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Documents authored by Trimble, James

Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2020.34
PACE Solver Description: Bute-Plus: A Bottom-Up Exact Solver for Treedepth

Authors: James Trimble

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
This note introduces Bute-Plus, an exact solver for the treedepth problem. The core of the solver is a positive-instance driven dynamic program that constructs an elimination tree of minimum depth in a bottom-up fashion. Three features greatly improve the algorithm’s run time. The first of these is a specialised trie data structure. The second is a domination rule. The third is a heuristic presolve step can quickly find a treedepth decomposition of optimal depth for many instances.
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James Trimble. PACE Solver Description: Bute-Plus: A Bottom-Up Exact Solver for Treedepth. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 34:1-34:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{trimble:LIPIcs.IPEC.2020.34,
  author =	{Trimble, James},
  title =	{{PACE Solver Description: Bute-Plus: A Bottom-Up Exact Solver for Treedepth}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{34:1--34:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.34},
  URN =		{urn:nbn:de:0030-drops-133371},
  doi =		{10.4230/LIPIcs.IPEC.2020.34},
  annote =	{Keywords: Treedepth, Elimination Tree, Graph Algorithms}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2020.35
PACE Solver Description: Tweed-Plus: A Subtree-Improving Heuristic Solver for Treedepth

Authors: James Trimble

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Abstract
This paper introduces Tweed-Plus, a heuristic solver for the treedepth problem. The solver uses two well-known algorithms to create an initial elimination tree: nested dissection (making use of the Metis library) and the minimum-degree heuristic. After creating an elimination tree of the entire input graph, the solver continues to apply nested dissection and the minimum-degree heuristic to parts of the graph with the aim of replacing subtrees of the elimination tree with alternatives of lower depth.
Cite as

James Trimble. PACE Solver Description: Tweed-Plus: A Subtree-Improving Heuristic Solver for Treedepth. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 35:1-35:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{trimble:LIPIcs.IPEC.2020.35,
  author =	{Trimble, James},
  title =	{{PACE Solver Description: Tweed-Plus: A Subtree-Improving Heuristic Solver for Treedepth}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{35:1--35:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.35},
  URN =		{urn:nbn:de:0030-drops-133382},
  doi =		{10.4230/LIPIcs.IPEC.2020.35},
  annote =	{Keywords: Treedepth, Elimination Tree, Heuristics}
}
Document
DOI: 10.4230/LIPIcs.SEA.2020.19
An Algorithm for the Exact Treedepth Problem

Authors: James Trimble

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract
We present a novel algorithm for the minimum-depth elimination tree problem, which is equivalent to the optimal treedepth decomposition problem. Our algorithm makes use of two cheaply-computed lower bound functions to prune the search tree, along with symmetry-breaking and domination rules. We present an empirical study showing that the algorithm outperforms the current state-of-the-art solver (which is based on a SAT encoding) by orders of magnitude on a range of graph classes.
Cite as

James Trimble. An Algorithm for the Exact Treedepth Problem. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{trimble:LIPIcs.SEA.2020.19,
  author =	{Trimble, James},
  title =	{{An Algorithm for the Exact Treedepth Problem}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.19},
  URN =		{urn:nbn:de:0030-drops-120938},
  doi =		{10.4230/LIPIcs.SEA.2020.19},
  annote =	{Keywords: Treedepth, Elimination Tree, Graph Algorithms}
}
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