelin, Shabtay, Wellnitz; ICALP'20], then to time Õ(P^{5/3}) [Klein, Polak, Rohwedder; SODA'23], and finally to time Õ(P^{7/5}) [Schieber, Sitaraman; WADS'23]. It remained an exciting open question whether these works can be improved further. In this work we develop an algorithm in near-linear time Õ(P) for the 1||∑ p_j U_j problem. This running time not only significantly improves upon the previous results, but also matches conditional lower bounds based on the Strong Exponential Time Hypothesis or the Set Cover Hypothesis and is therefore likely optimal (up to subpolynomial factors). Our new algorithm also extends to the case of m machines in time Õ(P^m). In contrast to the previous improvements, we take a different, more direct approach inspired by the recent reductions from Modular Subset Sum to dynamic string problems. We thereby arrive at a satisfyingly simple algorithm.
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Nick Fischer and Leo Wennmann. Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 64:1-64:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fischer_et_al:LIPIcs.ICALP.2024.64,
  author =	{Fischer, Nick and Wennmann, Leo},
  title =	{{Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{64:1--64:15},
  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.2024.64},
  URN =		{urn:nbn:de:0030-drops-202079},
  doi =		{10.4230/LIPIcs.ICALP.2024.64},
  annote =	{Keywords: Scheduling, Fine-Grained Complexity, Dynamic Strings}
}
Document
DOI: 10.4230/DagRep.13.5.114
Scalable Data Structures (Dagstuhl Seminar 23211)

Authors: Gerth Stølting Brodal, John Iacono, László Kozma, Vijaya Ramachandran, and Justin Dallant

Published in: Dagstuhl Reports, Volume 13, Issue 5 (2023)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23211 "Scalable Data Structures". Data structures enable the organization, storage and retrieval of data across a variety of applications. As they are deployed at unprecedented scales, data structures can profoundly affect the efficiency of almost all computational tasks. The study of data structures thus continues to be an important and active area of research with an interplay between data structure design and analysis, developments in computer hardware, and the needs of modern applications. The extended abstracts included in this report give a snapshot of the current state of research on scalable data structures and establish directions for future developments in the field.
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Gerth Stølting Brodal, John Iacono, László Kozma, Vijaya Ramachandran, and Justin Dallant. Scalable Data Structures (Dagstuhl Seminar 23211). In Dagstuhl Reports, Volume 13, Issue 5, pp. 114-135, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{brodal_et_al:DagRep.13.5.114,
  author =	{Brodal, Gerth St{\o}lting and Iacono, John and Kozma, L\'{a}szl\'{o} and Ramachandran, Vijaya and Dallant, Justin},
  title =	{{Scalable Data Structures (Dagstuhl Seminar 23211)}},
  pages =	{114--135},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{5},
  editor =	{Brodal, Gerth St{\o}lting and Iacono, John and Kozma, L\'{a}szl\'{o} and Ramachandran, Vijaya and Dallant, Justin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.5.114},
  URN =		{urn:nbn:de:0030-drops-193676},
  doi =		{10.4230/DagRep.13.5.114},
  annote =	{Keywords: algorithms, big data, computational models, data structures, GPU computing, parallel computation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.21
External-Memory Dictionaries with Worst-Case Update Cost

Authors: Rathish Das, John Iacono, and Yakov Nekrich

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

Abstract
The B^ε-tree [Brodal and Fagerberg 2003] is a simple I/O-efficient external-memory-model data structure that supports updates orders of magnitude faster than B-tree with a query performance comparable to the B-tree: for any positive constant ε < 1 insertions and deletions take O(1/B^(1-ε) log_B N) time (rather than O(log_BN) time for the classic B-tree), queries take O(log_B N) time and range queries returning k items take O(log_B N + k/B) time. Although the B^ε-tree has an optimal update/query tradeoff, the runtimes are amortized. Another structure, the write-optimized skip list, introduced by Bender et al. [PODS 2017], has the same performance as the B^ε-tree but with runtimes that are randomized rather than amortized. In this paper, we present a variant of the B^ε-tree with deterministic worst-case running times that are identical to the original’s amortized running times.
Cite as

