59 Search Results for "G�l, Anna"


Document
Gapped String Indexing in Subquadratic Space and Sublinear Query Time

Authors: Philip Bille, Inge Li Gørtz, Moshe Lewenstein, Solon P. Pissis, Eva Rotenberg, and Teresa Anna Steiner

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)


Abstract
In Gapped String Indexing, the goal is to compactly represent a string S of length n such that for any query consisting of two strings P₁ and P₂, called patterns, and an integer interval [α, β], called gap range, we can quickly find occurrences of P₁ and P₂ in S with distance in [α, β]. Gapped String Indexing is a central problem in computational biology and text mining and has thus received significant research interest, including parameterized and heuristic approaches. Despite this interest, the best-known time-space trade-offs for Gapped String Indexing are the straightforward 𝒪(n) space and 𝒪(n+ occ) query time or Ω(n²) space and Õ(|P₁| + |P₂| + occ) query time. We break through this barrier obtaining the first interesting trade-offs with polynomially subquadratic space and polynomially sublinear query time. In particular, we show that, for every 0 ≤ δ ≤ 1, there is a data structure for Gapped String Indexing with either Õ(n^{2-δ/3}) or Õ(n^{3-2δ}) space and Õ(|P₁| + |P₂| + n^{δ}⋅ (occ+1)) query time, where occ is the number of reported occurrences. As a new fundamental tool towards obtaining our main result, we introduce the Shifted Set Intersection problem: preprocess a collection of sets S₁, …, S_k of integers such that for any query consisting of three integers i,j,s, we can quickly output YES if and only if there exist a ∈ S_i and b ∈ S_j with a+s = b. We start by showing that the Shifted Set Intersection problem is equivalent to the indexing variant of 3SUM (3SUM Indexing) [Golovnev et al., STOC 2020]. We then give a data structure for Shifted Set Intersection with gaps, which entails a solution to the Gapped String Indexing problem. Furthermore, we enhance our data structure for deciding Shifted Set Intersection, so that we can support the reporting variant of the problem, i.e., outputting all certificates in the affirmative case. Via the obtained equivalence to 3SUM Indexing, we thus give new improved data structures for the reporting variant of 3SUM Indexing, and we show how this improves upon the state-of-the-art solution for Jumbled Indexing [Chan and Lewenstein, STOC 2015] for any alphabet of constant size σ > 5.

Cite as

Philip Bille, Inge Li Gørtz, Moshe Lewenstein, Solon P. Pissis, Eva Rotenberg, and Teresa Anna Steiner. Gapped String Indexing in Subquadratic Space and Sublinear Query Time. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{bille_et_al:LIPIcs.STACS.2024.16,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Lewenstein, Moshe and Pissis, Solon P. and Rotenberg, Eva and Steiner, Teresa Anna},
  title =	{{Gapped String Indexing in Subquadratic Space and Sublinear Query Time}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.16},
  URN =		{urn:nbn:de:0030-drops-197262},
  doi =		{10.4230/LIPIcs.STACS.2024.16},
  annote =	{Keywords: data structures, string indexing, indexing with gaps, two patterns}
}
Document
Computational Complexity of Discrete Problems (Dagstuhl Seminar 23111)

Authors: Anna Gál, Meena Mahajan, Rahul Santhanam, Till Tantau, and Manaswi Paraashar

Published in: Dagstuhl Reports, Volume 13, Issue 3 (2023)


Abstract
This report documents the program and activities of Dagstuhl Seminar 23111 "Computational Complexity of Discrete Problems", which was held in-person in March 2023 (the previous instance of the seminar series had been held online in March 2021). Following a description of the seminar’s objectives and its overall organization, this report lists the different major talks given during the seminar in alphabetical order of speakers, followed by the abstracts of the talks, including the main references and relevant sources where applicable. The return to an in-person setting allowed an intense atmosphere of active research and interaction throughout the five day seminar.

