44 Search Results for "Kaplan, Haim"

Document
DOI: 10.4230/LIPIcs.MFCS.2024.63
Fully-Adaptive Dynamic Connectivity of Square Intersection Graphs

Authors: Ivor van der Hoog, André Nusser, Eva Rotenberg, and Frank Staals

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
A classical problem in computational geometry and graph algorithms is: given a dynamic set 𝒮 of geometric shapes in the plane, efficiently maintain the connectivity of the intersection graph of 𝒮. Previous papers studied the setting where, before the updates, the data structure receives some parameter P. Then, updates could insert and delete disks as long as at all times the disks have a diameter that lies in a fixed range [1/P, 1]. As a consequence of that prerequisite, the aspect ratio ψ (i.e. the ratio between the largest and smallest diameter) of the disks would at all times satisfy ψ ≤ P. The state-of-the-art for storing disks in a dynamic connectivity data structure is a data structure that uses O(Pn) space and that has amortized O(P log⁴ n) expected amortized update time. Connectivity queries between disks are supported in O(log n / log log n) time. In the dynamic setting, one wishes for a more flexible data structure in which disks of any diameter may arrive and leave, independent of their diameter, changing the aspect ratio freely. Ideally, the aspect ratio should merely be part of the analysis. We restrict our attention to axis-aligned squares, and study fully-dynamic square intersection graph connectivity. Our result is fully-adaptive to the aspect ratio, spending time proportional to the current aspect ratio ψ, as opposed to some previously given maximum P. Our focus on squares allows us to simplify and streamline the connectivity pipeline from previous work. When n is the number of squares and ψ is the aspect ratio after insertion (or before deletion), our data structure answers connectivity queries in O(log n / log log n) time. We can update connectivity information in O(ψ log⁴ n + log⁶ n) amortized time. We also improve space usage from O(P ⋅ n log n) to O(n log³ n log ψ) - while generalizing to a fully-adaptive aspect ratio - which yields a space usage that is near-linear in n for any polynomially bounded ψ.
Cite as

Ivor van der Hoog, André Nusser, Eva Rotenberg, and Frank Staals. Fully-Adaptive Dynamic Connectivity of Square Intersection Graphs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 63:1-63:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{vanderhoog_et_al:LIPIcs.MFCS.2024.63,
  author =	{van der Hoog, Ivor and Nusser, Andr\'{e} and Rotenberg, Eva and Staals, Frank},
  title =	{{Fully-Adaptive Dynamic Connectivity of Square Intersection Graphs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{63:1--63:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.63},
  URN =		{urn:nbn:de:0030-drops-206197},
  doi =		{10.4230/LIPIcs.MFCS.2024.63},
  annote =	{Keywords: Computational geometry, planar geometry, data structures, geometric intersection graphs, fully-dynamic algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.69
Scheduling with Locality by Routing

Authors: Alison Hsiang-Hsuan Liu and Fu-Hong Liu

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
This work examines a strongly NP-hard routing problem on trees, in which multiple servers need to serve a given set of requests (on vertices), where the routes of the servers start from a common source and end at their respective terminals. Each server can travel free of cost on its source-to-terminal path but has to pay for travel on other edges. The objective is to minimize the maximum cost over all servers. As the servers may pay different costs for traveling through a common edge, balancing the loads of the servers can be difficult. We propose a polynomial-time 4-approximation algorithm that applies the parametric pruning framework but consists of two phases. The first phase of the algorithm partitions the requests into packets, and the second phase of the algorithm assigns the packets to the servers. Unlike the standard parametric pruning techniques, the challenge of our algorithm design and analysis is to harmoniously relate the quality of the partition in the first phase, the balances of the servers' loads in the second phase, and the hypothetical optimal values of the framework. For the problem in general graphs, we show that there is no algorithm better than 2-approximate unless P = NP. The problem is a generalization of unrelated machine scheduling and other classic scheduling problems. It also models scheduling problems where the job processing times depend on the machine serving the job and the other jobs served by that machine. This modeling provides a framework that physicalizes scheduling problems through the graph’s point of view.
Cite as

Alison Hsiang-Hsuan Liu and Fu-Hong Liu. Scheduling with Locality by Routing. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 69:1-69:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{liu_et_al:LIPIcs.MFCS.2024.69,
  author =	{Liu, Alison Hsiang-Hsuan and Liu, Fu-Hong},
  title =	{{Scheduling with Locality by Routing}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{69:1--69:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.69},
  URN =		{urn:nbn:de:0030-drops-206250},
  doi =		{10.4230/LIPIcs.MFCS.2024.69},
  annote =	{Keywords: Makespan minimization, Approximation algorithms, Routing problems, Parametric pruning framework}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.17
Local Enumeration and Majority Lower Bounds

