3 Search Results for "Takaoka, Tadao"

Document
DOI: 10.4230/LIPIcs.WADS.2025.14
Quantum Speedups for Polynomial-Time Dynamic Programming Algorithms

Authors: Susanna Caroppo, Giordano Da Lozzo, Giuseppe Di Battista, Michael T. Goodrich, and Martin Nöllenburg

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

Abstract
We introduce a quantum dynamic programming framework that allows us to directly extend to the quantum realm a large body of classical dynamic programming algorithms. The corresponding quantum dynamic programming algorithms retain the same space complexity as their classical counterpart, while achieving a computational speedup. For a combinatorial (search or optimization) problem P and an instance I of P, such a speedup can be expressed in terms of the average degree δ of the {dependency digraph} G_𝒫(I) of I, determined by a recursive formulation of P. The nodes of this graph are the subproblems of P induced by I and its arcs are directed from each subproblem to those on whose solution it relies. In particular, our framework allows us to solve the considered problems in Õ(|V(G_𝒫(I))| √δ) time. As an example, we obtain a quantum version of the Bellman-Ford algorithm for computing shortest paths from a single source vertex to all the other vertices in a weighted n-vertex digraph with m edges that runs in Õ(n√{nm}) time, which improves the best known classical upper bound when m ∈ Ω(n^{1.4}).
Cite as

Susanna Caroppo, Giordano Da Lozzo, Giuseppe Di Battista, Michael T. Goodrich, and Martin Nöllenburg. Quantum Speedups for Polynomial-Time Dynamic Programming Algorithms. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{caroppo_et_al:LIPIcs.WADS.2025.14,
  author =	{Caroppo, Susanna and Da Lozzo, Giordano and Di Battista, Giuseppe and Goodrich, Michael T. and N\"{o}llenburg, Martin},
  title =	{{Quantum Speedups for Polynomial-Time Dynamic Programming Algorithms}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{14:1--14:22},
  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.2025.14},
  URN =		{urn:nbn:de:0030-drops-242454},
  doi =		{10.4230/LIPIcs.WADS.2025.14},
  annote =	{Keywords: Dynamic Programming, Quantum Algorithms, Quantum Random Access Memory}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.93
On Incremental Approximate Shortest Paths in Directed Graphs

Authors: Adam Górkiewicz and Adam Karczmarz

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

Abstract
In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions. We give more efficient incremental (1+ε)-approximate APSP data structures that work against an adaptive adversary: a deterministic one with Õ(m^{3/2}n^{3/4}) total update time and a randomized one with Õ(m^{4/3}n^{5/6}) total update time. For sparse graphs, these both improve polynomially upon the best-known bound against an adaptive adversary [Karczmarz and Łącki, ESA 2019]. To achieve that, building on the ideas of [Chechik and Zhang, SODA 2021] and [Kyng, Meierhans and Probst Gutenberg, SODA 2022], we show a near-optimal (1+ε)-approximate incremental SSSP data structure for a special case when all edge updates are adjacent to the source, that might be of independent interest. We also describe a very simple and near-optimal offline incremental (1+ε)-approximate SSSP data structure. While online near-linear partially dynamic SSSP data structures have been elusive so far (except for dense instances), our result excludes using certain types of impossibility arguments to rule them out. Additionally, our offline solution leads to near-optimal and deterministic all-pairs bounded-leg shortest paths data structure for sparse graphs.
Cite as

Adam Górkiewicz and Adam Karczmarz. On Incremental Approximate Shortest Paths in Directed Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 93:1-93:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{gorkiewicz_et_al:LIPIcs.ICALP.2025.93,
  author =	{G\'{o}rkiewicz, Adam and Karczmarz, Adam},
  title =	{{On Incremental Approximate Shortest Paths in Directed Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{93:1--93:20},
  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.2025.93},
  URN =		{urn:nbn:de:0030-drops-234700},
  doi =		{10.4230/LIPIcs.ICALP.2025.93},
  annote =	{Keywords: dynamic shortest paths, incremental shortest paths, offline dynamic algorithms}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.56
Single Source Shortest Paths for All Flows with Integer Costs

Authors: Tadao Takaoka

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
We consider a shortest path problem for a directed graph with edges labeled with a cost and a capacity. The problem is to push an unsplittable flow $f$ from a specified source to all other vertices with the minimum cost for all f values. Let G = (V, E) with |V| = n and |E| = m. If there are t different capacity values, we can solve the single source shortest path problem t times for all f in O(tm + tn log n) time, which is O(m^2) when t = m. We improve this time to O(min{t, cn}m + cn^2), which is less than O(cmn) if edge costs are non-negative integers bounded by c. Our algorithm performs better for denser graphs.
Cite as

Tadao Takaoka. Single Source Shortest Paths for All Flows with Integer Costs. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 56-67, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

Copy BibTex To Clipboard

@InProceedings{takaoka:OASIcs.ATMOS.2015.56,
  author =	{Takaoka, Tadao},
  title =	{{Single Source Shortest Paths for All Flows with Integer Costs}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{56--67},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.56},
  URN =		{urn:nbn:de:0030-drops-54611},
  doi =		{10.4230/OASIcs.ATMOS.2015.56},
  annote =	{Keywords: information sharing, shortest path problem for all flows, priority queue, limited edge cost, transportation network}
}
  • Refine by Type
  • 3 Document/PDF
  • 2 Document/HTML

  • Refine by Publication Year
  • 2 2025
  • 1 2015

  • Refine by Author
  • 1 Caroppo, Susanna
  • 1 Da Lozzo, Giordano
  • 1 Di Battista, Giuseppe
  • 1 Goodrich, Michael T.
  • 1 Górkiewicz, Adam
  • Show More...

  • Refine by Series/Journal
  • 2 LIPIcs
  • 1 OASIcs

  • Refine by Classification
  • 1 Theory of computation → Dynamic graph algorithms
  • 1 Theory of computation → Dynamic programming
  • 1 Theory of computation → Quantum complexity theory

  • Refine by Keyword
  • 1 Dynamic Programming
  • 1 Quantum Algorithms
  • 1 Quantum Random Access Memory
  • 1 dynamic shortest paths
  • 1 incremental shortest paths
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact