10 Search Results for "Wu, Kaiyu"

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.WADS.2025.35
Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage

Authors: Meng He and Kaiyu Wu

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We improve the recent succinct data structure result of Balakrishnan et al. for chordal graphs with bounded vertex leafage (SWAT 2024). A chordal graph is a widely studied graph class which can be characterized as the intersection graph of subtrees of a host tree, denoted as a tree representation of the chordal graph. The vertex leafage and leafage parameters of a chordal graph deal with the existence of a tree representation with a bounded number of leaves in either the subtrees representing the vertices or the host tree itself. We simplify the lower bound proof of Balakrishnan et al. which applied to only chordal graphs with bounded vertex leafage, and extend it to a lower bound proof for chordal graphs with bounded leafage as well. For both classes of graphs, the information-theoretic lower bound we (re-)obtain for k = o(n) is (k-1)nlog n - knlog k - o(knlog n) bits, where the leafage or vertex leafage of the graph is at most k = o(n). We further extend the range of the parameter k to Θ(n) as well. Then we give a succinct data structure using (k-1)nlog (n/k) + o(knlog n) bits to answer adjacent queries, which test the adjacency between pairs of vertices, in O((log k)/(log log n) + 1) time compared to the O(klog n) time of the data structure of Balakrishnan et al. For the neighborhood query which lists the neighbours of a given vertex, our query time is O((log n)/(log log n)) per neighbour compared to O(k²log n) per neighbour. We also extend the data structure ideas to obtain a succinct data structure for chordal graphs with bounded leafage k, answering an open question of Balakrishnan et al. Our succinct data structure, which uses (k-1)nlog (n/k) + o(knlog n) bits, has query time O(1) for the adjacent query and O(1) per neighbour for the neighborhood query. Using slightly more space (an additional (1+ε)nlog n bits for any ε > 0) allows distance queries, which compute the number of edges in the shortest path between two given vertices, to be answered in O(1) time as well.
Cite as

Meng He and Kaiyu Wu. Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{he_et_al:LIPIcs.WADS.2025.35,
  author =	{He, Meng and Wu, Kaiyu},
  title =	{{Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{35:1--35:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.35},
  URN =		{urn:nbn:de:0030-drops-242660},
  doi =		{10.4230/LIPIcs.WADS.2025.35},
  annote =	{Keywords: Chordal Graph, Leafage, Vertex Leafage, Succinct Data Structure}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.86
Optimal Distance Labeling for Permutation Graphs

Authors: Paweł Gawrychowski and Wojciech Janczewski

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

Abstract
A permutation graph is the intersection graph of a set of segments between two parallel lines. In other words, they are defined by a permutation π on n elements, such that u and v are adjacent if an only if u < v but π(u) > π(v). We consider the problem of computing the distances in such a graph in the setting of informative labeling schemes. The goal of such a scheme is to assign a short bitstring 𝓁(u) to every vertex u, such that the distance between u and v can be computed using only 𝓁(u) and 𝓁(v), and no further knowledge about the whole graph (other than that it is a permutation graph). This elegantly captures the intuition that we would like our data structure to be distributed, and often leads to interesting combinatorial challenges while trying to obtain lower and upper bounds that match up to the lower-order terms. For distance labeling of permutation graphs on n vertices, Katz, Katz, and Peleg [STACS 2000] showed how to construct labels consisting of 𝒪(log² n) bits. Later, Bazzaro and Gavoille [Discret. Math. 309(11)] obtained an asymptotically optimal bound by showing how to construct labels consisting of 9log{n}+𝒪(1) bits, and proving that 3log{n}-𝒪(log{log{n}}) bits are necessary. This however leaves a quite large gap between the known lower and upper bounds. We close this gap by showing how to construct labels consisting of 3log{n}+𝒪(1) bits.
Cite as

Paweł Gawrychowski and Wojciech Janczewski. Optimal Distance Labeling for Permutation Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 86:1-86:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.ICALP.2025.86,
  author =	{Gawrychowski, Pawe{\l} and Janczewski, Wojciech},
  title =	{{Optimal Distance Labeling for Permutation Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{86:1--86:18},
  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.2025.86},
  URN =		{urn:nbn:de:0030-drops-234632},
  doi =		{10.4230/LIPIcs.ICALP.2025.86},
  annote =	{Keywords: informative labeling, permutation graph, distance labeling}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.12
Automatic Goal Clone Detection in Rocq

