5 Search Results for "Sato, Thomas N."

Document
DOI: 10.4230/LIPIcs.FSCD.2024.24
IMELL Cut Elimination with Linear Overhead

Authors: Beniamino Accattoli and Claudio Sacerdoti Coen

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
Recently, Accattoli introduced the Exponential Substitution Calculus (ESC) given by untyped proof terms for Intuitionistic Multiplicative Exponential Linear Logic (IMELL), endowed with rewriting rules at-a-distance for cut elimination. He also introduced a new cut elimination strategy, dubbed the good strategy, and showed that its number of steps is a time cost model with polynomial overhead for ESC/IMELL, and the first such one. Here, we refine Accattoli’s result by introducing an abstract machine for ESC and proving that it implements the good strategy and computes cut-free terms/proofs within a linear overhead.
Cite as

Beniamino Accattoli and Claudio Sacerdoti Coen. IMELL Cut Elimination with Linear Overhead. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 24:1-24:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{accattoli_et_al:LIPIcs.FSCD.2024.24,
  author =	{Accattoli, Beniamino and Sacerdoti Coen, Claudio},
  title =	{{IMELL Cut Elimination with Linear Overhead}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{24:1--24:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.24},
  URN =		{urn:nbn:de:0030-drops-203539},
  doi =		{10.4230/LIPIcs.FSCD.2024.24},
  annote =	{Keywords: Lambda calculus, linear logic, abstract machines}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.97
Cut Sparsification and Succinct Representation of Submodular Hypergraphs

Authors: Yotam Kenneth and Robert Krauthgamer

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

Abstract
In cut sparsification, all cuts of a hypergraph H = (V,E,w) are approximated within 1±ε factor by a small hypergraph H'. This widely applied method was generalized recently to a setting where the cost of cutting each hyperedge e is provided by a splitting function g_e: 2^e → ℝ_+. This generalization is called a submodular hypergraph when the functions {g_e}_{e ∈ E} are submodular, and it arises in machine learning, combinatorial optimization, and algorithmic game theory. Previous work studied the setting where H' is a reweighted sub-hypergraph of H, and measured the size of H' by the number of hyperedges in it. In this setting, we present two results: (i) all submodular hypergraphs admit sparsifiers of size polynomial in n = |V| and ε^{-1}; (ii) we propose a new parameter, called spread, and use it to obtain smaller sparsifiers in some cases. We also show that for a natural family of splitting functions, relaxing the requirement that H' be a reweighted sub-hypergraph of H yields a substantially smaller encoding of the cuts of H (almost a factor n in the number of bits). This is in contrast to graphs, where the most succinct representation is attained by reweighted subgraphs. A new tool in our construction of succinct representation is the notion of deformation, where a splitting function g_e is decomposed into a sum of functions of small description, and we provide upper and lower bounds for deformation of common splitting functions.
Cite as

Yotam Kenneth and Robert Krauthgamer. Cut Sparsification and Succinct Representation of Submodular Hypergraphs. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 97:1-97:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kenneth_et_al:LIPIcs.ICALP.2024.97,
  author =	{Kenneth, Yotam and Krauthgamer, Robert},
  title =	{{Cut Sparsification and Succinct Representation of Submodular Hypergraphs}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{97:1--97:17},
  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.2024.97},
  URN =		{urn:nbn:de:0030-drops-202406},
  doi =		{10.4230/LIPIcs.ICALP.2024.97},
  annote =	{Keywords: Cut Sparsification, Submodular Hypergraphs, Succinct Representation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.115
On the Cut-Query Complexity of Approximating Max-Cut

Authors: Orestis Plevrakis, Seyoon Ragavan, and S. Matthew Weinberg

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

Abstract
We consider the problem of query-efficient global max-cut on a weighted undirected graph in the value oracle model examined by [Rubinstein et al., 2018]. Graph algorithms in this cut query model and other query models have recently been studied for various other problems such as min-cut, connectivity, bipartiteness, and triangle detection. Max-cut in the cut query model can also be viewed as a natural special case of submodular function maximization: on query S ⊆ V, the oracle returns the total weight of the cut between S and V\S. Our first main technical result is a lower bound stating that a deterministic algorithm achieving a c-approximation for any c > 1/2 requires Ω(n) queries. This uses an extension of the cut dimension to rule out approximation (prior work of [Graur et al., 2020] introducing the cut dimension only rules out exact solutions). Secondly, we provide a randomized algorithm with Õ(n) queries that finds a c-approximation for any c < 1. We achieve this using a query-efficient sparsifier for undirected weighted graphs (prior work of [Rubinstein et al., 2018] holds only for unweighted graphs). To complement these results, for most constants c ∈ (0,1], we nail down the query complexity of achieving a c-approximation, for both deterministic and randomized algorithms (up to logarithmic factors). Analogously to general submodular function maximization in the same model, we observe a phase transition at c = 1/2: we design a deterministic algorithm for global c-approximate max-cut in O(log n) queries for any c < 1/2, and show that any randomized algorithm requires Ω(n/log n) queries to find a c-approximate max-cut for any c > 1/2. Additionally, we show that any deterministic algorithm requires Ω(n²) queries to find an exact max-cut (enough to learn the entire graph).
Cite as

