146 Search Results for "Navarro, Gonzalo"


Volume

LIPIcs, Volume 244

30th Annual European Symposium on Algorithms (ESA 2022)

ESA 2022, September 5-9, 2022, Berlin/Potsdam, Germany

Editors: Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, and Grzegorz Herman

Volume

LIPIcs, Volume 105

29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)

CPM 2018, July 2-4, 2018, Qingdao, China

Editors: Gonzalo Navarro, David Sankoff, and Binhai Zhu

Document
Trie-Compressed Adaptive Set Intersection

Authors: Diego Arroyuelo and Juan Pablo Castillo

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)


Abstract
We introduce space- and time-efficient algorithms and data structures for the offline set intersection problem. We show that a sorted integer set S ⊆ [0..u) of n elements can be represented using compressed space while supporting k-way intersections in adaptive O(kδlg(u/δ)) time, δ being the alternation measure introduced by Barbay and Kenyon. Our experimental results suggest that our approaches are competitive in practice, outperforming the most efficient alternatives (Partitioned Elias-Fano indexes, Roaring Bitmaps, and Recursive Universe Partitioning (RUP)) in several scenarios, offering in general relevant space-time trade-offs.

Cite as

Diego Arroyuelo and Juan Pablo Castillo. Trie-Compressed Adaptive Set Intersection. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{arroyuelo_et_al:LIPIcs.CPM.2023.1,
  author =	{Arroyuelo, Diego and Castillo, Juan Pablo},
  title =	{{Trie-Compressed Adaptive Set Intersection}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{1:1--1:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.1},
  URN =		{urn:nbn:de:0030-drops-179552},
  doi =		{10.4230/LIPIcs.CPM.2023.1},
  annote =	{Keywords: Set intersection problem, Adaptive Algorithms, Compressed and compact data structures}
}
Document
Merging Sorted Lists of Similar Strings

Authors: Gene Myers

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)


Abstract
Merging T sorted, non-redundant lists containing M elements into a single sorted, non-redundant result of size N ≥ M/T is a classic problem typically solved practically in O(M log T) time with a priority-queue data structure the most basic of which is the simple heap. We revisit this problem in the situation where the list elements are strings and the lists contain many identical or nearly identical elements. By keeping simple auxiliary information with each heap node, we devise an O(M log T+S) worst-case method that performs no more character comparisons than the sum of the lengths of all the strings S, and another O(M log (T/e¯)+S) method that becomes progressively more efficient as a function of the fraction of equal elements e¯ = M/N between input lists, reaching linear time when the lists are all identical. The methods perform favorably in practice versus an alternate formulation based on a trie.

Cite as

Gene Myers. Merging Sorted Lists of Similar Strings. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{myers:LIPIcs.CPM.2023.22,
  author =	{Myers, Gene},
  title =	{{Merging Sorted Lists of Similar Strings}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{22:1--22:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.22},
  URN =		{urn:nbn:de:0030-drops-179763},
  doi =		{10.4230/LIPIcs.CPM.2023.22},
  annote =	{Keywords: heap, trie, longest common prefix}
}
Document
Computing MEMs on Repetitive Text Collections

Authors: Gonzalo Navarro

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)


Abstract
We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern P[1..m] on a large repetitive text collection T[1..n], which is represented as a (hopefully much smaller) run-length context-free grammar of size g_{rl}. We show that the problem can be solved in time O(m² log^ε n), for any constant ε > 0, on a data structure of size O(g_{rl}). Further, on a locally consistent grammar of size O(δ log n/δ), the time decreases to O(m log m(log m + log^ε n)). The value δ is a function of the substring complexity of T and Ω(δ log n/δ) is a tight lower bound on the compressibility of repetitive texts T, so our structure has optimal size in terms of n and δ.

Cite as

Gonzalo Navarro. Computing MEMs on Repetitive Text Collections. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{navarro:LIPIcs.CPM.2023.24,
  author =	{Navarro, Gonzalo},
  title =	{{Computing MEMs on Repetitive Text Collections}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.24},
  URN =		{urn:nbn:de:0030-drops-179787},
  doi =		{10.4230/LIPIcs.CPM.2023.24},
  annote =	{Keywords: grammar-based indices, maximal exact matches, locally consistent grammars, substring complexity}
}
Document
L-Systems for Measuring Repetitiveness

Authors: Gonzalo Navarro and Cristian Urbina

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)