Authors: Ali Ghanbari

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract
Proof engineering in Rocq is a labor-intensive process, and as proof developments grow in size, redundancy and maintainability become challenges. One such redundancy is goal cloning, i.e., proving α-equivalent goals multiple times, leading to wasted effort and bloated proof scripts. In this paper, we introduce clone-finder, a novel technique for detecting goal clones in Rocq proofs. By leveraging the formal notion of α-equivalence for Gallina terms, clone-finder systematically identifies duplicated proof goals across large Rocq codebases. We evaluate clone-finder on 40 real-world Rocq projects from the CoqGym dataset. Our results reveal that each project contains an average of 27.73 instances of goal clone. We observed that the clones can be categorized as either exact goal duplication, generalization, or α-equivalent goals with different proofs, each signifying varying levels duplicate effort. Our findings highlight significant untapped potential for proof reuse in Rocq-based formal verification projects, paving the way for future improvements in automated proof engineering.
Cite as

Ali Ghanbari. Automatic Goal Clone Detection in Rocq. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghanbari:LIPIcs.ECOOP.2025.12,
  author =	{Ghanbari, Ali},
  title =	{{Automatic Goal Clone Detection in Rocq}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{12:1--12:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.12},
  URN =		{urn:nbn:de:0030-drops-233055},
  doi =		{10.4230/LIPIcs.ECOOP.2025.12},
  annote =	{Keywords: Clone Detection, Goal, Proof, Rocq, Gallina}
}
Document
DOI: 10.4230/LIPIcs.CPM.2024.17
Closing the Gap: Minimum Space Optimal Time Distance Labeling Scheme for Interval Graphs

Authors: Meng He and Kaiyu Wu

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract
We present a distance labeling scheme for an interval graph on n vertices that uses at most 3lg n + lg lg n + O(1) bits per vertex to answer distance queries, which ask for the distance between two given vertices, in constant time. Our labeling scheme improves the distance labeling scheme of Gavoille and Paul for connected interval graphs which uses at most 5lg n + O(1) bits per vertex to achieve constant query time. Our improved space cost matches a lower bound proven by Gavoille and Paul within additive lower order terms and is thus optimal. Based on this scheme, we further design a 6lg n + 2lg lg n +O(1) bit distance labeling scheme for circular-arc graphs, with constant distance query time, which improves the 10lg n + O(1) bit distance labeling scheme of Gavoille and Paul. We give a n/2 + O(lg^ 2n) bit labeling scheme for chordal graphs which answers distance queries in O(1) time. The best known lower bound is n/4 - o(n) bits.
Cite as

Meng He and Kaiyu Wu. Closing the Gap: Minimum Space Optimal Time Distance Labeling Scheme for Interval Graphs. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{he_et_al:LIPIcs.CPM.2024.17,
  author =	{He, Meng and Wu, Kaiyu},
  title =	{{Closing the Gap: Minimum Space Optimal Time Distance Labeling Scheme for Interval Graphs}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{17:1--17:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.17},
  URN =		{urn:nbn:de:0030-drops-201275},
  doi =		{10.4230/LIPIcs.CPM.2024.17},
  annote =	{Keywords: Distance Labeling, Interval Graph, Circular-Arc Graph, Chordal Graph}
}
Document
DOI: 10.4230/OASIcs.Tannen.1
Explaining Enterprise Knowledge Graphs with Large Language Models and Ontological Reasoning

Authors: Teodoro Baldazzi, Luigi Bellomarini, Stefano Ceri, Andrea Colombo, Andrea Gentili, Emanuel Sallinger, and Paolo Atzeni

Published in: OASIcs, Volume 119, The Provenance of Elegance in Computation - Essays Dedicated to Val Tannen (2024)

Abstract
In recent times, the demand for transparency and accountability in AI-driven decisions has intensified, particularly in high-stakes domains like finance and bio-medicine. This focus on the provenance of AI-generated conclusions underscores the need for decision-making processes that are not only transparent but also readily interpretable by humans, to built trust of both users and stakeholders. In this context, the integration of state-of-the-art Large Language Models (LLMs) with logic-oriented Enterprise Knowledge Graphs (EKGs) and the broader scope of Knowledge Representation and Reasoning (KRR) methodologies is currently at the cutting edge of industrial and academic research across numerous data-intensive areas. Indeed, such a synergy is paramount as LLMs bring a layer of adaptability and human-centric understanding that complements the structured insights of EKGs. Conversely, the central role of ontological reasoning is to capture the domain knowledge, accurately handling complex tasks over a given realm of interest, and to infuse the process with transparency and a clear provenance-based explanation of the conclusions drawn, addressing the fundamental challenge of LLMs' inherent opacity and fostering trust and accountability in AI applications. In this paper, we propose a novel neuro-symbolic framework that leverages the underpinnings of provenance in ontological reasoning to enhance state-of-the-art LLMs with domain awareness and explainability, enabling them to act as natural language interfaces to EKGs.
Cite as