Cite as

Anna Gál, Meena Mahajan, Rahul Santhanam, Till Tantau, and Manaswi Paraashar. Computational Complexity of Discrete Problems (Dagstuhl Seminar 23111). In Dagstuhl Reports, Volume 13, Issue 3, pp. 17-31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@Article{gal_et_al:DagRep.13.3.17,
  author =	{G\'{a}l, Anna and Mahajan, Meena and Santhanam, Rahul and Tantau, Till and Paraashar, Manaswi},
  title =	{{Computational Complexity of Discrete Problems (Dagstuhl Seminar 23111)}},
  pages =	{17--31},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{3},
  editor =	{G\'{a}l, Anna and Mahajan, Meena and Santhanam, Rahul and Tantau, Till and Paraashar, Manaswi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.13.3.17},
  URN =		{urn:nbn:de:0030-drops-192261},
  doi =		{10.4230/DagRep.13.3.17},
  annote =	{Keywords: circuit complexity, communication complexity, computational complexity, lower bounds, randomness}
}
Document
RANDOM
Efficient Interactive Proofs for Non-Deterministic Bounded Space

Authors: Joshua Cook and Ron D. Rothblum

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)


Abstract
The celebrated IP = PSPACE Theorem gives an efficient interactive proof for any bounded-space algorithm. In this work we study interactive proofs for non-deterministic bounded space computations. While Savitch’s Theorem shows that nondeterministic bounded-space algorithms can be simulated by deterministic bounded-space algorithms, this simulation has a quadratic overhead. We give interactive protocols for nondeterministic algorithms directly to get faster verifiers. More specifically, for any non-deterministic space S algorithm, we construct an interactive proof in which the verifier runs in time Õ(n+S²). This improves on the best previous bound of Õ(n+S³) and matches the result for deterministic space bounded algorithms, up to polylog(S) factors. We further generalize to alternating bounded space algorithms. For any language L decided by a time T, space S algorithm that uses d alternations, we construct an interactive proof in which the verifier runs in time Õ(n + S log(T) + S d) and the prover runs in time 2^O(S). For d = O(log(T)), this matches the best known interactive proofs for deterministic algorithms, up to polylog(S) factors, and improves on the previous best verifier time for nondeterministic algorithms by a factor of log(T). We also improve the best prior verifier time for unbounded alternations by a factor of S. Using known connections of bounded alternation algorithms to bounded depth circuits, we also obtain faster verifiers for bounded depth circuits with unbounded fan-in.

Cite as

Joshua Cook and Ron D. Rothblum. Efficient Interactive Proofs for Non-Deterministic Bounded Space. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 47:1-47:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{cook_et_al:LIPIcs.APPROX/RANDOM.2023.47,
  author =	{Cook, Joshua and Rothblum, Ron D.},
  title =	{{Efficient Interactive Proofs for Non-Deterministic Bounded Space}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{47:1--47:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.47},
  URN =		{urn:nbn:de:0030-drops-188727},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.47},
  annote =	{Keywords: Interactive Proofs, Alternating Algorithms, AC0\lbrack2\rbrack, Doubly Efficient Proofs}
}
Document
Invited Talk
A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem (Invited Talk)

Authors: Anna R. Karlin

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


Abstract
We describe recent joint work with Nathan Klein and Shayan Oveis Gharan showing that for any metric TSP instance, the max entropy algorithm studied by [Anna R. Karlin et al., 2021] returns a solution of expected cost at most 3/2-ε times the cost of the optimal solution to the subtour elimination LP and hence is a 3/2-ε approximation for the metric TSP problem. The research discussed comes from [Anna R. Karlin et al., 2021], [Anna R. Karlin et al., 2022] and [Anna R. Karlin et al., 2022].

Cite as

Anna R. Karlin. A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{karlin:LIPIcs.ICALP.2023.1,
  author =	{Karlin, Anna R.},
  title =	{{A (Slightly) Improved Approximation Algorithm for the Metric Traveling Salesperson Problem}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{1:1--1:1},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.1},
  URN =		{urn:nbn:de:0030-drops-180531},
  doi =		{10.4230/LIPIcs.ICALP.2023.1},
  annote =	{Keywords: Traveling Salesperson Problem, approximation algorithm}
}
Document
Compressed Indexing for Consecutive Occurrences

Authors: Paweł Gawrychowski, Garance Gourdel, Tatiana Starikovskaya, and Teresa Anna Steiner

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


Abstract
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact occurrence of a given pattern P. However, practical applications motivate the necessity of considering more complex queries, for example concerning near occurrences of two patterns. Recently, Bille et al. [CPM 2021] introduced a variant of such queries, called gapped consecutive occurrences, in which a query consists of two patterns P₁ and P₂ and a range [a,b], and one must find all consecutive occurrences (q₁,q₂) of P₁ and P₂ such that q₂-q₁ ∈ [a,b]. By their results, we cannot hope for a very efficient indexing structure for such queries, even if a = 0 is fixed (although at the same time they provided a non-trivial upper bound). Motivated by this, we focus on a text given as a straight-line program (SLP) and design an index taking space polynomial in the size of the grammar that answers such queries in time optimal up to polylog factors.