Rathish Das, John Iacono, and Yakov Nekrich. External-Memory Dictionaries with Worst-Case Update Cost. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 21:1-21:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{das_et_al:LIPIcs.ISAAC.2022.21,
  author =	{Das, Rathish and Iacono, John and Nekrich, Yakov},
  title =	{{External-Memory Dictionaries with Worst-Case Update Cost}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{21:1--21:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.21},
  URN =		{urn:nbn:de:0030-drops-173060},
  doi =		{10.4230/LIPIcs.ISAAC.2022.21},
  annote =	{Keywords: Data Structures, External Memory, Buffer Tree}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.39
Conditional Lower Bounds for Dynamic Geometric Measure Problems

Authors: Justin Dallant and John Iacono

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

Abstract
We give new polynomial lower bounds for a number of dynamic measure problems in computational geometry. These lower bounds hold in the Word-RAM model, conditioned on the hardness of either 3SUM, APSP, or the Online Matrix-Vector Multiplication problem [Henzinger et al., STOC 2015]. In particular we get lower bounds in the incremental and fully-dynamic settings for counting maximal or extremal points in ℝ³, different variants of Klee’s Measure Problem, problems related to finding the largest empty disk in a set of points, and querying the size of the i'th convex layer in a planar set of points. We also answer a question of Chan et al. [SODA 2022] by giving a conditional lower bound for dynamic approximate square set cover. While many conditional lower bounds for dynamic data structures have been proven since the seminal work of Pătraşcu [STOC 2010], few of them relate to computational geometry problems. This is the first paper focusing on this topic. Most problems we consider can be solved in O(nlog n) time in the static case and their dynamic versions have only been approached from the perspective of improving known upper bounds. One exception to this is Klee’s measure problem in ℝ², for which Chan [CGTA 2010] gave an unconditional Ω(√n) lower bound on the worst-case update time. By a similar approach, we show that such a lower bound also holds for an important special case of Klee’s measure problem in ℝ³ known as the Hypervolume Indicator problem, even for amortized runtime in the incremental setting.
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Justin Dallant and John Iacono. Conditional Lower Bounds for Dynamic Geometric Measure Problems. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dallant_et_al:LIPIcs.ESA.2022.39,
  author =	{Dallant, Justin and Iacono, John},
  title =	{{Conditional Lower Bounds for Dynamic Geometric Measure Problems}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{39:1--39:17},
  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.2022.39},
  URN =		{urn:nbn:de:0030-drops-169777},
  doi =		{10.4230/LIPIcs.ESA.2022.39},
  annote =	{Keywords: Computational geometry, Fine-grained complexity, Dynamic data structures}
}
Document
DOI: 10.4230/LIPIcs.FUN.2022.13
How Fast Can We Play Tetris Greedily with Rectangular Pieces?

Authors: Justin Dallant and John Iacono

Published in: LIPIcs, Volume 226, 11th International Conference on Fun with Algorithms (FUN 2022)

Abstract
Consider a variant of Tetris played on a board of width w and infinite height, where the pieces are axis-aligned rectangles of arbitrary integer dimensions, the pieces can only be moved before letting them drop, and a row does not disappear once it is full. Suppose we want to follow a greedy strategy: let each rectangle fall where it will end up the lowest given the current state of the board. To do so, we want a data structure which can always suggest a greedy move. In other words, we want a data structure which maintains a set of O(n) rectangles, supports queries which return where to drop the rectangle, and updates which insert a rectangle dropped at a certain position and return the height of the highest point in the updated set of rectangles. We show via a reduction from the Multiphase problem [Pătraşcu, 2010] that on a board of width w = Θ(n), if the OMv conjecture [Henzinger et al., 2015] is true, then both operations cannot be supported in time O(n^{1/2-ε}) simultaneously. The reduction also implies polynomial bounds from the 3-SUM conjecture and the APSP conjecture. On the other hand, we show that there is a data structure supporting both operations in O(n^{1/2}log^{3/2}n) time on boards of width n^O(1), matching the lower bound up to an n^o(1) factor.
Cite as

Justin Dallant and John Iacono. How Fast Can We Play Tetris Greedily with Rectangular Pieces?. In 11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dallant_et_al:LIPIcs.FUN.2022.13,
  author =	{Dallant, Justin and Iacono, John},
  title =	{{How Fast Can We Play Tetris Greedily with Rectangular Pieces?}},
  booktitle =	{11th International Conference on Fun with Algorithms (FUN 2022)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-232-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{226},
  editor =	{Fraigniaud, Pierre and Uno, Yushi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2022.13},
  URN =		{urn:nbn:de:0030-drops-159839},
  doi =		{10.4230/LIPIcs.FUN.2022.13},
  annote =	{Keywords: Tetris, Fine-grained complexity, Dynamic data structures, Axis-aligned rectangles}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.3
Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model

Authors: Boris Aronov, Mark de Berg, Jean Cardinal, Esther Ezra, John Iacono, and Micha Sharir

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
We present subquadratic algorithms in the algebraic decision-tree model for several 3Sum-hard geometric problems, all of which can be reduced to the following question: Given two sets A, B, each consisting of n pairwise disjoint segments in the plane, and a set C of n triangles in the plane, we want to count, for each triangle Δ ∈ C, the number of intersection points between the segments of A and those of B that lie in Δ. The problems considered in this paper have been studied by Chan (2020), who gave algorithms that solve them, in the standard real-RAM model, in O((n²/log²n) log^O(1) log n) time. We present solutions in the algebraic decision-tree model whose cost is O(n^{60/31+ε}), for any ε > 0. Our approach is based on a primal-dual range searching mechanism, which exploits the multi-level polynomial partitioning machinery recently developed by Agarwal, Aronov, Ezra, and Zahl (2020). A key step in the procedure is a variant of point location in arrangements, say of lines in the plane, which is based solely on the order type of the lines, a "handicap" that turns out to be beneficial for speeding up our algorithm.
Cite as

Boris Aronov, Mark de Berg, Jean Cardinal, Esther Ezra, John Iacono, and Micha Sharir. Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{aronov_et_al:LIPIcs.ISAAC.2021.3,
  author =	{Aronov, Boris and de Berg, Mark and Cardinal, Jean and Ezra, Esther and Iacono, John and Sharir, Micha},
  title =	{{Subquadratic Algorithms for Some 3Sum-Hard Geometric Problems in the Algebraic Decision Tree Model}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{3:1--3:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.3},
  URN =		{urn:nbn:de:0030-drops-154363},
  doi =		{10.4230/LIPIcs.ISAAC.2021.3},
  annote =	{Keywords: Computational geometry, Algebraic decision-tree model, Polynomial partitioning, Primal-dual range searching, Order types, Point location, Hierarchical partitions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.24
An Instance-Optimal Algorithm for Bichromatic Rectangular Visibility

