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K-Rho-Shortcutting Heuristics

Authors: Alexander Leonhardt, Ulrich Meyer, and Manuel Penschuck

Abstract

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Alexander Leonhardt, Ulrich Meyer, Manuel Penschuck. K-Rho-Shortcutting Heuristics (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22475,
   title = {{K-Rho-Shortcutting Heuristics}}, 
   author = {Leonhardt, Alexander and Meyer, Ulrich and Penschuck, Manuel},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:8965d090c1d32ea024b1bb4b111329990a156b37;origin=https://github.com/alleonhardt/k-rho-shortcutting;visit=swh:1:snp:8185b97dfef89ed4f4b0e5ae16a2b7baf76ea267;anchor=swh:1:rev:54e9d8b70fe67eb89761792fc4081482c6f11c9d}{\texttt{swh:1:dir:8965d090c1d32ea024b1bb4b111329990a156b37}} (visited on 2024-11-28)},
   url = {https://github.com/alleonhardt/k-rho-shortcutting},
   doi = {10.4230/artifacts.22475},
}

Document

DOI: 10.4230/LIPIcs.ESA.2024.84

Insights into (k, ρ)-Shortcutting Algorithms

Authors: Alexander Leonhardt, Ulrich Meyer, and Manuel Penschuck

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract

A graph is called a (k, ρ)-graph iff every node can reach ρ of its nearest neighbors in at most k hops. This property has proven useful in the analysis and design of parallel shortest-path algorithms [Blelloch et al., 2016; Dong et al., 2021]. Any graph can be transformed into a (k, ρ)-graph by adding shortcuts. Formally, the (k,ρ)-Minimum-Shortcut-Problem (kρ-MSP) asks to find an appropriate shortcut set of minimal cardinality. We show that kρ-MSP is NP-complete in the practical regime of k ≥ 3 and ρ = Θ(n^ε) for ε > 0. With a related construction, we bound the approximation factor of known kρ-MSP heuristics [Blelloch et al., 2016] from below and propose algorithmic countermeasures improving the approximation quality. Further, we describe an integer linear problem (ILP) that optimally solves kρ-MSP. Finally, we compare the practical performance and quality of all algorithms empirically.

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Alexander Leonhardt, Ulrich Meyer, and Manuel Penschuck. Insights into (k, ρ)-Shortcutting Algorithms. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 84:1-84:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{leonhardt_et_al:LIPIcs.ESA.2024.84,
  author =	{Leonhardt, Alexander and Meyer, Ulrich and Penschuck, Manuel},
  title =	{{Insights into (k, \rho)-Shortcutting Algorithms}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{84:1--84:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.84},
  URN =		{urn:nbn:de:0030-drops-211554},
  doi =		{10.4230/LIPIcs.ESA.2024.84},
  annote =	{Keywords: Complexity, Approximation, Optimal algorithms, Parallel shortest path}
}

Document

PACE Solver Description

DOI: 10.4230/LIPIcs.IPEC.2023.37

PACE Solver Description: Exact (GUTHMI) and Heuristic (GUTHM)

Authors: Alexander Leonhardt, Holger Dell, Anselm Haak, Frank Kammer, Johannes Meintrup, Ulrich Meyer, and Manuel Penschuck

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)

Abstract

Twin-width (tww) is a parameter measuring the similarity of an undirected graph to a co-graph [Édouard Bonnet et al., 2022]. It is useful to analyze the parameterized complexity of various graph problems. This paper presents two algorithms to compute the twin-width and to provide a contraction sequence as witness. The two algorithms are motivated by the PACE 2023 challenge, one for the exact track and one for the heuristic track. Each algorithm produces a contraction sequence witnessing (i) the minimal twin-width admissible by the graph in the exact track (ii) an upper bound on the twin-width as tight as possible in the heuristic track. Our heuristic algorithm relies on several greedy approaches with different performance characteristics to find and improve solutions. For large graphs we use locality sensitive hashing to approximately identify suitable contraction candidates. The exact solver follows a branch-and-bound design. It relies on the heuristic algorithm to provide initial upper bounds, and uses lower bounds via contraction sequences to show the optimality of a heuristic solution found in some branch.

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Alexander Leonhardt, Holger Dell, Anselm Haak, Frank Kammer, Johannes Meintrup, Ulrich Meyer, and Manuel Penschuck. PACE Solver Description: Exact (GUTHMI) and Heuristic (GUTHM). In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 37:1-37:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{leonhardt_et_al:LIPIcs.IPEC.2023.37,
  author =	{Leonhardt, Alexander and Dell, Holger and Haak, Anselm and Kammer, Frank and Meintrup, Johannes and Meyer, Ulrich and Penschuck, Manuel},
  title =	{{PACE Solver Description: Exact (GUTHMI) and Heuristic (GUTHM)}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{37:1--37:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.37},
  URN =		{urn:nbn:de:0030-drops-194563},
  doi =		{10.4230/LIPIcs.IPEC.2023.37},
  annote =	{Keywords: PACE 2023 Challenge, Heuristic, Exact, Twin-Width}
}

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Documents authored by Leonhardt, Alexander

K-Rho-Shortcutting Heuristics

Abstract

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Insights into (k, ρ)-Shortcutting Algorithms

Abstract

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PACE Solver Description: Exact (GUTHMI) and Heuristic (GUTHM)

Abstract

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