Cite as

Paweł Gawrychowski, Garance Gourdel, Tatiana Starikovskaya, and Teresa Anna Steiner. Compressed Indexing for Consecutive Occurrences. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2023.12,
  author =	{Gawrychowski, Pawe{\l} and Gourdel, Garance and Starikovskaya, Tatiana and Steiner, Teresa Anna},
  title =	{{Compressed Indexing for Consecutive Occurrences}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{12:1--12:22},
  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.2023.12},
  URN =		{urn:nbn:de:0030-drops-179666},
  doi =		{10.4230/LIPIcs.CPM.2023.12},
  annote =	{Keywords: Compressed indexing, two patterns, consecutive occurrences}
}
Document
Dynamic Data Structures for Parameterized String Problems

Authors: Jędrzej Olkowski, Michał Pilipczuk, Mateusz Rychlicki, Karol Węgrzycki, and Anna Zych-Pawlewicz

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
We revisit classic string problems considered in the area of parameterized complexity, and study them through the lens of dynamic data structures. That is, instead of asking for a static algorithm that solves the given instance efficiently, our goal is to design a data structure that efficiently maintains a solution, or reports a lack thereof, upon updates in the instance. We first consider the CLOSEST STRING problem, for which we design randomized dynamic data structures with amortized update times d^𝒪(d) and |Σ|^𝒪(d), respectively, where Σ is the alphabet and d is the assumed bound on the maximum distance. These are obtained by combining known static approaches to CLOSEST STRING with color-coding. Next, we note that from a result of Frandsen et al. [J. ACM'97] one can easily infer a meta-theorem that provides dynamic data structures for parameterized string problems with worst-case update time of the form 𝒪_k(log log n), where k is the parameter in question and n is the length of the string. We showcase the utility of this meta-theorem by giving such data structures for problems DISJOINT FACTORS and EDIT DISTANCE. We also give explicit data structures for these problems, with worst-case update times 𝒪(k 2^k log log n) and 𝒪(k²log log n), respectively. Finally, we discuss how a lower bound methodology introduced by Amarilli et al. [ICALP'21] can be used to show that obtaining update time 𝒪(f(k)) for DISJOINT FACTORS and EDIT DISTANCE is unlikely already for a constant value of the parameter k.

Cite as

Jędrzej Olkowski, Michał Pilipczuk, Mateusz Rychlicki, Karol Węgrzycki, and Anna Zych-Pawlewicz. Dynamic Data Structures for Parameterized String Problems. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 50:1-50:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{olkowski_et_al:LIPIcs.STACS.2023.50,
  author =	{Olkowski, J\k{e}drzej and Pilipczuk, Micha{\l} and Rychlicki, Mateusz and W\k{e}grzycki, Karol and Zych-Pawlewicz, Anna},
  title =	{{Dynamic Data Structures for Parameterized String Problems}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{50:1--50:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.50},
  URN =		{urn:nbn:de:0030-drops-177026},
  doi =		{10.4230/LIPIcs.STACS.2023.50},
  annote =	{Keywords: Parameterized algorithms, Dynamic data structures, String problems, Closest String, Edit Distance, Disjoint Factors, Predecessor problem}
}
Document
Certificate Games

Authors: Sourav Chakraborty, Anna Gál, Sophie Laplante, Rajat Mittal, and Anupa Sunny

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)