Authors: Jean Cardinal, Justin Dallant, and John Iacono

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
Afshani, Barbay and Chan (2017) introduced the notion of instance-optimal algorithm in the order-oblivious setting. An algorithm A is instance-optimal in the order-oblivious setting for a certain class of algorithms 𝒜 if the following hold: - A takes as input a sequence of objects from some domain; - for any instance σ and any algorithm A' ∈ 𝒜, the runtime of A on σ is at most a constant factor removed from the runtime of A' on the worst possible permutation of σ. If we identify permutations of a sequence as representing the same instance, this essentially states that A is optimal on every possible input (and not only in the worst case). We design instance-optimal algorithms for the problem of reporting, given a bichromatic set of points in the plane S, all pairs consisting of points of different color which span an empty axis-aligned rectangle (or reporting all points which appear in such a pair). This problem has applications for training-set reduction in nearest-neighbour classifiers. It is also related to the problem consisting of finding the decision boundaries of a euclidean nearest-neighbour classifier, for which Bremner et al. (2005) gave an optimal output-sensitive algorithm. By showing the existence of an instance-optimal algorithm in the order-oblivious setting for this problem we push the methods of Afshani et al. closer to their limits by adapting and extending them to a setting which exhibits highly non-local features. Previous problems for which instance-optimal algorithms were proven to exist were based solely on local relationships between points in a set.
Cite as

Jean Cardinal, Justin Dallant, and John Iacono. An Instance-Optimal Algorithm for Bichromatic Rectangular Visibility. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cardinal_et_al:LIPIcs.ESA.2021.24,
  author =	{Cardinal, Jean and Dallant, Justin and Iacono, John},
  title =	{{An Instance-Optimal Algorithm for Bichromatic Rectangular Visibility}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.24},
  URN =		{urn:nbn:de:0030-drops-146057},
  doi =		{10.4230/LIPIcs.ESA.2021.24},
  annote =	{Keywords: computational geometry, instance-optimality, colored point sets, empty rectangles, visibility}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.25
Worst-Case Efficient Dynamic Geometric Independent Set

Authors: Jean Cardinal, John Iacono, and Grigorios Koumoutsos

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We consider the problem of maintaining an approximate maximum independent set of geometric objects under insertions and deletions. We present a data structure that maintains a constant-factor approximate maximum independent set for broad classes of fat objects in d dimensions, where d is assumed to be a constant, in sublinear worst-case update time. This gives the first results for dynamic independent set in a wide variety of geometric settings, such as disks, fat polygons, and their high-dimensional equivalents. For axis-aligned squares and hypercubes, our result improves upon all (recently announced) previous works. We obtain, in particular, a dynamic (4+ε)-approximation for squares, with O(log⁴ n) worst-case update time. Our result is obtained via a two-level approach. First, we develop a dynamic data structure which stores all objects and provides an approximate independent set when queried, with output-sensitive running time. We show that via standard methods such a structure can be used to obtain a dynamic algorithm with amortized update time bounds. Then, to obtain worst-case update time algorithms, we develop a generic deamortization scheme that with each insertion/deletion keeps (i) the update time bounded and (ii) the number of changes in the independent set constant. We show that such a scheme is applicable to fat objects by showing an appropriate generalization of a separator theorem. Interestingly, we show that our deamortization scheme is also necessary in order to obtain worst-case update bounds: If for a class of objects our scheme is not applicable, then no constant-factor approximation with sublinear worst-case update time is possible. We show that such a lower bound applies even for seemingly simple classes of geometric objects including axis-aligned rectangles in the plane.
Cite as

Jean Cardinal, John Iacono, and Grigorios Koumoutsos. Worst-Case Efficient Dynamic Geometric Independent Set. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cardinal_et_al:LIPIcs.ESA.2021.25,
  author =	{Cardinal, Jean and Iacono, John and Koumoutsos, Grigorios},
  title =	{{Worst-Case Efficient Dynamic Geometric Independent Set}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{25:1--25:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.25},
  URN =		{urn:nbn:de:0030-drops-146061},
  doi =		{10.4230/LIPIcs.ESA.2021.25},
  annote =	{Keywords: Maximum independent set, deamortization, approximation}
}
Document
DOI: 10.4230/DagRep.11.1.1
Scalable Data Structures (Dagstuhl Seminar 21071)

Authors: Gerth Stølting Brodal, John Iacono, Markus E. Nebel, and Vijaya Ramachandran