Abstract
In order to use them for compression, we extend L-systems (without ε-rules) with two parameters d and n, and also a coding τ, which determines unambiguously a string w = τ(φ^d(s))[1:n], where φ is the morphism of the system, and s is its axiom. The length of the shortest description of an L-system generating w is known as 𝓁, and it is arguably a relevant measure of repetitiveness that builds on the self-similarities that arise in the sequence. In this paper, we deepen the study of the measure 𝓁 and its relation with a better-established measure called δ, which builds on substring complexity. Our results show that 𝓁 and δ are largely orthogonal, in the sense that one can be much larger than the other, depending on the case. This suggests that both mechanisms capture different kinds of regularities related to repetitiveness. We then show that the recently introduced NU-systems, which combine the capabilities of L-systems with bidirectional macro schemes, can be asymptotically strictly smaller than both mechanisms for the same fixed string family, which makes the size ν of the smallest NU-system the unique smallest reachable repetitiveness measure to date. We conclude that in order to achieve better compression, we should combine morphism substitution with copy-paste mechanisms.

Cite as

Gonzalo Navarro and Cristian Urbina. L-Systems for Measuring Repetitiveness. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{navarro_et_al:LIPIcs.CPM.2023.25,
  author =	{Navarro, Gonzalo and Urbina, Cristian},
  title =	{{L-Systems for Measuring Repetitiveness}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2023.25},
  URN =		{urn:nbn:de:0030-drops-179792},
  doi =		{10.4230/LIPIcs.CPM.2023.25},
  annote =	{Keywords: L-systems, String morphisms, Repetitiveness measures, Text compression}
}
Document
Invited Talk
Compact Data Structures Meet Databases (Invited Talk)

Authors: Gonzalo Navarro

Published in: LIPIcs, Volume 255, 26th International Conference on Database Theory (ICDT 2023)


Abstract
We describe two success stories on the application of compact data structures (cds) to solve the problem of the excessively redundant space requirements posed by worst-case-optimal (wco) algorithms for multijoins in databases, and particularly basic graph patterns on graph databases. The aim of cds is to represent the data and additional data structures on it, using total space close to that of the plain (and, sometimes, compressed) data, while efficiently simulating the data structure operations. Cds turn out to be a perfect approach for the described problem: We designed and implemented cds that effectively use space close to that of the plain or compressed data, which is orders of magnitude less than existing systems, while retaining worst-case optimality and performing competitively with those systems in query time, sometimes being even considerably faster.

Cite as

Gonzalo Navarro. Compact Data Structures Meet Databases (Invited Talk). In 26th International Conference on Database Theory (ICDT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 255, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{navarro:LIPIcs.ICDT.2023.2,
  author =	{Navarro, Gonzalo},
  title =	{{Compact Data Structures Meet Databases}},
  booktitle =	{26th International Conference on Database Theory (ICDT 2023)},
  pages =	{2:1--2:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-270-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{255},
  editor =	{Geerts, Floris and Vandevoort, Brecht},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2023.2},
  URN =		{urn:nbn:de:0030-drops-177446},
  doi =		{10.4230/LIPIcs.ICDT.2023.2},
  annote =	{Keywords: succinct data structures, tries, multidimensional grids, text searching}
}
Document
Complete Volume
LIPIcs, Volume 244, ESA 2022, Complete Volume

Authors: Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, and Grzegorz Herman

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


Abstract
LIPIcs, Volume 244, ESA 2022, Complete Volume

Cite as

30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 1-1406, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@Proceedings{chechik_et_al:LIPIcs.ESA.2022,
  title =	{{LIPIcs, Volume 244, ESA 2022, Complete Volume}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{1--1406},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022},
  URN =		{urn:nbn:de:0030-drops-169374},
  doi =		{10.4230/LIPIcs.ESA.2022},
  annote =	{Keywords: LIPIcs, Volume 244, ESA 2022, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, and Grzegorz Herman

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


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 0:i-0:xxii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{chechik_et_al:LIPIcs.ESA.2022.0,
  author =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{0:i--0:xxii},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.0},
  URN =		{urn:nbn:de:0030-drops-169382},
  doi =		{10.4230/LIPIcs.ESA.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Enumerating Minimal Connected Dominating Sets

Authors: Faisal N. Abu-Khzam, Henning Fernau, Benjamin Gras, Mathieu Liedloff, and Kevin Mann

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


Abstract
The question to enumerate all (inclusion-wise) minimal connected dominating sets in a graph of order n in time significantly less than 2ⁿ is an open question that was asked in many places. We answer this question affirmatively, by providing an enumeration algorithm that runs in time 𝒪(1.9896ⁿ), using polynomial space only. The key to this result is the consideration of this enumeration problem on 2-degenerate graphs, which is proven to be possible in time 𝒪(1.9767ⁿ). Apart from solving this old open question, we also show new lower bound results. More precisely, we construct a family of graphs of order n with Ω(1.4890ⁿ) many minimal connected dominating sets, while previous examples achieved Ω(1.4422ⁿ). Our example happens to yield 4-degenerate graphs. Additionally, we give lower bounds for the previously not considered classes of 2-degenerate and of 3-degenerate graphs, which are Ω(1.3195ⁿ) and Ω(1.4723ⁿ), respectively. We also address essential questions concerning output-sensitive enumeration. Namely, we give reasons why our algorithm cannot be turned into an enumeration algorithm that guarantees polynomial delay without much efforts. More precisely, we prove that it is NP-complete to decide, given a graph G and a vertex set U, if there exists a minimal connected dominating set D with U ⊆ D, even if G is known to be 2-degenerate. Our reduction also shows that even any subexponential delay is not easy to achieve for enumerating minimal connected dominating sets. Another reduction shows that no FPT-algorithms can be expected for this extension problem concerning minimal connected dominating sets, parameterized by |U|. This also adds one more problem to the still rather few natural parameterized problems that are complete for the class W[3]. We also relate our enumeration problem to the famous open Hitting Set Transversal problem, which can be phrased in our context as the question to enumerate all minimal dominating sets of a graph with polynomial delay by showing that a polynomial-delay enumeration algorithm for minimal connected dominating sets implies an affirmative algorithmic solution to the Hitting Set Transversal problem.

Cite as

Faisal N. Abu-Khzam, Henning Fernau, Benjamin Gras, Mathieu Liedloff, and Kevin Mann. Enumerating Minimal Connected Dominating Sets. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{abukhzam_et_al:LIPIcs.ESA.2022.1,
  author =	{Abu-Khzam, Faisal N. and Fernau, Henning and Gras, Benjamin and Liedloff, Mathieu and Mann, Kevin},
  title =	{{Enumerating Minimal Connected Dominating Sets}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{1:1--1:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.1},
  URN =		{urn:nbn:de:0030-drops-169390},
  doi =		{10.4230/LIPIcs.ESA.2022.1},
  annote =	{Keywords: enumeration problems, connected domination, degenerate graphs}
}
Document
Non-Adaptive Edge Counting and Sampling via Bipartite Independent Set Queries

Authors: Raghavendra Addanki, Andrew McGregor, and Cameron Musco

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


Abstract
We study the problem of estimating the number of edges in an n-vertex graph, accessed via the Bipartite Independent Set query model introduced by Beame et al. (TALG '20). In this model, each query returns a Boolean, indicating the existence of at least one edge between two specified sets of nodes. We present a non-adaptive algorithm that returns a (1± ε) relative error approximation to the number of edges, with query complexity Õ(ε^{-5}log⁵ n), where Õ(⋅) hides poly(log log n) dependencies. This is the first non-adaptive algorithm in this setting achieving poly(1/ε,log n) query complexity. Prior work requires Ω(log² n) rounds of adaptivity. We avoid this by taking a fundamentally different approach, inspired by work on single-pass streaming algorithms. Moreover, for constant ε, our query complexity significantly improves on the best known adaptive algorithm due to Bhattacharya et al. (STACS '22), which requires O(ε^{-2} log^{11} n) queries. Building on our edge estimation result, we give the first {non-adaptive} algorithm for outputting a nearly uniformly sampled edge with query complexity Õ(ε^{-6} log⁶ n), improving on the works of Dell et al. (SODA '20) and Bhattacharya et al. (STACS '22), which require Ω(log³ n) rounds of adaptivity. Finally, as a consequence of our edge sampling algorithm, we obtain a Õ(n log^8 n) query algorithm for connectivity, using two rounds of adaptivity. This improves on a three-round algorithm of Assadi et al. (ESA '21) and is tight; there is no non-adaptive algorithm for connectivity making o(n²) queries.

Cite as

Raghavendra Addanki, Andrew McGregor, and Cameron Musco. Non-Adaptive Edge Counting and Sampling via Bipartite Independent Set Queries. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 2:1-2:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{addanki_et_al:LIPIcs.ESA.2022.2,
  author =	{Addanki, Raghavendra and McGregor, Andrew and Musco, Cameron},
  title =	{{Non-Adaptive Edge Counting and Sampling via Bipartite Independent Set Queries}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{2:1--2:16},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.2},
  URN =		{urn:nbn:de:0030-drops-169400},
  doi =		{10.4230/LIPIcs.ESA.2022.2},
  annote =	{Keywords: sublinear graph algorithms, bipartite independent set queries, edge sampling and counting, graph connectivity, query adaptivity}
}
Document
Hardness of Token Swapping on Trees

Authors: Oswin Aichholzer, Erik D. Demaine, Matias Korman, Anna Lubiw, Jayson Lynch, Zuzana Masárová, Mikhail Rudoy, Virginia Vassilevska Williams, and Nicole Wein

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


Abstract
Given a graph where every vertex has exactly one labeled token, how can we most quickly execute a given permutation on the tokens? In (sequential) token swapping, the goal is to use the shortest possible sequence of swaps, each of which exchanges the tokens at the two endpoints of an edge of the graph. In parallel token swapping, the goal is to use the fewest rounds, each of which consists of one or more swaps on the edges of a matching. We prove that both of these problems remain NP-hard when the graph is restricted to be a tree. These token swapping problems have been studied by disparate groups of researchers in discrete mathematics, theoretical computer science, robot motion planning, game theory, and engineering. Previous work establishes NP-completeness on general graphs (for both problems), constant-factor approximation algorithms, and some poly-time exact algorithms for simple graph classes such as cliques, stars, paths, and cycles. Sequential and parallel token swapping on trees were first studied over thirty years ago (as "sorting with a transposition tree") and over twenty-five years ago (as "routing permutations via matchings"), yet their complexities were previously unknown. We also show limitations on approximation of sequential token swapping on trees: we identify a broad class of algorithms that encompass all three known polynomial-time algorithms that achieve the best known approximation factor (which is 2) and show that no such algorithm can achieve an approximation factor less than 2.

Cite as

Oswin Aichholzer, Erik D. Demaine, Matias Korman, Anna Lubiw, Jayson Lynch, Zuzana Masárová, Mikhail Rudoy, Virginia Vassilevska Williams, and Nicole Wein. Hardness of Token Swapping on Trees. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{aichholzer_et_al:LIPIcs.ESA.2022.3,
  author =	{Aichholzer, Oswin and Demaine, Erik D. and Korman, Matias and Lubiw, Anna and Lynch, Jayson and Mas\'{a}rov\'{a}, Zuzana and Rudoy, Mikhail and Vassilevska Williams, Virginia and Wein, Nicole},
  title =	{{Hardness of Token Swapping on Trees}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{3:1--3:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.3},
  URN =		{urn:nbn:de:0030-drops-169413},
  doi =		{10.4230/LIPIcs.ESA.2022.3},
  annote =	{Keywords: Sorting, Token swapping, Trees, NP-hard, Approximation}
}
Document
Tight Bounds for Online Matching in Bounded-Degree Graphs with Vertex Capacities

Authors: Susanne Albers and Sebastian Schubert

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


Abstract
We study the b-matching problem in bipartite graphs G = (S,R,E). Each vertex s ∈ S is a server with individual capacity b_s. The vertices r ∈ R are requests that arrive online and must be assigned instantly to an eligible server. The goal is to maximize the size of the constructed matching. We assume that G is a (k,d)-graph [J. Naor and D. Wajc, 2018], where k specifies a lower bound on the degree of each server and d is an upper bound on the degree of each request. This setting models matching problems in timely applications. We present tight upper and lower bounds on the performance of deterministic online algorithms. In particular, we develop a new online algorithm via a primal-dual analysis. The optimal competitive ratio tends to 1, for arbitrary k ≥ d, as the server capacities increase. Hence, nearly optimal solutions can be computed online. Our results also hold for the vertex-weighted problem extension, and thus for AdWords and auction problems in which each bidder issues individual, equally valued bids. Our bounds improve the previous best competitive ratios. The asymptotic competitiveness of 1 is a significant improvement over the previous factor of 1-1/e^{k/d}, for the interesting range where k/d ≥ 1 is small. Recall that 1-1/e ≈ 0.63. Matching problems that admit a competitive ratio arbitrarily close to 1 are rare. Prior results rely on randomization or probabilistic input models.

Cite as

Susanne Albers and Sebastian Schubert. Tight Bounds for Online Matching in Bounded-Degree Graphs with Vertex Capacities. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{albers_et_al:LIPIcs.ESA.2022.4,
  author =	{Albers, Susanne and Schubert, Sebastian},
  title =	{{Tight Bounds for Online Matching in Bounded-Degree Graphs with Vertex Capacities}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{4:1--4:16},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.4},
  URN =		{urn:nbn:de:0030-drops-169420},
  doi =		{10.4230/LIPIcs.ESA.2022.4},
  annote =	{Keywords: online algorithms, deterministic algorithms, primal-dual analysis, b-matching, bounded-degree graph, variable vertex capacities, unweighted matching, vertex-weighted matching}
}
Document
TSP in a Simple Polygon

Authors: Henk Alkema, Mark de Berg, Morteza Monemizadeh, and Leonidas Theocharous

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


Abstract
We study the Traveling Salesman Problem inside a simple polygon. In this problem, which we call tsp in a simple polygon, we wish to compute a shortest tour that visits a given set S of n sites inside a simple polygon P with m edges while staying inside the polygon. This natural problem has, to the best of our knowledge, not been studied so far from a theoretical perspective. It can be solved exactly in poly(n,m) + 2^O(√nlog n) time, using an algorithm by Marx, Pilipczuk, and Pilipczuk (FOCS 2018) for subset tsp as a subroutine. We present a much simpler algorithm that solves tsp in a simple polygon directly and that has the same running time.

Cite as

Henk Alkema, Mark de Berg, Morteza Monemizadeh, and Leonidas Theocharous. TSP in a Simple Polygon. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{alkema_et_al:LIPIcs.ESA.2022.5,
  author =	{Alkema, Henk and de Berg, Mark and Monemizadeh, Morteza and Theocharous, Leonidas},
  title =	{{TSP in a Simple Polygon}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{5:1--5:14},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.5},
  URN =		{urn:nbn:de:0030-drops-169434},
  doi =		{10.4230/LIPIcs.ESA.2022.5},
  annote =	{Keywords: Traveling Salesman Problem, Subexponential algorithms, TSP with obstacles}
}
Document
Classical and Quantum Algorithms for Variants of Subset-Sum via Dynamic Programming

Authors: Jonathan Allcock, Yassine Hamoudi, Antoine Joux, Felix Klingelhöfer, and Miklos Santha

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


Abstract
Subset-Sum is an NP-complete problem where one must decide if a multiset of n integers contains a subset whose elements sum to a target value m. The best known classical and quantum algorithms run in time Õ(2^{n/2}) and Õ(2^{n/3}), respectively, based on the well-known meet-in-the-middle technique. Here we introduce a novel classical dynamic-programming-based data structure with applications to Subset-Sum and a number of variants, including Equal-Sums (where one seeks two disjoint subsets with the same sum), 2-Subset-Sum (a relaxed version of Subset-Sum where each item in the input set can be used twice in the summation), and Shifted-Sums, a generalization of both of these variants, where one seeks two disjoint subsets whose sums differ by some specified value. Given any modulus p, our data structure can be constructed in time O(np), after which queries can be made in time O(n) to the lists of subsets summing to any value modulo p. We use this data structure in combination with variable-time amplitude amplification and a new quantum pair finding algorithm, extending the quantum claw finding algorithm to the multiple solutions case, to give an O(2^{0.504n}) quantum algorithm for Shifted-Sums. This provides a notable improvement on the best known O(2^{0.773n}) classical running time established by Mucha et al. [Mucha et al., 2019]. We also study Pigeonhole Equal-Sums, a variant of Equal-Sums where the existence of a solution is guaranteed by the pigeonhole principle. For this problem we give faster classical and quantum algorithms with running time Õ(2^{n/2}) and Õ(2^{2n/5}), respectively.

Cite as

Jonathan Allcock, Yassine Hamoudi, Antoine Joux, Felix Klingelhöfer, and Miklos Santha. Classical and Quantum Algorithms for Variants of Subset-Sum via Dynamic Programming. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{allcock_et_al:LIPIcs.ESA.2022.6,
  author =	{Allcock, Jonathan and Hamoudi, Yassine and Joux, Antoine and Klingelh\"{o}fer, Felix and Santha, Miklos},
  title =	{{Classical and Quantum Algorithms for Variants of Subset-Sum via Dynamic Programming}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{6:1--6:18},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.6},
  URN =		{urn:nbn:de:0030-drops-169444},
  doi =		{10.4230/LIPIcs.ESA.2022.6},
  annote =	{Keywords: Quantum algorithm, classical algorithm, dynamic programming, representation technique, subset-sum, equal-sum, shifted-sum}
}
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