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

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

Abstract
Depth-3 circuit lower bounds and k-SAT algorithms are intimately related; the state-of-the-art Σ^k_3-circuit lower bound (Or-And-Or circuits with bottom fan-in at most k) and the k-SAT algorithm of Paturi, Pudlák, Saks, and Zane (J. ACM'05) are based on the same combinatorial theorem regarding k-CNFs. In this paper we define a problem which reveals new interactions between the two, and suggests a concrete approach to significantly stronger circuit lower bounds and improved k-SAT algorithms. For a natural number k and a parameter t, we consider the Enum(k, t) problem defined as follows: given an n-variable k-CNF and an initial assignment α, output all satisfying assignments at Hamming distance t(n) of α, assuming that there are no satisfying assignments of Hamming distance less than t(n) of α. We observe that an upper bound b(n, k, t) on the complexity of Enum(k, t) simultaneously implies depth-3 circuit lower bounds and k-SAT algorithms: - Depth-3 circuits: Any Σ^k_3 circuit computing the Majority function has size at least binom(n,n/2)/b(n, k, n/2). - k-SAT: There exists an algorithm solving k-SAT in time O(∑_{t=1}^{n/2}b(n, k, t)). A simple construction shows that b(n, k, n/2) ≥ 2^{(1 - O(log(k)/k))n}. Thus, matching upper bounds for b(n, k, n/2) would imply a Σ^k_3-circuit lower bound of 2^Ω(log(k)n/k) and a k-SAT upper bound of 2^{(1 - Ω(log(k)/k))n}. The former yields an unrestricted depth-3 lower bound of 2^ω(√n) solving a long standing open problem, and the latter breaks the Super Strong Exponential Time Hypothesis. In this paper, we propose a randomized algorithm for Enum(k, t) and introduce new ideas to analyze it. We demonstrate the power of our ideas by considering the first non-trivial instance of the problem, i.e., Enum(3, n/2). We show that the expected running time of our algorithm is 1.598ⁿ, substantially improving on the trivial bound of 3^{n/2} ≃ 1.732ⁿ. This already improves Σ^3_3 lower bounds for Majority function to 1.251ⁿ. The previous bound was 1.154ⁿ which follows from the work of Håstad, Jukna, and Pudlák (Comput. Complex.'95). By restricting ourselves to monotone CNFs, Enum(k, t) immediately becomes a hypergraph Turán problem. Therefore our techniques might be of independent interest in extremal combinatorics.
Cite as

Mohit Gurumukhani, Ramamohan Paturi, Pavel Pudlák, Michael Saks, and Navid Talebanfard. Local Enumeration and Majority Lower Bounds. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 17:1-17:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{gurumukhani_et_al:LIPIcs.CCC.2024.17,
  author =	{Gurumukhani, Mohit and Paturi, Ramamohan and Pudl\'{a}k, Pavel and Saks, Michael and Talebanfard, Navid},
  title =	{{Local Enumeration and Majority Lower Bounds}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{17:1--17:25},
  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.2024.17},
  URN =		{urn:nbn:de:0030-drops-204136},
  doi =		{10.4230/LIPIcs.CCC.2024.17},
  annote =	{Keywords: Depth 3 circuits, k-CNF satisfiability, Circuit lower bounds, Majority function}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.28
Finding Missing Items Requires Strong Forms of Randomness

Authors: Amit Chakrabarti and Manuel Stoeckl

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

Abstract
Adversarially robust streaming algorithms are required to process a stream of elements and produce correct outputs, even when each stream element can be chosen as a function of earlier algorithm outputs. As with classic streaming algorithms, which must only be correct for the worst-case fixed stream, adversarially robust algorithms with access to randomness can use significantly less space than deterministic algorithms. We prove that for the Missing Item Finding problem in streaming, the space complexity also significantly depends on how adversarially robust algorithms are permitted to use randomness. (In contrast, the space complexity of classic streaming algorithms does not depend as strongly on the way randomness is used.) For Missing Item Finding on streams of length 𝓁 with elements in {1,…,n}, and ≤ 1/poly(𝓁) error, we show that when 𝓁 = O(2^√{log n}), "random seed" adversarially robust algorithms, which only use randomness at initialization, require 𝓁^Ω(1) bits of space, while "random tape" adversarially robust algorithms, which may make random decisions at any time, may use O(polylog(𝓁)) random bits. When 𝓁 is between n^Ω(1) and O(√n), "random tape" adversarially robust algorithms need 𝓁^Ω(1) space, while "random oracle" adversarially robust algorithms, which can read from a long random string for free, may use O(polylog(𝓁)) space. The space lower bound for the "random seed" case follows, by a reduction given in prior work, from a lower bound for pseudo-deterministic streaming algorithms given in this paper.
Cite as