Published in: Dagstuhl Reports, Volume 11, Issue 1 (2021)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 21071 "Scalable Data Structure". Even if the field of data structures is quite mature, new trends and limitations in computer hardware together with the ever-increasing amounts of data that need to be processed raise new questions with respect to efficiency and continuously challenge the existing models of computation. Thermal and electrical power constraints have caused technology to reach "the power wall" with stagnating single processor performance, meaning that all nontrivial applications need to address scalability with multiple processors, a memory hierarchy and other communication challenges. Scalable data structures are pivotal to this process since they form the backbone of the algorithms driving these applications. The extended abstracts included in this report contain both recent state of the art advances and lay the foundation for new directions within data structures research.
Cite as

Gerth Stølting Brodal, John Iacono, Markus E. Nebel, and Vijaya Ramachandran. Scalable Data Structures (Dagstuhl Seminar 21071). In Dagstuhl Reports, Volume 11, Issue 1, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Article{brodal_et_al:DagRep.11.1.1,
  author =	{Brodal, Gerth St{\o}lting and Iacono, John and Nebel, Markus E. and Ramachandran, Vijaya},
  title =	{{Scalable Data Structures (Dagstuhl Seminar 21071)}},
  pages =	{1--23},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2021},
  volume =	{11},
  number =	{1},
  editor =	{Brodal, Gerth St{\o}lting and Iacono, John and Nebel, Markus E. and Ramachandran, Vijaya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.11.1.1},
  URN =		{urn:nbn:de:0030-drops-143481},
  doi =		{10.4230/DagRep.11.1.1},
  annote =	{Keywords: algorithms, big data, data structures, GPU computing, large data sets, models of computation, parallel algorithms}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.16
The Variable-Processor Cup Game

Authors: William Kuszmaul and Alek Westover

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
The problem of scheduling tasks on p processors so that no task ever gets too far behind is often described as a game with cups and water. In the p-processor cup game on n cups, there are two players, a filler and an emptier, that take turns adding and removing water from a set of n cups. In each turn, the filler adds p units of water to the cups, placing at most 1 unit of water in each cup, and then the emptier selects p cups to remove up to 1 unit of water from. The emptier’s goal is to minimize the backlog, which is the height of the fullest cup. The p-processor cup game has been studied in many different settings, dating back to the late 1960’s. All of the past work shares one common assumption: that p is fixed. This paper initiates the study of what happens when the number of available processors p varies over time, resulting in what we call the variable-processor cup game. Remarkably, the optimal bounds for the variable-processor cup game differ dramatically from its classical counterpart. Whereas the p-processor cup has optimal backlog Θ(log n), the variable-processor game has optimal backlog Θ(n). Moreover, there is an efficient filling strategy that yields backlog Ω(n^{1 - ε}) in quasi-polynomial time against any deterministic emptying strategy. We additionally show that straightforward uses of randomization cannot be used to help the emptier. In particular, for any positive constant Δ, and any Δ-greedy-like randomized emptying algorithm 𝒜, there is a filling strategy that achieves backlog Ω(n^{1 - ε}) against 𝒜 in quasi-polynomial time.
Cite as

William Kuszmaul and Alek Westover. The Variable-Processor Cup Game. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{kuszmaul_et_al:LIPIcs.ITCS.2021.16,
  author =	{Kuszmaul, William and Westover, Alek},
  title =	{{The Variable-Processor Cup Game}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{16:1--16:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.16},
  URN =		{urn:nbn:de:0030-drops-135559},
  doi =		{10.4230/LIPIcs.ITCS.2021.16},
  annote =	{Keywords: scheduling, cup games, online algorithms, lower bounds}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2020.20
Sparse Regression via Range Counting