Abstract
We introduce and study Certificate Game complexity, a measure of complexity based on the probability of winning a game where two players are given inputs with different function values and are asked to output some index i such that x_i≠ y_i, in a zero-communication setting. We give upper and lower bounds for private coin, public coin, shared entanglement and non-signaling strategies, and give some separations. We show that complexity in the public coin model is upper bounded by Randomized query and Certificate complexity. On the other hand, it is lower bounded by fractional and randomized certificate complexity, making it a good candidate to prove strong lower bounds on randomized query complexity. Complexity in the private coin model is bounded from below by zero-error randomized query complexity. The quantum measure highlights an interesting and surprising difference between classical and quantum query models. Whereas the public coin certificate game complexity is bounded from above by randomized query complexity, the quantum certificate game complexity can be quadratically larger than quantum query complexity. We use non-signaling, a notion from quantum information, to give a lower bound of n on the quantum certificate game complexity of the OR function, whose quantum query complexity is Θ(√n), then go on to show that this "non-signaling bottleneck" applies to all functions with high sensitivity, block sensitivity or fractional block sensitivity. We also consider the single-bit version of certificate games, where the inputs of the two players are restricted to having Hamming distance 1. We prove that the single-bit version of certificate game complexity with shared randomness is equal to sensitivity up to constant factors, thus giving a new characterization of sensitivity. On the other hand, the single-bit version of certificate game complexity with private randomness is equal to λ², where λ is the spectral sensitivity.

Cite as

Sourav Chakraborty, Anna Gál, Sophie Laplante, Rajat Mittal, and Anupa Sunny. Certificate Games. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 32:1-32:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{chakraborty_et_al:LIPIcs.ITCS.2023.32,
  author =	{Chakraborty, Sourav and G\'{a}l, Anna and Laplante, Sophie and Mittal, Rajat and Sunny, Anupa},
  title =	{{Certificate Games}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{32:1--32:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.32},
  URN =		{urn:nbn:de:0030-drops-175353},
  doi =		{10.4230/LIPIcs.ITCS.2023.32},
  annote =	{Keywords: block sensitivity, boolean function complexity, certificate complexity, query complexity, sensitivity, zero-communication two-player games}
}
Document
On the Axiomatisation of Branching Bisimulation Congruence over CCS

Authors: Luca Aceto, Valentina Castiglioni, Anna Ingólfsdóttir, and Bas Luttik

Published in: LIPIcs, Volume 243, 33rd International Conference on Concurrency Theory (CONCUR 2022)


Abstract
In this paper we investigate the equational theory of (the restriction, relabelling, and recursion free fragment of) CCS modulo rooted branching bisimilarity, which is a classic, bisimulation-based notion of equivalence that abstracts from internal computational steps in process behaviour. Firstly, we show that CCS is not finitely based modulo the considered congruence. As a key step of independent interest in the proof of that negative result, we prove that each CCS process has a unique parallel decomposition into indecomposable processes modulo branching bisimilarity. As a second main contribution, we show that, when the set of actions is finite, rooted branching bisimilarity has a finite equational basis over CCS enriched with the left merge and communication merge operators from ACP.

Cite as

Luca Aceto, Valentina Castiglioni, Anna Ingólfsdóttir, and Bas Luttik. On the Axiomatisation of Branching Bisimulation Congruence over CCS. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{aceto_et_al:LIPIcs.CONCUR.2022.6,
  author =	{Aceto, Luca and Castiglioni, Valentina and Ing\'{o}lfsd\'{o}ttir, Anna and Luttik, Bas},
  title =	{{On the Axiomatisation of Branching Bisimulation Congruence over CCS}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2022.6},
  URN =		{urn:nbn:de:0030-drops-170692},
  doi =		{10.4230/LIPIcs.CONCUR.2022.6},
  annote =	{Keywords: Equational basis, Weak semantics, CCS, Parallel composition}
}
Document
Dynamic Coloring of Unit Interval Graphs with Limited Recourse Budget

Authors: Bartłomiej Bosek and Anna Zych-Pawlewicz

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


Abstract
In this paper we study the problem of coloring a unit interval graph which changes dynamically. In our model the unit intervals are added or removed one at the time, and have to be colored immediately, so that no two overlapping intervals share the same color. After each update only a limited number of intervals are allowed to be recolored. The limit on the number of recolorings per update is called the recourse budget. In this paper we show, that if the graph remains k-colorable at all times, the updates consist of insertions only, and the final instance consists of n intervals, then we can achieve an amortized recourse budget of 𝒪({k⁷ log n}) while maintaining a proper coloring with k colors. This is an exponential improvement over the result in [Bartłomiej Bosek et al., 2020] in terms of both k and n. We complement this result by showing the lower bound of Ω(n) on the amortized recourse budget in the fully dynamic setting. Our incremental algorithm can be efficiently implemented. As an additional application of our techniques we include a new combinatorial result on coloring unit circular arc graphs. Let L be the maximum number of arcs intersecting in one point for some set of unit circular arcs 𝒜. We show that if there is a set 𝒜' of non-intersecting unit arcs of size L²-1 such that 𝒜 ∪ 𝒜' does not contain L+1 arcs intersecting in one point, then it is possible to color 𝒜 with L colors. This complements the work on circular arc coloring [Belkale and Chandran, 2009; Tucker, 1975; Valencia-Pabon, 2003], which specifies sufficient conditions needed to color 𝒜 with L+1 colors or more.