Amit Chakrabarti and Manuel Stoeckl. Finding Missing Items Requires Strong Forms of Randomness. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{chakrabarti_et_al:LIPIcs.CCC.2024.28,
  author =	{Chakrabarti, Amit and Stoeckl, Manuel},
  title =	{{Finding Missing Items Requires Strong Forms of Randomness}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.28},
  URN =		{urn:nbn:de:0030-drops-204242},
  doi =		{10.4230/LIPIcs.CCC.2024.28},
  annote =	{Keywords: Data streaming, lower bounds, space complexity, adversarial robustness, derandomization, sketching, sampling}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.14
Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions

Authors: Andreas Grigorjew, Fernando H. C. Dias, Andrea Cracco, Romeo Rizzi, and Alexandru I. Tomescu

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

Abstract
Given a flow network, the Minimum Flow Decomposition (MFD) problem is finding the smallest possible set of weighted paths whose superposition equals the flow. It is a classical, strongly NP-hard problem that is proven to be useful in RNA transcript assembly and applications outside of Bioinformatics. We improve an existing ILP (Integer Linear Programming) model by Dias et al. [RECOMB 2022] for DAGs by decreasing the solver’s search space using solution safety and several other optimizations. This results in a significant speedup compared to the original ILP, of up to 34× on average on the hardest instances. Moreover, we show that our optimizations apply also to MFD problem variants, resulting in speedups that go up to 219× on the hardest instances. We also developed an ILP model of reduced dimensionality for an MFD variant in which the solution path weights are restricted to a given set. This model can find an optimal MFD solution for most instances, and overall, its accuracy significantly outperforms that of previous greedy algorithms while being up to an order of magnitude faster than our optimized ILP.
Cite as

Andreas Grigorjew, Fernando H. C. Dias, Andrea Cracco, Romeo Rizzi, and Alexandru I. Tomescu. Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{grigorjew_et_al:LIPIcs.SEA.2024.14,
  author =	{Grigorjew, Andreas and Dias, Fernando H. C. and Cracco, Andrea and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{14:1--14:19},
  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.2024.14},
  URN =		{urn:nbn:de:0030-drops-203792},
  doi =		{10.4230/LIPIcs.SEA.2024.14},
  annote =	{Keywords: Flow decomposition, Integer Linear Programming, Safety, RNA-seq, RNA transcript assembly, isoform}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.28
Finding the Minimum Cost Acceptable Element in a Sorted Matrix

Authors: Sebastián Urrutia and Vinicius dos Santos

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

Abstract
In this work we introduce the problem of finding a minimum cost acceptable element in an n × n matrix M whose columns and rows are sorted in non-decreasing order. More precisely, given a sorted matrix M and access to a given oracle function f: ℕ × ℕ → {True, False}, one has to find a pair (i, j) of indices such that f(i,j) returns True and the value M[i,j] is as small as possible. Assuming the computation of f(i,j) takes time bounded by a constant, a naive algorithm scanning all the positions of the matrix takes time O(n²). Another natural approach, based on a priority queue, takes time O(z log z) in which z stands for the position of the first pair of indices for which the oracle returns True in a sorted list of all elements of M. In the worst case, when z = n², the naive algorithm is better than the priority queue one. In this work we introduce different algorithms with complexities depending on n and z, such as O(n √z) and O(min(n²,z²)), and compare them, both theoretically and experimentally, in terms of running time and number of calls to the oracle. Among other things, we find that in most cases our algorithms do not make a significantly larger number of calls to the oracle than the priority queue-based algorithm, which achieves the minimum of such call when all elements of the matrix are distinct, while being much faster in large instances.
Cite as

Sebastián Urrutia and Vinicius dos Santos. Finding the Minimum Cost Acceptable Element in a Sorted Matrix. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 28:1-28:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{urrutia_et_al:LIPIcs.SEA.2024.28,
  author =	{Urrutia, Sebasti\'{a}n and dos Santos, Vinicius},
  title =	{{Finding the Minimum Cost Acceptable Element in a Sorted Matrix}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{28:1--28:14},
  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.2024.28},
  URN =		{urn:nbn:de:0030-drops-203939},
  doi =		{10.4230/LIPIcs.SEA.2024.28},
  annote =	{Keywords: Search, Sorted matrix, Oracle function, Algorithm complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.15
List Update with Delays or Time Windows

Authors: Yossi Azar, Shahar Lewkowicz, and Danny Vainstein

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

Abstract
We address the problem of List Update, which is considered one of the fundamental problems in online algorithms and competitive analysis. In this context, we are presented with a list of elements and receive requests for these elements over time. Our objective is to fulfill these requests, incurring a cost proportional to their position in the list. Additionally, we can swap any two consecutive elements at a cost of 1. The renowned "Move to Front" algorithm, introduced by Sleator and Tarjan, immediately moves any requested element to the front of the list. They demonstrated that this algorithm achieves a competitive ratio of 2. While this bound is impressive, the actual cost of the algorithm’s solution can be excessively high. For example, if we request the last half of the list, the resulting solution cost becomes quadratic in the list’s length. To address this issue, we consider a more generalized problem called List Update with Time Windows. In this variant, each request arrives with a specific deadline by which it must be served, rather than being served immediately. Moreover, we allow the algorithm to process multiple requests simultaneously, accessing the corresponding elements in a single pass. The cost incurred in this case is determined by the position of the furthest element accessed, leading to a significant reduction in the total solution cost. We introduce this problem to explore lower solution costs, but it necessitates the development of new algorithms. For instance, Move-to-Front fails when handling the simple scenario of requesting the last half of the list with overlapping time windows. In our work, we present a natural O(1) competitive algorithm for this problem. While the algorithm itself is intuitive, its analysis is intricate, requiring the use of a novel potential function. Additionally, we delve into a more general problem called List Update with Delays, where the fixed deadlines are replaced with arbitrary delay functions. In this case, the cost includes not only the access and swapping costs, but also penalties for the delays incurred until the requests are served. This problem encompasses a special case known as the prize collecting version, where a request may go unserved up to a given deadline, resulting in a specified penalty. For this more comprehensive problem, we establish an O(1) competitive algorithm. However, the algorithm for the delay version is more complex, and its analysis involves significantly more intricate considerations.
Cite as

Yossi Azar, Shahar Lewkowicz, and Danny Vainstein. List Update with Delays or Time Windows. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{azar_et_al:LIPIcs.ICALP.2024.15,
  author =	{Azar, Yossi and Lewkowicz, Shahar and Vainstein, Danny},
  title =	{{List Update with Delays or Time Windows}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{15:1--15:20},
  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.2024.15},
  URN =		{urn:nbn:de:0030-drops-201583},
  doi =		{10.4230/LIPIcs.ICALP.2024.15},
  annote =	{Keywords: Online, List Update, Delay, Time Window, Deadline}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.31
Tight Bounds on Adjacency Labels for Monotone Graph Classes

Authors: Édouard Bonnet, Julien Duron, John Sylvester, Viktor Zamaraev, and Maksim Zhukovskii

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

Abstract
A class of graphs admits an adjacency labeling scheme of size b(n), if the vertices in each of its n-vertex graphs can be assigned binary strings (called labels) of length b(n) so that the adjacency of two vertices can be determined solely from their labels. We give bounds on the size of adjacency labels for every family of monotone (i.e., subgraph-closed) classes with a "well-behaved" growth function between 2^Ω(n log n) and 2^O(n^{2-δ}) for any δ > 0. Specifically, we show that for any function f: ℕ → ℝ satisfying log n ⩽ f(n) ⩽ n^{1-δ} for any fixed δ > 0, and some sub-multiplicativity condition, there are monotone graph classes with growth 2^O(nf(n)) that do not admit adjacency labels of size at most f(n) log n. On the other hand, any such class does admit adjacency labels of size O(f(n)log n). Surprisingly this bound is a Θ(log n) factor away from the information-theoretic bound of Ω(f(n)). Our bounds are tight upto constant factors, and the special case when f = log implies that the recently-refuted Implicit Graph Conjecture [Hatami and Hatami, FOCS 2022] also fails within monotone classes. We further show that the Implicit Graph Conjecture holds for all monotone small classes. In other words, any monotone class with growth rate at most n! cⁿ for some constant c > 0, admits adjacency labels of information-theoretic order optimal size. In fact, we show a more general result that is of independent interest: any monotone small class of graphs has bounded degeneracy. We conjecture that the Implicit Graph Conjecture holds for all hereditary small classes.
Cite as

Édouard Bonnet, Julien Duron, John Sylvester, Viktor Zamaraev, and Maksim Zhukovskii. Tight Bounds on Adjacency Labels for Monotone Graph Classes. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{bonnet_et_al:LIPIcs.ICALP.2024.31,
  author =	{Bonnet, \'{E}douard and Duron, Julien and Sylvester, John and Zamaraev, Viktor and Zhukovskii, Maksim},
  title =	{{Tight Bounds on Adjacency Labels for Monotone Graph Classes}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{31:1--31:20},
  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.2024.31},
  URN =		{urn:nbn:de:0030-drops-201741},
  doi =		{10.4230/LIPIcs.ICALP.2024.31},
  annote =	{Keywords: Adjacency labeling, degeneracy, monotone classes, small classes, factorial classes, implicit graph conjecture}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.65
Optimal Electrical Oblivious Routing on Expanders

Authors: Cella Florescu, Rasmus Kyng, Maximilian Probst Gutenberg, and Sushant Sachdeva

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

Abstract
In this paper, we investigate the question of whether the electrical flow routing is a good oblivious routing scheme on an m-edge graph G = (V, E) that is a Φ-expander, i.e. where |∂ S| ≥ Φ ⋅ vol(S) for every S ⊆ V, vol(S) ≤ vol(V)/2. Beyond its simplicity and structural importance, this question is well-motivated by the current state-of-the-art of fast algorithms for 𝓁_∞ oblivious routings that reduce to the expander-case which is in turn solved by electrical flow routing. Our main result proves that the electrical routing is an O(Φ^{-1} log m)-competitive oblivious routing in the 𝓁₁- and 𝓁_∞-norms. We further observe that the oblivious routing is O(log² m)-competitive in the 𝓁₂-norm and, in fact, O(log m)-competitive if 𝓁₂-localization is O(log m) which is widely believed. Using these three upper bounds, we can smoothly interpolate to obtain upper bounds for every p ∈ [2, ∞] and q given by 1/p + 1/q = 1. Assuming 𝓁₂-localization in O(log m), we obtain that in 𝓁_p and 𝓁_q, the electrical oblivious routing is O(Φ^{-(1-2/p)}log m) competitive. Using the currently known result for 𝓁₂-localization, this ratio deteriorates by at most a sublogarithmic factor for every p, q ≠ 2. We complement our upper bounds with lower bounds that show that the electrical routing for any such p and q is Ω(Φ^{-(1-2/p)} log m)-competitive. This renders our results in 𝓁₁ and 𝓁_∞ unconditionally tight up to constants, and the result in any 𝓁_p- and 𝓁_q-norm to be tight in case of 𝓁₂-localization in O(log m).
Cite as

Cella Florescu, Rasmus Kyng, Maximilian Probst Gutenberg, and Sushant Sachdeva. Optimal Electrical Oblivious Routing on Expanders. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 65:1-65:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{florescu_et_al:LIPIcs.ICALP.2024.65,
  author =	{Florescu, Cella and Kyng, Rasmus and Gutenberg, Maximilian Probst and Sachdeva, Sushant},
  title =	{{Optimal Electrical Oblivious Routing on Expanders}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{65:1--65:19},
  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.2024.65},
  URN =		{urn:nbn:de:0030-drops-202083},
  doi =		{10.4230/LIPIcs.ICALP.2024.65},
  annote =	{Keywords: Expanders, Oblivious routing for 𝓁\underlinep, Electrical flow routing}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.95
Fully Dynamic Strongly Connected Components in Planar Digraphs

Authors: Adam Karczmarz and Marcin Smulewicz

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

Abstract
In this paper we consider maintaining strongly connected components (SCCs) of a directed planar graph subject to edge insertions and deletions. We show a data structure maintaining an implicit representation of the SCCs within Õ(n^{6/7}) worst-case time per update. The data structure supports, in O(log²{n}) time, reporting vertices of any specified SCC (with constant overhead per reported vertex) and aggregating vertex information (e.g., computing the maximum label) over all the vertices of that SCC. Furthermore, it can maintain global information about the structure of SCCs, such as the number of SCCs, or the size of the largest SCC. To the best of our knowledge, no fully dynamic SCCs data structures with sublinear update time have been previously known for any major subclass of digraphs. Our result should be contrasted with the n^{1-o(1)} amortized update time lower bound conditional on SETH, which holds even for dynamically maintaining whether a general digraph has more than two SCCs.
Cite as

