12 Search Results for "Gu, Yong"

Document
DOI: 10.4230/LIPIcs.ESA.2025.74
Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications

Authors: Paweł Gawrychowski, Egor Gorbachev, and Tomasz Kociumaka

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Min-plus matrix multiplication is a fundamental tool for designing algorithms operating on distances in graphs and different problems solvable by dynamic programming. We know that, assuming the APSP hypothesis, no subcubic-time algorithm exists for the case of general matrices. However, in many applications the matrices admit certain structural properties that can be used to design faster algorithms. For example, when considering a planar graph, one often works with a Monge matrix A, meaning that the density matrix A^◻ has non-negative entries, that is, A^◻_{i,j} := A_{i+1,j} + A_{i,j+1} - A_{i,j} -A_{i+1,j+1} ≥ 0. The min-plus product of two n×n Monge matrices can be computed in 𝒪(n²) time using the famous SMAWK algorithm. In applications such as longest common subsequence, edit distance, and longest increasing subsequence, the matrices are even more structured, as observed by Tiskin [J. Discrete Algorithms, 2008]: they are (or can be converted to) simple unit-Monge matrices, meaning that the density matrix is a permutation matrix and, furthermore, the first column and the last row of the matrix consist of only zeroes. Such matrices admit an implicit representation of size 𝒪(n) and, as shown by Tiskin [SODA 2010 & Algorithmica, 2015], their min-plus product can be computed in 𝒪(nlog n) time. Russo [SPIRE 2010 & Theor. Comput. Sci., 2012] identified a general structural property of matrices that admit such efficient representation and min-plus multiplication algorithms: the core size δ, defined as the number of non-zero entries in the density matrices of the input and output matrices. He provided an adaptive implementation of the SMAWK algorithm that runs in 𝒪((n+δ)log³ n) or 𝒪((n+δ)log² n) time (depending on the representation of the input matrices). In this work, we further investigate the core size as the parameter that enables efficient min-plus matrix multiplication. On the combinatorial side, we provide a (linear) bound on the core size of the product matrix in terms of the core sizes of the input matrices. On the algorithmic side, we generalize Tiskin’s algorithm (but, arguably, with a more elementary analysis) to solve the core-sparse Monge matrix multiplication problem in 𝒪(n+δlog δ) ⊆ 𝒪(n + δ log n) time, matching the complexity for simple unit-Monge matrices. As witnessed by the recent work of Gorbachev and Kociumaka [STOC'25] for edit distance with integer weights, our generalization opens up the possibility of speed-ups for weighted sequence alignment problems. Furthermore, our multiplication algorithm is also capable of producing an efficient data structure for recovering the witness for any given entry of the output matrix. This allows us, for example, to preprocess an integer array of size n in Õ(n) time so that the longest increasing subsequence of any sub-array can be reconstructed in Õ(𝓁) time, where 𝓁 is the length of the reported subsequence. In comparison, Karthik C. S. and Rahul [arXiv, 2024] recently achieved 𝒪(𝓁+n^{1/2}polylog n)-time reporting after 𝒪(n^{3/2}polylog n)-time preprocessing.
Cite as

Paweł Gawrychowski, Egor Gorbachev, and Tomasz Kociumaka. Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 74:1-74:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.ESA.2025.74,
  author =	{Gawrychowski, Pawe{\l} and Gorbachev, Egor and Kociumaka, Tomasz},
  title =	{{Core-Sparse Monge Matrix Multiplication: Improved Algorithm and Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{74:1--74:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.74},
  URN =		{urn:nbn:de:0030-drops-245427},
  doi =		{10.4230/LIPIcs.ESA.2025.74},
  annote =	{Keywords: Min-plus matrix multiplication, Monge matrix, longest increasing subsequence}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.14
Canonical for Automated Theorem Proving in Lean

Authors: Chase Norman and Jeremy Avigad

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic supports higher-order and dependently-typed goals, structural recursion over indexed inductive types, and definitional equality. Canonical finds proofs for 84% of Natural Number Game problems in 51 seconds total.
Cite as