Orestis Plevrakis, Seyoon Ragavan, and S. Matthew Weinberg. On the Cut-Query Complexity of Approximating Max-Cut. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 115:1-115:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{plevrakis_et_al:LIPIcs.ICALP.2024.115,
  author =	{Plevrakis, Orestis and Ragavan, Seyoon and Weinberg, S. Matthew},
  title =	{{On the Cut-Query Complexity of Approximating Max-Cut}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{115:1--115:20},
  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.2024.115},
  URN =		{urn:nbn:de:0030-drops-202587},
  doi =		{10.4230/LIPIcs.ICALP.2024.115},
  annote =	{Keywords: query complexity, maximum cut, approximation algorithms, graph sparsification}
}
Document
Position
DOI: 10.4230/TGDK.2.1.2
Grounding Stream Reasoning Research

Authors: Pieter Bonte, Jean-Paul Calbimonte, Daniel de Leng, Daniele Dell'Aglio, Emanuele Della Valle, Thomas Eiter, Federico Giannini, Fredrik Heintz, Konstantin Schekotihin, Danh Le-Phuoc, Alessandra Mileo, Patrik Schneider, Riccardo Tommasini, Jacopo Urbani, and Giacomo Ziffer

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
In the last decade, there has been a growing interest in applying AI technologies to implement complex data analytics over data streams. To this end, researchers in various fields have been organising a yearly event called the "Stream Reasoning Workshop" to share perspectives, challenges, and experiences around this topic. In this paper, the previous organisers of the workshops and other community members provide a summary of the main research results that have been discussed during the first six editions of the event. These results can be categorised into four main research areas: The first is concerned with the technological challenges related to handling large data streams. The second area aims at adapting and extending existing semantic technologies to data streams. The third and fourth areas focus on how to implement reasoning techniques, either considering deductive or inductive techniques, to extract new and valuable knowledge from the data in the stream. This summary is written not only to provide a crystallisation of the field, but also to point out distinctive traits of the stream reasoning community. Moreover, it also provides a foundation for future research by enumerating a list of use cases and open challenges, to stimulate others to join this exciting research area.
Cite as

Pieter Bonte, Jean-Paul Calbimonte, Daniel de Leng, Daniele Dell'Aglio, Emanuele Della Valle, Thomas Eiter, Federico Giannini, Fredrik Heintz, Konstantin Schekotihin, Danh Le-Phuoc, Alessandra Mileo, Patrik Schneider, Riccardo Tommasini, Jacopo Urbani, and Giacomo Ziffer. Grounding Stream Reasoning Research. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 2:1-2:47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{bonte_et_al:TGDK.2.1.2,
  author =	{Bonte, Pieter and Calbimonte, Jean-Paul and de Leng, Daniel and Dell'Aglio, Daniele and Della Valle, Emanuele and Eiter, Thomas and Giannini, Federico and Heintz, Fredrik and Schekotihin, Konstantin and Le-Phuoc, Danh and Mileo, Alessandra and Schneider, Patrik and Tommasini, Riccardo and Urbani, Jacopo and Ziffer, Giacomo},
  title =	{{Grounding Stream Reasoning Research}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:47},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.2},
  URN =		{urn:nbn:de:0030-drops-198597},
  doi =		{10.4230/TGDK.2.1.2},
  annote =	{Keywords: Stream Reasoning, Stream Processing, RDF streams, Streaming Linked Data, Continuous query processing, Temporal Logics, High-performance computing, Databases}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.44
On the Complexity of Tree Edit Distance with Variables

Authors: Tatsuya Akutsu, Tomoya Mori, Naotoshi Nakamura, Satoshi Kozawa, Yuhei Ueno, and Thomas N. Sato

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

Abstract
In this paper, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas. We analyze the computational complexity of several variants of this model. In particular, we show that the problem is NP-complete for ordered trees. We also show for unordered trees that the problem of deciding whether or not the distance is 0 is graph isomorphism complete but can be solved in polynomial time if the maximum outdegree of input trees is bounded by a constant. We also present parameterized and exponential-time algorithms for ordered and unordered cases, respectively.
Cite as

Tatsuya Akutsu, Tomoya Mori, Naotoshi Nakamura, Satoshi Kozawa, Yuhei Ueno, and Thomas N. Sato. On the Complexity of Tree Edit Distance with Variables. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{akutsu_et_al:LIPIcs.ISAAC.2022.44,
  author =	{Akutsu, Tatsuya and Mori, Tomoya and Nakamura, Naotoshi and Kozawa, Satoshi and Ueno, Yuhei and Sato, Thomas N.},
  title =	{{On the Complexity of Tree Edit Distance with Variables}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.44},
  URN =		{urn:nbn:de:0030-drops-173295},
  doi =		{10.4230/LIPIcs.ISAAC.2022.44},
  annote =	{Keywords: Tree edit distance, unification, parameterized algorithms}
}
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