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Documents authored by Gu, Yong

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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-dev.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
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-dev.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-dev.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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