Chase Norman and Jeremy Avigad. Canonical for Automated Theorem Proving in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{norman_et_al:LIPIcs.ITP.2025.14,
  author =	{Norman, Chase and Avigad, Jeremy},
  title =	{{Canonical for Automated Theorem Proving in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.14},
  URN =		{urn:nbn:de:0030-drops-246128},
  doi =		{10.4230/LIPIcs.ITP.2025.14},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Proving, Dependent Type Theory, Inhabitation, Unification, Program Synthesis, Formal Methods}
}
Document
DOI: 10.4230/LIPIcs.GIScience.2025.4
Precomputed Topological Relations for Integrated Geospatial Analysis Across Knowledge Graphs

Authors: Katrina Schweikert, David K. Kedrowski, Shirly Stephen, and Torsten Hahmann

Published in: LIPIcs, Volume 346, 13th International Conference on Geographic Information Science (GIScience 2025)

Abstract
Geospatial Knowledge Graphs (GeoKGs) represent a significant advancement in the integration of AI-driven geographic information, facilitating interoperable and semantically rich geospatial analytics across various domains. This paper explores the use of topologically enriched GeoKGs, built on an explicit representation of S2 Geometry alongside precomputed topological relations, for constructing efficient geospatial analysis workflows within and across knowledge graphs (KGs). Using the SAWGraph knowledge graph as a case study focused on enviromental contamination by PFAS, we demonstrate how this framework supports fundamental GIS operations - such as spatial filtering, proximity analysis, overlay operations and network analysis - in a GeoKG setting while allowing for the easy linking of these operations with one another and with semantic filters. This enables the efficient execution of complex geospatial analyses as semantically-explicit queries and enhances the usability of geospatial data across graphs. Additionally, the framework eliminates the need for explicit support for GeoSPARQL’s topological operations in the utilized graph databases and better integrates spatial knowledge into the overall semantic inference process supported by RDFS and OWL ontologies.
Cite as

Katrina Schweikert, David K. Kedrowski, Shirly Stephen, and Torsten Hahmann. Precomputed Topological Relations for Integrated Geospatial Analysis Across Knowledge Graphs. In 13th International Conference on Geographic Information Science (GIScience 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 346, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schweikert_et_al:LIPIcs.GIScience.2025.4,
  author =	{Schweikert, Katrina and Kedrowski, David K. and Stephen, Shirly and Hahmann, Torsten},
  title =	{{Precomputed Topological Relations for Integrated Geospatial Analysis Across Knowledge Graphs}},
  booktitle =	{13th International Conference on Geographic Information Science (GIScience 2025)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-378-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{346},
  editor =	{Sila-Nowicka, Katarzyna and Moore, Antoni and O'Sullivan, David and Adams, Benjamin and Gahegan, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2025.4},
  URN =		{urn:nbn:de:0030-drops-238332},
  doi =		{10.4230/LIPIcs.GIScience.2025.4},
  annote =	{Keywords: knowledge graph, GeoKG, spatial analysis, ontology, SPARQL, GeoSPARQL, discrete global grid system, S2 geometry, GeoAI, PFAS}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.57
Undirected 3-Fault Replacement Path in Nearly Cubic Time

Authors: Shucheng Chi, Ran Duan, Benyu Wang, and Tianle Xie

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
Given a graph G = (V,E) (n = |V|, m = |E|) and two vertices s,t ∈ V, the f-fault replacement path (fFRP) problem computes for every set F of at most f edges, the distance from s to t when edges in F fail. A recent result shows that 2FRP in directed graphs can be solved in Õ(n³) time [Vassilevska Williams, Woldeghebriel, Xu 2022]. In this paper, we show a 3FRP algorithm in deterministic Õ(n³) time for undirected weighted graphs, which almost matches the size of the output. This implies that fFRP in undirected graphs can be solved in nearly optimal Õ(n^f) time for all f ≥ 3. To construct our 3FRP algorithm, we introduce an incremental distance sensitivity oracle (DSO) for undirected graphs with Õ(n²) worst-case update time, while preprocessing time, space, and query time are still Õ(n³), Õ(n²) and Õ(1), respectively, which match the static DSO [Bernstein and Karger 2009]. Here in a DSO, we can preprocess a graph so that the distance between any pair of vertices given any failed edge can be answered efficiently. From the recent result in [Peng and Rubinstein 2023], we can obtain an offline dynamic DSO from the incremental worst-case DSO, which makes the construction of our 3FRP algorithm more convenient. By the offline dynamic DSO, we can also construct a 2-fault single-source replacement path (2-fault SSRP) algorithm in Õ(n³) time, that is, from a given vertex s, we want to find the distance to any vertex t when any pair of edges fail. Thus the Õ(n³) time complexity for 2-fault SSRP is also nearly optimal. Now we know that in undirected graphs 1FRP can be solved in Õ(m) time [Nardelli, Proietti, Widmayer 2001], and 2FRP and 3FRP in undirected graphs can be solved in Õ(n³) time. In this paper, we also show that a truly subcubic algorithm for 2FRP in undirected weighted graphs does not exist under APSP hypothesis.
Cite as

Shucheng Chi, Ran Duan, Benyu Wang, and Tianle Xie. Undirected 3-Fault Replacement Path in Nearly Cubic Time. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 57:1-57:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chi_et_al:LIPIcs.ICALP.2025.57,
  author =	{Chi, Shucheng and Duan, Ran and Wang, Benyu and Xie, Tianle},
  title =	{{Undirected 3-Fault Replacement Path in Nearly Cubic Time}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{57:1--57:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.57},
  URN =		{urn:nbn:de:0030-drops-234346},
  doi =		{10.4230/LIPIcs.ICALP.2025.57},
  annote =	{Keywords: Graph Algorithm, Shortest Path, Replacement Path}
}
Document
Position
DOI: 10.4230/TGDK.1.1.5
Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities

Authors: Jiaoyan Chen, Hang Dong, Janna Hastings, Ernesto Jiménez-Ruiz, Vanessa López, Pierre Monnin, Catia Pesquita, Petr Škoda, and Valentina Tamma

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
The term life sciences refers to the disciplines that study living organisms and life processes, and include chemistry, biology, medicine, and a range of other related disciplines. Research efforts in life sciences are heavily data-driven, as they produce and consume vast amounts of scientific data, much of which is intrinsically relational and graph-structured. The volume of data and the complexity of scientific concepts and relations referred to therein promote the application of advanced knowledge-driven technologies for managing and interpreting data, with the ultimate aim to advance scientific discovery. In this survey and position paper, we discuss recent developments and advances in the use of graph-based technologies in life sciences and set out a vision for how these technologies will impact these fields into the future. We focus on three broad topics: the construction and management of Knowledge Graphs (KGs), the use of KGs and associated technologies in the discovery of new knowledge, and the use of KGs in artificial intelligence applications to support explanations (explainable AI). We select a few exemplary use cases for each topic, discuss the challenges and open research questions within these topics, and conclude with a perspective and outlook that summarizes the overarching challenges and their potential solutions as a guide for future research.
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Jiaoyan Chen, Hang Dong, Janna Hastings, Ernesto Jiménez-Ruiz, Vanessa López, Pierre Monnin, Catia Pesquita, Petr Škoda, and Valentina Tamma. Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 5:1-5:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{chen_et_al:TGDK.1.1.5,
  author =	{Chen, Jiaoyan and Dong, Hang and Hastings, Janna and Jim\'{e}nez-Ruiz, Ernesto and L\'{o}pez, Vanessa and Monnin, Pierre and Pesquita, Catia and \v{S}koda, Petr and Tamma, Valentina},
  title =	{{Knowledge Graphs for the Life Sciences: Recent Developments, Challenges and Opportunities}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:33},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.5},
  URN =		{urn:nbn:de:0030-drops-194791},
  doi =		{10.4230/TGDK.1.1.5},
  annote =	{Keywords: Knowledge graphs, Life science, Knowledge discovery, Explainable AI}
}
Document
Survey
DOI: 10.4230/TGDK.1.1.11
How Does Knowledge Evolve in Open Knowledge Graphs?

Authors: Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Openly available, collaboratively edited Knowledge Graphs (KGs) are key platforms for the collective management of evolving knowledge. The present work aims t o provide an analysis of the obstacles related to investigating and processing specifically this central aspect of evolution in KGs. To this end, we discuss (i) the dimensions of evolution in KGs, (ii) the observability of evolution in existing, open, collaboratively constructed Knowledge Graphs over time, and (iii) possible metrics to analyse this evolution. We provide an overview of relevant state-of-the-art research, ranging from metrics developed for Knowledge Graphs specifically to potential methods from related fields such as network science. Additionally, we discuss technical approaches - and their current limitations - related to storing, analysing and processing large and evolving KGs in terms of handling typical KG downstream tasks.
Cite as

Axel Polleres, Romana Pernisch, Angela Bonifati, Daniele Dell'Aglio, Daniil Dobriy, Stefania Dumbrava, Lorena Etcheverry, Nicolas Ferranti, Katja Hose, Ernesto Jiménez-Ruiz, Matteo Lissandrini, Ansgar Scherp, Riccardo Tommasini, and Johannes Wachs. How Does Knowledge Evolve in Open Knowledge Graphs?. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 11:1-11:59, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{polleres_et_al:TGDK.1.1.11,
  author =	{Polleres, Axel and Pernisch, Romana and Bonifati, Angela and Dell'Aglio, Daniele and Dobriy, Daniil and Dumbrava, Stefania and Etcheverry, Lorena and Ferranti, Nicolas and Hose, Katja and Jim\'{e}nez-Ruiz, Ernesto and Lissandrini, Matteo and Scherp, Ansgar and Tommasini, Riccardo and Wachs, Johannes},
  title =	{{How Does Knowledge Evolve in Open Knowledge Graphs?}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{11:1--11:59},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.11},
  URN =		{urn:nbn:de:0030-drops-194855},
  doi =		{10.4230/TGDK.1.1.11},
  annote =	{Keywords: KG evolution, temporal KG, versioned KG, dynamic KG}
}
Document
Survey
DOI: 10.4230/TGDK.1.1.4
Knowledge Graph Embeddings: Open Challenges and Opportunities

Authors: Russa Biswas, Lucie-Aimée Kaffee, Michael Cochez, Stefania Dumbrava, Theis E. Jendal, Matteo Lissandrini, Vanessa Lopez, Eneldo Loza Mencía, Heiko Paulheim, Harald Sack, Edlira Kalemi Vakaj, and Gerard de Melo

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
While Knowledge Graphs (KGs) have long been used as valuable sources of structured knowledge, in recent years, KG embeddings have become a popular way of deriving numeric vector representations from them, for instance, to support knowledge graph completion and similarity search. This study surveys advances as well as open challenges and opportunities in this area. For instance, the most prominent embedding models focus primarily on structural information. However, there has been notable progress in incorporating further aspects, such as semantics, multi-modal, temporal, and multilingual features. Most embedding techniques are assessed using human-curated benchmark datasets for the task of link prediction, neglecting other important real-world KG applications. Many approaches assume a static knowledge graph and are unable to account for dynamic changes. Additionally, KG embeddings may encode data biases and lack interpretability. Overall, this study provides an overview of promising research avenues to learn improved KG embeddings that can address a more diverse range of use cases.
Cite as

Russa Biswas, Lucie-Aimée Kaffee, Michael Cochez, Stefania Dumbrava, Theis E. Jendal, Matteo Lissandrini, Vanessa Lopez, Eneldo Loza Mencía, Heiko Paulheim, Harald Sack, Edlira Kalemi Vakaj, and Gerard de Melo. Knowledge Graph Embeddings: Open Challenges and Opportunities. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 4:1-4:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{biswas_et_al:TGDK.1.1.4,
  author =	{Biswas, Russa and Kaffee, Lucie-Aim\'{e}e and Cochez, Michael and Dumbrava, Stefania and Jendal, Theis E. and Lissandrini, Matteo and Lopez, Vanessa and Menc{\'\i}a, Eneldo Loza and Paulheim, Heiko and Sack, Harald and Vakaj, Edlira Kalemi and de Melo, Gerard},
  title =	{{Knowledge Graph Embeddings: Open Challenges and Opportunities}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:32},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.4},
  URN =		{urn:nbn:de:0030-drops-194783},
  doi =		{10.4230/TGDK.1.1.4},
  annote =	{Keywords: Knowledge Graphs, KG embeddings, Link prediction, KG applications}
}
Document
Vision
DOI: 10.4230/TGDK.1.1.3
Knowledge Engineering Using Large Language Models

Authors: Bradley P. Allen, Lise Stork, and Paul Groth

Published in: TGDK, Volume 1, Issue 1 (2023): Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge, Volume 1, Issue 1

Abstract
Knowledge engineering is a discipline that focuses on the creation and maintenance of processes that generate and apply knowledge. Traditionally, knowledge engineering approaches have focused on knowledge expressed in formal languages. The emergence of large language models and their capabilities to effectively work with natural language, in its broadest sense, raises questions about the foundations and practice of knowledge engineering. Here, we outline the potential role of LLMs in knowledge engineering, identifying two central directions: 1) creating hybrid neuro-symbolic knowledge systems; and 2) enabling knowledge engineering in natural language. Additionally, we formulate key open research questions to tackle these directions.
Cite as

Bradley P. Allen, Lise Stork, and Paul Groth. Knowledge Engineering Using Large Language Models. In Special Issue on Trends in Graph Data and Knowledge. Transactions on Graph Data and Knowledge (TGDK), Volume 1, Issue 1, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{allen_et_al:TGDK.1.1.3,
  author =	{Allen, Bradley P. and Stork, Lise and Groth, Paul},
  title =	{{Knowledge Engineering Using Large Language Models}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:19},
  ISSN =	{2942-7517},
  year =	{2023},
  volume =	{1},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.1.1.3},
  URN =		{urn:nbn:de:0030-drops-194777},
  doi =		{10.4230/TGDK.1.1.3},
  annote =	{Keywords: knowledge engineering, large language models}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.76
Constructing a Distance Sensitivity Oracle in O(n^2.5794 M) Time

Authors: Yong Gu and Hanlin Ren

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
We continue the study of distance sensitivity oracles (DSOs). Given a directed graph G with n vertices and edge weights in {1, 2, … , M}, we want to build a data structure such that given any source vertex u, any target vertex v, and any failure f (which is either a vertex or an edge), it outputs the length of the shortest path from u to v not going through f. Our main result is a DSO with preprocessing time O(n^2.5794 M) and constant query time. Previously, the best preprocessing time of DSOs for directed graphs is O(n^2.7233 M), and even in the easier case of undirected graphs, the best preprocessing time is O(n^2.6865 M) [Ren, ESA 2020]. One drawback of our DSOs, though, is that it only supports distance queries but not path queries. Our main technical ingredient is an algorithm that computes the inverse of a degree-d polynomial matrix (i.e. a matrix whose entries are degree-d univariate polynomials) modulo x^r. The algorithm is adapted from [Zhou, Labahn and Storjohann, Journal of Complexity, 2015], and we replace some of its intermediate steps with faster rectangular matrix multiplication algorithms. We also show how to compute unique shortest paths in a directed graph with edge weights in {1, 2, … , M}, in O(n^2.5286 M) time. This algorithm is crucial in the preprocessing algorithm of our DSO. Our solution improves the O(n^2.6865 M) time bound in [Ren, ESA 2020], and matches the current best time bound for computing all-pairs shortest paths.
Cite as

Yong Gu and Hanlin Ren. Constructing a Distance Sensitivity Oracle in O(n^2.5794 M) Time. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 76:1-76:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{gu_et_al:LIPIcs.ICALP.2021.76,
  author =	{Gu, Yong and Ren, Hanlin},
  title =	{{Constructing a Distance Sensitivity Oracle in O(n^2.5794 M) Time}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{76:1--76:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.76},
  URN =		{urn:nbn:de:0030-drops-141450},
  doi =		{10.4230/LIPIcs.ICALP.2021.76},
  annote =	{Keywords: graph theory, shortest paths, distance sensitivity oracles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.79
Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time

Authors: Hanlin Ren

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We consider the problem of building Distance Sensitivity Oracles (DSOs). Given a directed graph G = (V, E) with edge weights in {1, 2, … , M}, we need to preprocess it into a data structure, and answer the following queries: given vertices u,v,x ∈ V, output the length of the shortest path from u to v that does not go through x. Our main result is a simple DSO with Õ(n^2.7233 M²) preprocessing time and O(1) query time. Moreover, if the input graph is undirected, the preprocessing time can be improved to Õ(n^2.6865 M²). Our algorithms are randomized with correct probability ≥ 1-1/n^c, for a constant c that can be made arbitrarily large. Previously, there is a DSO with Õ(n^2.8729 M) preprocessing time and polylog(n) query time [Chechik and Cohen, STOC'20]. At the core of our DSO is the following observation from [Bernstein and Karger, STOC'09]: if there is a DSO with preprocessing time P and query time Q, then we can construct a DSO with preprocessing time P+Õ(Mn²)⋅ Q and query time O(1). (Here Õ(⋅) hides polylog(n) factors.)
Cite as

Hanlin Ren. Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ren:LIPIcs.ESA.2020.79,
  author =	{Ren, Hanlin},
  title =	{{Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{79:1--79:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.79},
  URN =		{urn:nbn:de:0030-drops-129450},
  doi =		{10.4230/LIPIcs.ESA.2020.79},
  annote =	{Keywords: Graph theory, Failure-prone structures}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.24
Roundtrip Spanners with (2k-1) Stretch

Authors: Ruoxu Cen, Ran Duan, and Yong Gu

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
A roundtrip spanner of a directed graph G is a subgraph of G preserving roundtrip distances approximately for all pairs of vertices. Despite extensive research, there is still a small stretch gap between roundtrip spanners in directed graphs and undirected graphs. For a directed graph with real edge weights in [1,W], we first propose a new deterministic algorithm that constructs a roundtrip spanner with (2k-1) stretch and O(k n^(1+1/k) log (nW)) edges for every integer k > 1, then remove the dependence of size on W to give a roundtrip spanner with (2k-1) stretch and O(k n^(1+1/k) log n) edges. While keeping the edge size small, our result improves the previous 2k+ε stretch roundtrip spanners in directed graphs [Roditty, Thorup, Zwick'02; Zhu, Lam'18], and almost matches the undirected (2k-1)-spanner with O(n^(1+1/k)) edges [Althöfer et al. '93] when k is a constant, which is optimal under Erdös conjecture.
Cite as

Ruoxu Cen, Ran Duan, and Yong Gu. Roundtrip Spanners with (2k-1) Stretch. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 24:1-24:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cen_et_al:LIPIcs.ICALP.2020.24,
  author =	{Cen, Ruoxu and Duan, Ran and Gu, Yong},
  title =	{{Roundtrip Spanners with (2k-1) Stretch}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{24:1--24:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.24},
  URN =		{urn:nbn:de:0030-drops-124313},
  doi =		{10.4230/LIPIcs.ICALP.2020.24},
  annote =	{Keywords: Graph theory, Deterministic algorithm, Roundtrip spanners}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.44
Improved Time Bounds for All Pairs Non-decreasing Paths in General Digraphs

Authors: Ran Duan, Yong Gu, and Le Zhang

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We present improved algorithms for solving the All Pairs Non-decreasing Paths (APNP) problem on weighted digraphs. Currently, the best upper bound on APNP is O~(n^{(9+omega)/4})=O(n^{2.844}), obtained by Vassilevska Williams [TALG 2010 and SODA'08], where omega<2.373 is the usual exponent of matrix multiplication. Our first algorithm improves the time bound to O~(n^{2+omega/3})=O(n^{2.791}). The algorithm determines, for every pair of vertices s, t, the minimum last edge weight on a non-decreasing path from s to t, where a non-decreasing path is a path on which the edge weights form a non-decreasing sequence. The algorithm proposed uses the combinatorial properties of non-decreasing paths. Also a slightly improved algorithm with running time O(n^{2.78}) is presented.
Cite as

Ran Duan, Yong Gu, and Le Zhang. Improved Time Bounds for All Pairs Non-decreasing Paths in General Digraphs. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{duan_et_al:LIPIcs.ICALP.2018.44,
  author =	{Duan, Ran and Gu, Yong and Zhang, Le},
  title =	{{Improved Time Bounds for All Pairs Non-decreasing Paths in General Digraphs}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.44},
  URN =		{urn:nbn:de:0030-drops-90487},
  doi =		{10.4230/LIPIcs.ICALP.2018.44},
  annote =	{Keywords: Graph algorithms, Matrix multiplication, Non-decreasing paths}
}
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