Teodoro Baldazzi, Luigi Bellomarini, Stefano Ceri, Andrea Colombo, Andrea Gentili, Emanuel Sallinger, and Paolo Atzeni. Explaining Enterprise Knowledge Graphs with Large Language Models and Ontological Reasoning. In The Provenance of Elegance in Computation - Essays Dedicated to Val Tannen. Open Access Series in Informatics (OASIcs), Volume 119, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baldazzi_et_al:OASIcs.Tannen.1,
  author =	{Baldazzi, Teodoro and Bellomarini, Luigi and Ceri, Stefano and Colombo, Andrea and Gentili, Andrea and Sallinger, Emanuel and Atzeni, Paolo},
  title =	{{Explaining Enterprise Knowledge Graphs with Large Language Models and Ontological Reasoning}},
  booktitle =	{The Provenance of Elegance in Computation - Essays Dedicated to Val Tannen},
  pages =	{1:1--1:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-320-1},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{119},
  editor =	{Amarilli, Antoine and Deutsch, Alin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Tannen.1},
  URN =		{urn:nbn:de:0030-drops-200971},
  doi =		{10.4230/OASIcs.Tannen.1},
  annote =	{Keywords: provenance, ontological reasoning, language models, knowledge graphs}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.18
Distance Queries over Dynamic Interval Graphs

Authors: Jingbang Chen, Meng He, J. Ian Munro, Richard Peng, Kaiyu Wu, and Daniel J. Zhang

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
We design the first dynamic distance oracles for interval graphs, which are intersection graphs of a set of intervals on the real line, and for proper interval graphs, which are intersection graphs of a set of intervals in which no interval is properly contained in another. For proper interval graphs, we design a linear space data structure which supports distance queries (computing the distance between two query vertices) and vertex insertion or deletion in O(lg n) worst-case time, where n is the number of vertices currently in G. Under incremental (insertion only) or decremental (deletion only) settings, we design linear space data structures that support distance queries in O(lg n) worst-case time and vertex insertion or deletion in O(lg n) amortized time, where n is the maximum number of vertices in the graph. Under fully dynamic settings, we design a data structure that represents an interval graph G in O(n) words of space to support distance queries in O(n lg n/S(n)) worst-case time and vertex insertion or deletion in O(S(n)+lg n) worst-case time, where n is the number of vertices currently in G and S(n) is an arbitrary function that satisfies S(n) = Ω(1) and S(n) = O(n). This implies an O(n)-word solution with O(√{nlg n})-time support for both distance queries and updates. All four data structures can answer shortest path queries by reporting the vertices in the shortest path between two query vertices in O(lg n) worst-case time per vertex. We also study the hardness of supporting distance queries under updates over an intersection graph of 3D axis-aligned line segments, which generalizes our problem to 3D. Finally, we solve the problem of computing the diameter of a dynamic connected interval graph.
Cite as

Jingbang Chen, Meng He, J. Ian Munro, Richard Peng, Kaiyu Wu, and Daniel J. Zhang. Distance Queries over Dynamic Interval Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.ISAAC.2023.18,
  author =	{Chen, Jingbang and He, Meng and Munro, J. Ian and Peng, Richard and Wu, Kaiyu and Zhang, Daniel J.},
  title =	{{Distance Queries over Dynamic Interval Graphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{18:1--18:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.18},
  URN =		{urn:nbn:de:0030-drops-193207},
  doi =		{10.4230/LIPIcs.ISAAC.2023.18},
  annote =	{Keywords: interval graph, proper interval graph, intersection graph, geometric intersection graph, distance oracle, distance query, shortest path query, dynamic graph}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.59
Shortest Beer Path Queries in Interval Graphs

Authors: Rathish Das, Meng He, Eitan Kondratovsky, J. Ian Munro, Anurag Murty Naredla, and Kaiyu Wu

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

Abstract
Our interest is in paths between pairs of vertices that go through at least one of a subset of the vertices known as beer vertices. Such a path is called a beer path, and the beer distance between two vertices is the length of the shortest beer path. We show that we can represent unweighted interval graphs using 2n log n + O(n) + O(|B|log n) bits where |B| is the number of beer vertices. This data structure answers beer distance queries in O(log^ε n) time for any constant ε > 0 and shortest beer path queries in O(log^ε n + d) time, where d is the beer distance between the two nodes. We also show that proper interval graphs may be represented using 3n + o(n) bits to support beer distance queries in O(f(n)log n) time for any f(n) ∈ ω(1) and shortest beer path queries in O(d) time. All of these results also have time-space trade-offs. Lastly we show that the information theoretic lower bound for beer proper interval graphs is very close to the space of our structure, namely log(4+2√3)n - o(n) (or about 2.9 n) bits.
Cite as

Rathish Das, Meng He, Eitan Kondratovsky, J. Ian Munro, Anurag Murty Naredla, and Kaiyu Wu. Shortest Beer Path Queries in Interval Graphs. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 59:1-59:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{das_et_al:LIPIcs.ISAAC.2022.59,
  author =	{Das, Rathish and He, Meng and Kondratovsky, Eitan and Munro, J. Ian and Naredla, Anurag Murty and Wu, Kaiyu},
  title =	{{Shortest Beer Path Queries in Interval Graphs}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{59:1--59:17},
  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.2022.59},
  URN =		{urn:nbn:de:0030-drops-173442},
  doi =		{10.4230/LIPIcs.ISAAC.2022.59},
  annote =	{Keywords: Beer Path, Interval Graph}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2020.25
Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees

Authors: Meng He, J. Ian Munro, Yakov Nekrich, Sebastian Wild, and Kaiyu Wu

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract
We present the first succinct distance oracles for (unweighted) interval graphs and related classes of graphs, using a novel succinct data structure for ordinal trees that supports the mapping between preorder (i.e., depth-first) ranks and level-order (breadth-first) ranks of nodes in constant time. Our distance oracles for interval graphs also support navigation queries - testing adjacency, computing node degrees, neighborhoods, and shortest paths - all in optimal time. Our technique also yields optimal distance oracles for proper interval graphs (unit-interval graphs) and circular-arc graphs. Our tree data structure supports all operations provided by different approaches in previous work, as well as mapping to and from level-order ranks and retrieving the last (first) internal node before (after) a given node in a level-order traversal, all in constant time.
Cite as

Meng He, J. Ian Munro, Yakov Nekrich, Sebastian Wild, and Kaiyu Wu. Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{he_et_al:LIPIcs.ISAAC.2020.25,
  author =	{He, Meng and Munro, J. Ian and Nekrich, Yakov and Wild, Sebastian and Wu, Kaiyu},
  title =	{{Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.25},
  URN =		{urn:nbn:de:0030-drops-133693},
  doi =		{10.4230/LIPIcs.ISAAC.2020.25},
  annote =	{Keywords: succinct data structures, distance oracles, ordinal tree, level order, breadth-first order, interval graphs, proper interval graphs, succinct graph representation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.67
Succinct Data Structures for Chordal Graphs

Authors: J. Ian Munro and Kaiyu Wu

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We study the problem of approximate shortest path queries in chordal graphs and give a n log n + o(n log n) bit data structure to answer the approximate distance query to within an additive constant of 1 in O(1) time. We study the problem of succinctly storing a static chordal graph to answer adjacency, degree, neighbourhood and shortest path queries. Let G be a chordal graph with n vertices. We design a data structure using the information theoretic minimal n^2/4 + o(n^2) bits of space to support the queries: - whether two vertices u,v are adjacent in time f(n) for any f(n) in omega(1). - the degree of a vertex in O(1) time. - the vertices adjacent to u in (f(n))^2 time per neighbour - the length of the shortest path from u to v in O(nf(n)) time
Cite as

J. Ian Munro and Kaiyu Wu. Succinct Data Structures for Chordal Graphs. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 67:1-67:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{munro_et_al:LIPIcs.ISAAC.2018.67,
  author =	{Munro, J. Ian and Wu, Kaiyu},
  title =	{{Succinct Data Structures for Chordal Graphs}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{67:1--67:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.67},
  URN =		{urn:nbn:de:0030-drops-100153},
  doi =		{10.4230/LIPIcs.ISAAC.2018.67},
  annote =	{Keywords: Succinct Data Structure, Chordal Graph}
}
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