Authors: Jean Cardinal and Aurélien Ooms

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
The sparse regression problem, also known as best subset selection problem, can be cast as follows: Given a set S of n points in ℝ^d, a point y∈ ℝ^d, and an integer 2 ≤ k ≤ d, find an affine combination of at most k points of S that is nearest to y. We describe a O(n^{k-1} log^{d-k+2} n)-time randomized (1+ε)-approximation algorithm for this problem with d and ε constant. This is the first algorithm for this problem running in time o(n^k). Its running time is similar to the query time of a data structure recently proposed by Har-Peled, Indyk, and Mahabadi (ICALP'18), while not requiring any preprocessing. Up to polylogarithmic factors, it matches a conditional lower bound relying on a conjecture about affine degeneracy testing. In the special case where k = d = O(1), we provide a simple O_δ(n^{d-1+δ})-time deterministic exact algorithm, for any δ > 0. Finally, we show how to adapt the approximation algorithm for the sparse linear regression and sparse convex regression problems with the same running time, up to polylogarithmic factors.
Cite as

Jean Cardinal and Aurélien Ooms. Sparse Regression via Range Counting. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 20:1-20:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cardinal_et_al:LIPIcs.SWAT.2020.20,
  author =	{Cardinal, Jean and Ooms, Aur\'{e}lien},
  title =	{{Sparse Regression via Range Counting}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{20:1--20:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.20},
  URN =		{urn:nbn:de:0030-drops-122677},
  doi =		{10.4230/LIPIcs.SWAT.2020.20},
  annote =	{Keywords: Sparse Linear Regression, Orthogonal Range Searching, Affine Degeneracy Testing, Nearest Neighbors, Hyperplane Arrangements}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2020.8
Testing Polynomials for Vanishing on Cartesian Products of Planar Point Sets

Authors: Boris Aronov, Esther Ezra, and Micha Sharir

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
We present subquadratic algorithms, in the algebraic decision-tree model of computation, for detecting whether there exists a triple of points, belonging to three respective sets A, B, and C of points in the plane, that satisfy a certain polynomial equation or two equations. The best known instance of such a problem is testing for the existence of a collinear triple of points in A×B×C, a classical 3SUM-hard problem that has so far defied any attempt to obtain a subquadratic solution, whether in the (uniform) real RAM model, or in the algebraic decision-tree model. While we are still unable to solve this problem, in full generality, in subquadratic time, we obtain such a solution, in the algebraic decision-tree model, that uses only roughly O(n^(28/15)) constant-degree polynomial sign tests, for the special case where two of the sets lie on one-dimensional curves and the third is placed arbitrarily in the plane. Our technique is fairly general, and applies to any other problem where we seek a triple that satisfies a single polynomial equation, e.g., determining whether A× B× C contains a triple spanning a unit-area triangle. This result extends recent work by Barba et al. [Luis Barba et al., 2019] and by Chan [Timothy M. Chan, 2020], where all three sets A, B, and C are assumed to be one-dimensional. While there are common features in the high-level approaches, here and in [Luis Barba et al., 2019], the actual analysis in this work becomes more involved and requires new methods and techniques, involving polynomial partitions and other related tools. As a second application of our technique, we again have three n-point sets A, B, and C in the plane, and we want to determine whether there exists a triple (a,b,c) ∈ A×B×C that simultaneously satisfies two real polynomial equations. For example, this is the setup when testing for the existence of pairs of similar triangles spanned by the input points, in various contexts discussed later in the paper. We show that problems of this kind can be solved with roughly O(n^(24/13)) constant-degree polynomial sign tests. These problems can be extended to higher dimensions in various ways, and we present subquadratic solutions to some of these extensions, in the algebraic decision-tree model.
Cite as

Boris Aronov, Esther Ezra, and Micha Sharir. Testing Polynomials for Vanishing on Cartesian Products of Planar Point Sets. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{aronov_et_al:LIPIcs.SoCG.2020.8,
  author =	{Aronov, Boris and Ezra, Esther and Sharir, Micha},
  title =	{{Testing Polynomials for Vanishing on Cartesian Products of Planar Point Sets}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.8},
  URN =		{urn:nbn:de:0030-drops-121666},
  doi =		{10.4230/LIPIcs.SoCG.2020.8},
  annote =	{Keywords: Algebraic decision tree, Polynomial partition, Collinearity testing, 3SUM-hard problems, Polynomials vanishing on Cartesian products}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.58
External Memory Planar Point Location with Fast Updates