Adam Karczmarz and Marcin Smulewicz. Fully Dynamic Strongly Connected Components in Planar Digraphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 95:1-95:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{karczmarz_et_al:LIPIcs.ICALP.2024.95,
  author =	{Karczmarz, Adam and Smulewicz, Marcin},
  title =	{{Fully Dynamic Strongly Connected Components in Planar Digraphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{95:1--95:20},
  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.2024.95},
  URN =		{urn:nbn:de:0030-drops-202388},
  doi =		{10.4230/LIPIcs.ICALP.2024.95},
  annote =	{Keywords: dynamic strongly connected components, dynamic strong connectivity, dynamic reachability, planar graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.120
Caching Connections in Matchings

Authors: Yaniv Sadeh and Haim Kaplan

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

Abstract
Motivated by the desire to utilize a limited number of configurable optical switches by recent advances in Software Defined Networks (SDNs), we define an online problem which we call the Caching in Matchings problem. This problem has a natural combinatorial structure and therefore may find additional applications in theory and practice. In the Caching in Matchings problem our cache consists of k matchings of connections between servers that form a bipartite graph. To cache a connection we insert it into one of the k matchings possibly evicting at most two other connections from this matching. This problem resembles the problem known as Connection Caching [Cohen et al., 2000], where we also cache connections but our only restriction is that they form a graph with bounded degree k. Our results show a somewhat surprising qualitative separation between the problems: The competitive ratio of any online algorithm for caching in matchings must depend on the size of the graph. Specifically, we give a deterministic O(nk) competitive and randomized O(n log k) competitive algorithms for caching in matchings, where n is the number of servers and k is the number of matchings. We also show that the competitive ratio of any deterministic algorithm is Ω(max(n/k,k)) and of any randomized algorithm is Ω(log (n/(k² log k)) ⋅ log k). In particular, the lower bound for randomized algorithms is Ω(log n) regardless of k, and can be as high as Ω(log² n) if k = n^{1/3}, for example. We also show that if we allow the algorithm to use at least 2k-1 matchings compared to k used by the optimum then we match the competitive ratios of connection catching which are independent of n. Interestingly, we also show that even a single extra matching for the algorithm allows to get substantially better bounds.
Cite as

Yaniv Sadeh and Haim Kaplan. Caching Connections in Matchings. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 120:1-120:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{sadeh_et_al:LIPIcs.ICALP.2024.120,
  author =	{Sadeh, Yaniv and Kaplan, Haim},
  title =	{{Caching Connections in Matchings}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{120:1--120:20},
  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.2024.120},
  URN =		{urn:nbn:de:0030-drops-202639},
  doi =		{10.4230/LIPIcs.ICALP.2024.120},
  annote =	{Keywords: Caching, Matchings, Caching in Matchings, Edge Coloring, Online Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.42
Optimal Energetic Paths for Electric Cars

Authors: Dani Dorfman, Haim Kaplan, Robert E. Tarjan, and Uri Zwick

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
A weighted directed graph G = (V,A,c), where A ⊆ V× V and c:A → ℝ, naturally describes a road network in which an electric car, or vehicle (EV), can roam. An arc uv ∈ A models a road segment connecting the two vertices (junctions) u and v. The cost c(uv) of the arc uv is the amount of energy the car needs to travel from u to v. This amount can be positive, zero or negative. We consider both the more realistic scenario where there are no negative cycles in the graph, as well as the more challenging scenario, which can also be motivated, where negative cycles may be present. The electric car has a battery that can store up to B units of energy. The car can traverse an arc uv ∈ A only if it is at u and the charge b in its battery satisfies b ≥ c(uv). If the car traverses the arc uv then it reaches v with a charge of min{b-c(uv),B} in its battery. Arcs with a positive cost deplete the battery while arcs with negative costs may charge the battery, but not above its capacity of B. If the car is at a vertex u and cannot traverse any outgoing arcs of u, then it is stuck and cannot continue traveling. We consider the following natural problem: Given two vertices s,t ∈ V, can the car travel from s to t, starting at s with an initial charge b, where 0 ≤ b ≤ B? If so, what is the maximum charge with which the car can reach t? Equivalently, what is the smallest depletion δ_{B,b}(s,t) such that the car can reach t with a charge of b-δ_{B,b}(s,t) in its battery, and which path should the car follow to achieve this? We also refer to δ_{B,b}(s,t) as the energetic cost of traveling from s to t. We let δ_{B,b}(s,t) = ∞ if the car cannot travel from s to t starting with an initial charge of b. The problem of computing energetic costs is a strict generalization of the standard shortest paths problem. When there are no negative cycles, the single-source version of the problem can be solved using simple adaptations of the classical Bellman-Ford and Dijkstra algorithms. More involved algorithms are required when the graph may contain negative cycles.
Cite as

