3 Search Results for "O'Brien, Michael P."

Document
DOI: 10.4230/LIPIcs.SEA.2024.14
Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions

Authors: Andreas Grigorjew, Fernando H. C. Dias, Andrea Cracco, Romeo Rizzi, and Alexandru I. Tomescu

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
Given a flow network, the Minimum Flow Decomposition (MFD) problem is finding the smallest possible set of weighted paths whose superposition equals the flow. It is a classical, strongly NP-hard problem that is proven to be useful in RNA transcript assembly and applications outside of Bioinformatics. We improve an existing ILP (Integer Linear Programming) model by Dias et al. [RECOMB 2022] for DAGs by decreasing the solver’s search space using solution safety and several other optimizations. This results in a significant speedup compared to the original ILP, of up to 34× on average on the hardest instances. Moreover, we show that our optimizations apply also to MFD problem variants, resulting in speedups that go up to 219× on the hardest instances. We also developed an ILP model of reduced dimensionality for an MFD variant in which the solution path weights are restricted to a given set. This model can find an optimal MFD solution for most instances, and overall, its accuracy significantly outperforms that of previous greedy algorithms while being up to an order of magnitude faster than our optimized ILP.
Cite as

Andreas Grigorjew, Fernando H. C. Dias, Andrea Cracco, Romeo Rizzi, and Alexandru I. Tomescu. Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{grigorjew_et_al:LIPIcs.SEA.2024.14,
  author =	{Grigorjew, Andreas and Dias, Fernando H. C. and Cracco, Andrea and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Accelerating ILP Solvers for Minimum Flow Decompositions Through Search Space and Dimensionality Reductions}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.14},
  URN =		{urn:nbn:de:0030-drops-203792},
  doi =		{10.4230/LIPIcs.SEA.2024.14},
  annote =	{Keywords: Flow decomposition, Integer Linear Programming, Safety, RNA-seq, RNA transcript assembly, isoform}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.37
Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

Authors: Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, and Andrew van der Poel

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
We develop a framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world networks) while still guaranteeing approximation ratios. The idea is to edit a given graph via vertex- or edge-deletions to put the graph into an algorithmically tractable class, apply known approximation algorithms for that class, and then lift the solution to apply to the original graph. We give a general characterization of when an optimization problem is amenable to this approach, and show that it includes many well-studied graph problems, such as Independent Set, Vertex Cover, Feedback Vertex Set, Minimum Maximal Matching, Chromatic Number, (l-)Dominating Set, Edge (l-)Dominating Set, and Connected Dominating Set. To enable this framework, we develop new editing algorithms that find the approximately-fewest edits required to bring a given graph into one of a few important graph classes (in some cases these are bicriteria algorithms which simultaneously approximate both the number of editing operations and the target parameter of the family). For bounded degeneracy, we obtain an O(r log{n})-approximation and a bicriteria (4,4)-approximation which also extends to a smoother bicriteria trade-off. For bounded treewidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w}))-approximation, and for bounded pathwidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w} * log n))-approximation. For treedepth 2 (related to bounded expansion), we obtain a 4-approximation. We also prove complementary hardness-of-approximation results assuming P != NP: in particular, these problems are all log-factor inapproximable, except the last which is not approximable below some constant factor 2 (assuming UGC).
Cite as

Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, and Andrew van der Poel. Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{demaine_et_al:LIPIcs.ESA.2019.37,
  author =	{Demaine, Erik D. and Goodrich, Timothy D. and Kloster, Kyle and Lavallee, Brian and Liu, Quanquan C. and Sullivan, Blair D. and Vakilian, Ali and van der Poel, Andrew},
  title =	{{Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.37},
  URN =		{urn:nbn:de:0030-drops-111583},
  doi =		{10.4230/LIPIcs.ESA.2019.37},
  annote =	{Keywords: structural rounding, graph editing, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.79
Being Even Slightly Shallow Makes Life Hard

Authors: Irene Muzi, Michael P. O'Brien, Felix Reidl, and Blair D. Sullivan

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
We study the computational complexity of identifying dense substructures, namely r/2-shallow topological minors and r-subdivisions. Of particular interest is the case r = 1, when these substructures correspond to very localized relaxations of subgraphs. Since Densest Subgraph can be solved in polynomial time, we ask whether these slight relaxations also admit efficient algorithms. In the following, we provide a negative answer: Dense r/2-Shallow Topological Minor and Dense r-Subdivsion are already NP-hard for r = 1 in very sparse graphs. Further, they do not admit algorithms with running time 2^(o(tw^2)) n^O(1) when parameterized by the treewidth of the input graph for r > 2 unless ETH fails.
Cite as

Irene Muzi, Michael P. O'Brien, Felix Reidl, and Blair D. Sullivan. Being Even Slightly Shallow Makes Life Hard. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{muzi_et_al:LIPIcs.MFCS.2017.79,
  author =	{Muzi, Irene and O'Brien, Michael P. and Reidl, Felix and Sullivan, Blair D.},
  title =	{{Being Even Slightly Shallow Makes Life Hard}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{79:1--79:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.79},
  URN =		{urn:nbn:de:0030-drops-81257},
  doi =		{10.4230/LIPIcs.MFCS.2017.79},
  annote =	{Keywords: Topological minors, NP Completeness, Treewidth, ETH, FPT algorithms}
}
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