Cite as

Bartłomiej Bosek and Anna Zych-Pawlewicz. Dynamic Coloring of Unit Interval Graphs with Limited Recourse Budget. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bosek_et_al:LIPIcs.ESA.2022.25,
  author =	{Bosek, Bart{\l}omiej and Zych-Pawlewicz, Anna},
  title =	{{Dynamic Coloring of Unit Interval Graphs with Limited Recourse Budget}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{25:1--25:14},
  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.2022.25},
  URN =		{urn:nbn:de:0030-drops-169637},
  doi =		{10.4230/LIPIcs.ESA.2022.25},
  annote =	{Keywords: dynamic algorithms, unit interval graphs, coloring, recourse budget, parametrized dynamic algorithms}
}
Document
An Experimental Study of Algorithms for Packing Arborescences

Authors: Loukas Georgiadis, Dionysios Kefallinos, Anna Mpanti, and Stavros D. Nikolopoulos

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)


Abstract
A classic result of Edmonds states that the maximum number of edge-disjoint arborescences of a directed graph G, rooted at a designated vertex s, equals the minimum cardinality c_G(s) of an s-cut of G. This concept is related to the edge connectivity λ(G) of a strongly connected directed graph G, defined as the minimum number of edges whose deletion leaves a graph that is not strongly connected. In this paper, we address the question of how efficiently we can compute a maximum packing of edge-disjoint arborescences in practice, compared to the time required to determine the edge connectivity of a graph. To that end, we explore the design space of efficient algorithms for packing arborescences of a directed graph in practice and conduct a thorough empirical study to highlight the merits and weaknesses of each technique. In particular, we present an efficient implementation of Gabow’s arborescence packing algorithm and provide a simple but efficient heuristic that significantly improves its running time in practice.

Cite as

Loukas Georgiadis, Dionysios Kefallinos, Anna Mpanti, and Stavros D. Nikolopoulos. An Experimental Study of Algorithms for Packing Arborescences. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{georgiadis_et_al:LIPIcs.SEA.2022.14,
  author =	{Georgiadis, Loukas and Kefallinos, Dionysios and Mpanti, Anna and Nikolopoulos, Stavros D.},
  title =	{{An Experimental Study of Algorithms for Packing Arborescences}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.14},
  URN =		{urn:nbn:de:0030-drops-165480},
  doi =		{10.4230/LIPIcs.SEA.2022.14},
  annote =	{Keywords: Arborescences, Edge Connectivity, Graph Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Social Distancing Network Creation

Authors: Tobias Friedrich, Hans Gawendowicz, Pascal Lenzner, and Anna Melnichenko

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
During a pandemic people have to find a trade-off between meeting others and staying safely at home. While meeting others is pleasant, it also increases the risk of infection. We consider this dilemma by introducing a game-theoretic network creation model in which selfish agents can form bilateral connections. They benefit from network neighbors, but at the same time, they want to maximize their distance to all other agents. This models the inherent conflict that social distancing rules impose on the behavior of selfish agents in a social network. Besides addressing this familiar issue, our model can be seen as the inverse to the well-studied Network Creation Game by Fabrikant et al. [PODC 2003] where agents aim at being as central as possible in the created network. Thus, our work is in-line with studies that compare minimization problems with their maximization versions. We look at two variants of network creation governed by social distancing. In the first variant, there are no restrictions on the connections being formed. We characterize optimal and equilibrium networks, and we derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant is the model’s generalization that allows restrictions on the connections that can be formed. As our main result, we prove that Swap-Maximal Routing-Cost Spanning Trees, an efficiently computable weaker variant of Maximum Routing-Cost Spanning Trees, actually resemble equilibria for a significant range of the parameter space. Moreover, we give almost tight bounds on the Price of Anarchy and Price of Stability. These results imply that, compared the well-studied inverse models, under social distancing the agents' selfish behavior has a significantly stronger impact on the quality of the equilibria, i.e., allowing socially much worse stable states.

Cite as

Tobias Friedrich, Hans Gawendowicz, Pascal Lenzner, and Anna Melnichenko. Social Distancing Network Creation. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 62:1-62:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{friedrich_et_al:LIPIcs.ICALP.2022.62,
  author =	{Friedrich, Tobias and Gawendowicz, Hans and Lenzner, Pascal and Melnichenko, Anna},
  title =	{{Social Distancing Network Creation}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{62:1--62:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.62},
  URN =		{urn:nbn:de:0030-drops-164038},
  doi =		{10.4230/LIPIcs.ICALP.2022.62},
  annote =	{Keywords: Algorithmic Game Theory, Equilibrium Existence, Price of Anarchy, Network Creation Game, Social Distancing, Maximization vs. Minimization Problems}
}
Document
The Fine-Grained Complexity of Episode Matching

Authors: Philip Bille, Inge Li Gørtz, Shay Mozes, Teresa Anna Steiner, and Oren Weimann

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)


Abstract
Given two strings S and P, the Episode Matching problem is to find the shortest substring of S that contains P as a subsequence. The best known upper bound for this problem is Õ(nm) by Das et al. (1997), where n,m are the lengths of S and P, respectively. Although the problem is well studied and has many applications in data mining, this bound has never been improved. In this paper we show why this is the case by proving that no O((nm)^{1-ε}) algorithm (even for binary strings) exists, unless the Strong Exponential Time Hypothesis (SETH) is false. We then consider the indexing version of the problem, where S is preprocessed into a data structure for answering episode matching queries P. We show that for any τ, there is a data structure using O(n+(n/(τ)) ^k) space that answers episode matching queries for any P of length k in O(k⋅ τ ⋅ log log n) time. We complement this upper bound with an almost matching lower bound, showing that any data structure that answers episode matching queries for patterns of length k in time O(n^δ), must use Ω(n^{k-kδ-o(1)}) space, unless the Strong k-Set Disjointness Conjecture is false. Finally, for the special case of k = 2, we present a faster construction of the data structure using fast min-plus multiplication of bounded integer matrices.

Cite as

Philip Bille, Inge Li Gørtz, Shay Mozes, Teresa Anna Steiner, and Oren Weimann. The Fine-Grained Complexity of Episode Matching. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bille_et_al:LIPIcs.CPM.2022.4,
  author =	{Bille, Philip and G{\o}rtz, Inge Li and Mozes, Shay and Steiner, Teresa Anna and Weimann, Oren},
  title =	{{The Fine-Grained Complexity of Episode Matching}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{4:1--4:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.4},
  URN =		{urn:nbn:de:0030-drops-161312},
  doi =		{10.4230/LIPIcs.CPM.2022.4},
  annote =	{Keywords: Pattern matching, fine-grained complexity, longest common subsequence}
}
Document
Compact Representation for Matrices of Bounded Twin-Width

Authors: Michał Pilipczuk, Marek Sokołowski, and Anna Zych-Pawlewicz

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)


Abstract
For every fixed d ∈ ℕ, we design a data structure that represents a binary n × n matrix that is d-twin-ordered. The data structure occupies 𝒪_d(n) bits, which is the least one could hope for, and can be queried for entries of the matrix in time 𝒪_d(log log n) per query.

Cite as

Michał Pilipczuk, Marek Sokołowski, and Anna Zych-Pawlewicz. Compact Representation for Matrices of Bounded Twin-Width. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 52:1-52:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{pilipczuk_et_al:LIPIcs.STACS.2022.52,
  author =	{Pilipczuk, Micha{\l} and Soko{\l}owski, Marek and Zych-Pawlewicz, Anna},
  title =	{{Compact Representation for Matrices of Bounded Twin-Width}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{52:1--52:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.52},
  URN =		{urn:nbn:de:0030-drops-158620},
  doi =		{10.4230/LIPIcs.STACS.2022.52},
  annote =	{Keywords: twin-width, compact representation, adjacency oracle}
}
Document
Interval Edge Coloring of Bipartite Graphs with Small Vertex Degrees

Authors: Anna Małafiejska, Michał Małafiejski, Krzysztof M. Ocetkiewicz, and Krzysztof Pastuszak

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


Abstract
An edge coloring of a graph G is called interval edge coloring if for each v ∈ V(G) the set of colors on edges incident to v forms an interval of integers. A graph G is interval colorable if there is an interval coloring of G. For an interval colorable graph G, by the interval chromatic index of G, denoted by χ'_i(G), we mean the smallest number k such that G is interval colorable with k colors. A bipartite graph G is called (α,β)-biregular if each vertex in one part has degree α and each vertex in the other part has degree β. A graph G is called (α*,β*)-bipartite if G is a subgraph of an (α,β)-biregular graph and the maximum degree in one part is α and the maximum degree in the other part is β. In the paper we study the problem of interval edge colorings of (k*,2*)-bipartite graphs, for k ∈ {3,4,5}, and of (5*,3*)-bipartite graphs. We prove that every (5*,2*)-bipartite graph admits an interval edge coloring using at most 6 colors, which can be found in O(n^{3/2}) time, and we prove that an interval edge 5-coloring of a (5*,2*)-bipartite graph can be found in O(n^{3/2}) time, if it exists. We show that every (4^*,2^*)-bipartite graph admits an interval edge 4-coloring, which can be found in O(n) time. The two following problems of interval edge coloring are known to be NP-complete: 6-coloring of (6,3)-biregular graphs (Asratian and Casselgren (2006)) and 5-coloring of (5*,5*)-bipartite graphs (Giaro (1997)). In the paper we prove NP-completeness of 5-coloring of (5*,3*)-bipartite graphs.

Cite as

Anna Małafiejska, Michał Małafiejski, Krzysztof M. Ocetkiewicz, and Krzysztof Pastuszak. Interval Edge Coloring of Bipartite Graphs with Small Vertex Degrees. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 26:1-26:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{malafiejska_et_al:LIPIcs.ISAAC.2021.26,
  author =	{Ma{\l}afiejska, Anna and Ma{\l}afiejski, Micha{\l} and Ocetkiewicz, Krzysztof M. and Pastuszak, Krzysztof},
  title =	{{Interval Edge Coloring of Bipartite Graphs with Small Vertex Degrees}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{26:1--26:12},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.26},
  URN =		{urn:nbn:de:0030-drops-154596},
  doi =		{10.4230/LIPIcs.ISAAC.2021.26},
  annote =	{Keywords: interval edge coloring, biregular graphs, coloring algorithm}
}
Document
On Classical Decidable Logics Extended with Percentage Quantifiers and Arithmetics

Authors: Bartosz Bednarczyk, Maja Orłowska, Anna Pacanowska, and Tony Tan

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)


Abstract
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of restriction imposed on formulae from the language. Despite the success of the mentioned logics in areas like formal verification and knowledge representation, such first-order fragments are too weak to express even the simplest statistical constraints, required for modelling of influence networks or in statistical reasoning. In this work we investigate the extensions of these classical decidable logics with percentage quantifiers, specifying how frequently a formula is satisfied in the indented model. We show, surprisingly, that all the mentioned decidable fragments become undecidable under such extension, sharpening the existing results in the literature. Our negative results are supplemented by decidability of the two-variable guarded fragment with even more expressive counting, namely Presburger constraints. Our results can be applied to infer decidability of various modal and description logics, e.g. Presburger Modal Logics with Converse or ALCI, with expressive cardinality constraints.

Cite as

Bartosz Bednarczyk, Maja Orłowska, Anna Pacanowska, and Tony Tan. On Classical Decidable Logics Extended with Percentage Quantifiers and Arithmetics. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 36:1-36:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{bednarczyk_et_al:LIPIcs.FSTTCS.2021.36,
  author =	{Bednarczyk, Bartosz and Or{\l}owska, Maja and Pacanowska, Anna and Tan, Tony},
  title =	{{On Classical Decidable Logics Extended with Percentage Quantifiers and Arithmetics}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{36:1--36:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.36},
  URN =		{urn:nbn:de:0030-drops-155478},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.36},
  annote =	{Keywords: statistical reasoning, knowledge representation, satisfiability, fragments of first-order logic, guarded fragment, two-variable fragment, (un)decidability}
}
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