Dani Dorfman, Haim Kaplan, Robert E. Tarjan, and Uri Zwick. Optimal Energetic Paths for Electric Cars. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 42:1-42:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{dorfman_et_al:LIPIcs.ESA.2023.42,
  author =	{Dorfman, Dani and Kaplan, Haim and Tarjan, Robert E. and Zwick, Uri},
  title =	{{Optimal Energetic Paths for Electric Cars}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{42:1--42:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.42},
  URN =		{urn:nbn:de:0030-drops-186955},
  doi =		{10.4230/LIPIcs.ESA.2023.42},
  annote =	{Keywords: Electric cars, Optimal Paths, Battery depletion}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.67
The Unweighted and Weighted Reverse Shortest Path Problem for Disk Graphs

Authors: Haim Kaplan, Matthew J. Katz, Rachel Saban, and Micha Sharir

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We study the reverse shortest path problem on disk graphs in the plane. In this problem we consider the proximity graph of a set of n disks in the plane of arbitrary radii: In this graph two disks are connected if the distance between them is at most some threshold parameter r. The case of intersection graphs is a special case with r = 0. We give an algorithm that, given a target length k, computes the smallest value of r for which there is a path of length at most k between some given pair of disks in the proximity graph. Our algorithm runs in O^*(n^{5/4}) randomized expected time, which improves to O^*(n^{6/5}) for unit disk graphs, where all the disks have the same radius. Our technique is robust and can be applied to many variants of the problem. One significant variant is the case of weighted proximity graphs, where edges are assigned real weights equal to the distance between the disks or between their centers, and k is replaced by a target weight w. In other variants, we want to optimize a parameter different from r, such as a scale factor of the radii of the disks. The main technique for the decision version of the problem (determining whether the graph with a given r has the desired property) is based on efficient implementations of BFS (for the unweighted case) and of Dijkstra’s algorithm (for the weighted case), using efficient data structures for maintaining the bichromatic closest pair for certain bicliques and several distance functions. The optimization problem is then solved by combining the resulting decision procedure with enhanced variants of the interval shrinking and bifurcation technique of [R. Ben Avraham et al., 2015].
Cite as

Haim Kaplan, Matthew J. Katz, Rachel Saban, and Micha Sharir. The Unweighted and Weighted Reverse Shortest Path Problem for Disk Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 67:1-67:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{kaplan_et_al:LIPIcs.ESA.2023.67,
  author =	{Kaplan, Haim and Katz, Matthew J. and Saban, Rachel and Sharir, Micha},
  title =	{{The Unweighted and Weighted Reverse Shortest Path Problem for Disk Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{67:1--67:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.67},
  URN =		{urn:nbn:de:0030-drops-187208},
  doi =		{10.4230/LIPIcs.ESA.2023.67},
  annote =	{Keywords: Computational geometry, geometric optimization, disk graphs, BFS, Dijkstra’s algorithm, reverse shortest path}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.9
Expander Decomposition with Fewer Inter-Cluster Edges Using a Spectral Cut Player

Authors: Daniel Agassy, Dani Dorfman, and Haim Kaplan

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
A (ϕ,ε)-expander decomposition of a graph G (with n vertices and m edges) is a partition of V into clusters V₁,…,V_k with conductance Φ(G[V_i]) ≥ ϕ, such that there are at most ε m inter-cluster edges. Such a decomposition plays a crucial role in many graph algorithms. We give a randomized Õ(m/ϕ) time algorithm for computing a (ϕ, ϕlog²n)-expander decomposition. This improves upon the (ϕ, ϕlog³n)-expander decomposition also obtained in Õ(m/ϕ) time by [Saranurak and Wang, SODA 2019] (SW) and brings the number of inter-cluster edges within logarithmic factor of optimal. One crucial component of SW’s algorithm is a non-stop version of the cut-matching game of [Khandekar, Rao, Vazirani, JACM 2009] (KRV): The cut player does not stop when it gets from the matching player an unbalanced sparse cut, but continues to play on a trimmed part of the large side. The crux of our improvement is the design of a non-stop version of the cleverer cut player of [Orecchia, Schulman, Vazirani, Vishnoi, STOC 2008] (OSVV). The cut player of OSSV uses a more sophisticated random walk, a subtle potential function, and spectral arguments. Designing and analysing a non-stop version of this game was an explicit open question asked by SW.
Cite as