Authors: John Iacono, Ben Karsin, and Grigorios Koumoutsos

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
We study dynamic planar point location in the External Memory Model or Disk Access Model (DAM). Previous work in this model achieves polylog query and polylog amortized update time. We present a data structure with O(log_B^2 N) query time and O(1/B^(1-epsilon) log_B N) amortized update time, where N is the number of segments, B the block size and epsilon is a small positive constant, under the assumption that all faces have constant size. This is a B^(1-epsilon) factor faster for updates than the fastest previous structure, and brings the cost of insertion and deletion down to subconstant amortized time for reasonable choices of N and B. Our structure solves the problem of vertical ray-shooting queries among a dynamic set of interior-disjoint line segments; this is well-known to solve dynamic planar point location for a connected subdivision of the plane with faces of constant size.
Cite as

John Iacono, Ben Karsin, and Grigorios Koumoutsos. External Memory Planar Point Location with Fast Updates. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 58:1-58:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{iacono_et_al:LIPIcs.ISAAC.2019.58,
  author =	{Iacono, John and Karsin, Ben and Koumoutsos, Grigorios},
  title =	{{External Memory Planar Point Location with Fast Updates}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{58:1--58:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.58},
  URN =		{urn:nbn:de:0030-drops-115548},
  doi =		{10.4230/LIPIcs.ISAAC.2019.58},
  annote =	{Keywords: point location, data structures, dynamic algorithms, computational geometry}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.60
External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms

Authors: John Iacono, Riko Jacob, and Konstantinos Tsakalidis

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We present priority queues in the external memory model with block size B and main memory size M that support on N elements, operation Update (a combination of operations Insert and DecreaseKey) in O(1/Blog_{M/B} N/B) amortized I/Os and operations ExtractMin and Delete in O(ceil[(M^epsilon)/B log_{M/B} N/B] log_{M/B} N/B) amortized I/Os, for any real epsilon in (0,1), using O(N/Blog_{M/B} N/B) blocks. Previous I/O-efficient priority queues either support these operations in O(1/Blog_2 N/B) amortized I/Os [Kumar and Schwabe, SPDP '96] or support only operations Insert, Delete and ExtractMin in optimal O(1/Blog_{M/B} N/B) amortized I/Os, however without supporting DecreaseKey [Fadel et al., TCS '99]. We also present buffered repository trees that support on a multi-set of N elements, operation Insert in O(1/Blog_M/B N/B) I/Os and operation Extract on K extracted elements in O(M^{epsilon} log_M/B N/B + K/B) amortized I/Os, using O(N/B) blocks. Previous results achieve O(1/Blog_2 N/B) I/Os and O(log_2 N/B + K/B) I/Os, respectively [Buchsbaum et al., SODA '00]. Our results imply improved O(E/Blog_{M/B} E/B) I/Os for single-source shortest paths, depth-first search and breadth-first search algorithms on massive directed dense graphs (V,E) with E = Omega (V^(1+epsilon)), epsilon > 0 and V = Omega (M), which is equal to the I/O-optimal bound for sorting E values in external memory.
Cite as

John Iacono, Riko Jacob, and Konstantinos Tsakalidis. External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{iacono_et_al:LIPIcs.ESA.2019.60,
  author =	{Iacono, John and Jacob, Riko and Tsakalidis, Konstantinos},
  title =	{{External Memory Priority Queues with Decrease-Key and Applications to Graph Algorithms}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{60:1--60:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.60},
  URN =		{urn:nbn:de:0030-drops-111817},
  doi =		{10.4230/LIPIcs.ESA.2019.60},
  annote =	{Keywords: priority queues, external memory, graph algorithms, shortest paths, depth-first search, breadth-first search}
}
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