Daniel Agassy, Dani Dorfman, and Haim Kaplan. Expander Decomposition with Fewer Inter-Cluster Edges Using a Spectral Cut Player. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{agassy_et_al:LIPIcs.ICALP.2023.9,
  author =	{Agassy, Daniel and Dorfman, Dani and Kaplan, Haim},
  title =	{{Expander Decomposition with Fewer Inter-Cluster Edges Using a Spectral Cut Player}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.9},
  URN =		{urn:nbn:de:0030-drops-180619},
  doi =		{10.4230/LIPIcs.ICALP.2023.9},
  annote =	{Keywords: Exapander Decomposition, Cut-Matching Game}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.19
Fast Approximation of Search Trees on Trees with Centroid Trees

Authors: Benjamin Aram Berendsohn, Ishay Golinsky, Haim Kaplan, and László Kozma

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Search trees on trees (STTs) generalize the fundamental binary search tree (BST) data structure: in STTs the underlying search space is an arbitrary tree, whereas in BSTs it is a path. An optimal BST of size n can be computed for a given distribution of queries in 𝒪(n²) time [Knuth, Acta Inf. 1971] and centroid BSTs provide a nearly-optimal alternative, computable in 𝒪(n) time [Mehlhorn, SICOMP 1977]. By contrast, optimal STTs are not known to be computable in polynomial time, and the fastest constant-approximation algorithm runs in 𝒪(n³) time [Berendsohn, Kozma, SODA 2022]. Centroid trees can be defined for STTs analogously to BSTs, and they have been used in a wide range of algorithmic applications. In the unweighted case (i.e., for a uniform distribution of queries), the centroid tree can be computed in 𝒪(n) time [Brodal, Fagerberg, Pedersen, Östlin, ICALP 2001; Della Giustina, Prezza, Venturini, SPIRE 2019]. These algorithms, however, do not readily extend to the weighted case. Moreover, no approximation guarantees were previously known for centroid trees in either the unweighted or weighted cases. In this paper we revisit centroid trees in a general, weighted setting, and we settle both the algorithmic complexity of constructing them, and the quality of their approximation. For constructing a weighted centroid tree, we give an output-sensitive 𝒪(n log h) ⊆ 𝒪(n log n) time algorithm, where h is the height of the resulting centroid tree. If the weights are of polynomial complexity, the running time is 𝒪(n log log n). We show these bounds to be optimal, in a general decision tree model of computation. For approximation, we prove that the cost of a centroid tree is at most twice the optimum, and this guarantee is best possible, both in the weighted and unweighted cases. We also give tight, fine-grained bounds on the approximation-ratio for bounded-degree trees and on the approximation-ratio of more general α-centroid trees.
Cite as

Benjamin Aram Berendsohn, Ishay Golinsky, Haim Kaplan, and László Kozma. Fast Approximation of Search Trees on Trees with Centroid Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{berendsohn_et_al:LIPIcs.ICALP.2023.19,
  author =	{Berendsohn, Benjamin Aram and Golinsky, Ishay and Kaplan, Haim and Kozma, L\'{a}szl\'{o}},
  title =	{{Fast Approximation of Search Trees on Trees with Centroid Trees}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{19:1--19:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.19},
  URN =		{urn:nbn:de:0030-drops-180711},
  doi =		{10.4230/LIPIcs.ICALP.2023.19},
  annote =	{Keywords: centroid tree, search trees on trees, approximation}
}
  • Refine by Author
  • 30 Kaplan, Haim
  • 9 Sharir, Micha
  • 6 Mulzer, Wolfgang
  • 6 Zwick, Uri
  • 5 Dorfman, Dani
  • Show More...

  • Refine by Classification
  • 10 Theory of computation → Computational geometry
  • 6 Theory of computation → Data structures design and analysis
  • 4 Theory of computation → Design and analysis of algorithms
  • 3 Mathematics of computing → Combinatorics
  • 3 Theory of computation → Graph algorithms analysis
  • Show More...

  • Refine by Keyword
  • 4 Computational geometry
  • 2 Approximate incidences
  • 2 Locality sensitive hashing
  • 2 bipartite matching
  • 2 data structure
  • Show More...

  • Refine by Type
  • 44 document

  • Refine by Publication Year
  • 11 2024
  • 7 2019
  • 5 2018
  • 5 2023
  • 4 2017
  • Show More...

© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact