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Documents authored by Noe, Alexander

Document
DOI: 10.4230/LIPIcs.ESA.2022.45
A Local Search Algorithm for Large Maximum Weight Independent Set Problems

Authors: Yuanyuan Dong, Andrew V. Goldberg, Alexander Noe, Nikos Parotsidis, Mauricio G.C. Resende, and Quico Spaen

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Motivated by a real-world vehicle routing application, we consider the maximum-weight independent set problem: Given a node-weighted graph, find a set of independent (mutually nonadjacent) nodes whose node-weight sum is maximum. Some of the graphs arising in the vehicle routing application are large, having hundreds of thousands of nodes and hundreds of millions of edges. To solve instances of this size, we develop a new local search algorithm, which is a metaheuristic based on the greedy randomized adaptive search (GRASP) framework. This algorithm, named METAMIS, uses a wider range of simple local search operations than previously described in the literature. We introduce data structures that make these operations efficient. A new variant of path-relinking is introduced to escape local optima and so is a new alternating augmenting-path local search move that improves algorithm performance. We compare an implementation of our algorithm with a state-of-the-art publicly available code on public benchmark sets, including some large instances. Our algorithm is, in general, competitive and outperforms this openly available code on large vehicle routing instances of the maximum weight independent set problem. We hope that our results will lead to even better maximum-weight independent set algorithms.
Cite as

Yuanyuan Dong, Andrew V. Goldberg, Alexander Noe, Nikos Parotsidis, Mauricio G.C. Resende, and Quico Spaen. A Local Search Algorithm for Large Maximum Weight Independent Set Problems. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dong_et_al:LIPIcs.ESA.2022.45,
  author =	{Dong, Yuanyuan and Goldberg, Andrew V. and Noe, Alexander and Parotsidis, Nikos and Resende, Mauricio G.C. and Spaen, Quico},
  title =	{{A Local Search Algorithm for Large Maximum Weight Independent Set Problems}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{45:1--45:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.45},
  URN =		{urn:nbn:de:0030-drops-169839},
  doi =		{10.4230/LIPIcs.ESA.2022.45},
  annote =	{Keywords: GRASP, local search, maximum-weight independent set, path-relinking, heuristic, metaheuristic}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.59
Finding All Global Minimum Cuts in Practice

Authors: Monika Henzinger, Alexander Noe, Christian Schulz, and Darren Strash

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs. Our algorithm uses a multitude of kernelization rules to reduce the graph to a small equivalent instance and then finds all minimum cuts using an optimized version of the algorithm of Nagamochi, Nakao and Ibaraki. In shared memory we are able to find all minimum cuts of graphs with up to billions of edges and millions of minimum cuts in a few minutes. We also give a new linear time algorithm to find the most balanced minimum cuts given as input the representation of all minimum cuts.
Cite as

Monika Henzinger, Alexander Noe, Christian Schulz, and Darren Strash. Finding All Global Minimum Cuts in Practice. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2020.59,
  author =	{Henzinger, Monika and Noe, Alexander and Schulz, Christian and Strash, Darren},
  title =	{{Finding All Global Minimum Cuts in Practice}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{59:1--59:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.59},
  URN =		{urn:nbn:de:0030-drops-129255},
  doi =		{10.4230/LIPIcs.ESA.2020.59},
  annote =	{Keywords: Minimum Cut, Graph Algorithm, Algorithm Engineering, Cut Enumeration, Balanced Cut, Global Minimum Cut, Large-scale Graph Analysis}
}
Document
DOI: 10.4230/LIPIcs.SEA.2018.4
ILP-based Local Search for Graph Partitioning

Authors: Alexandra Henzinger, Alexander Noe, and Christian Schulz

Published in: LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

Abstract
Computing high-quality graph partitions is a challenging problem with numerous applications. In this paper, we present a novel meta-heuristic for the balanced graph partitioning problem. Our approach is based on integer linear programs that solve the partitioning problem to optimality. However, since those programs typically do not scale to large inputs, we adapt them to heuristically improve a given partition. We do so by defining a much smaller model that allows us to use symmetry breaking and other techniques that make the approach scalable. For example, in Walshaw's well-known benchmark tables we are able to improve roughly half of all entries when the number of blocks is high.
Cite as

Alexandra Henzinger, Alexander Noe, and Christian Schulz. ILP-based Local Search for Graph Partitioning. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{henzinger_et_al:LIPIcs.SEA.2018.4,
  author =	{Henzinger, Alexandra and Noe, Alexander and Schulz, Christian},
  title =	{{ILP-based Local Search for Graph Partitioning}},
  booktitle =	{17th International Symposium on Experimental Algorithms (SEA 2018)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-070-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{103},
  editor =	{D'Angelo, Gianlorenzo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018.4},
  URN =		{urn:nbn:de:0030-drops-89399},
  doi =		{10.4230/LIPIcs.SEA.2018.4},
  annote =	{Keywords: Graph Partitioning, Integer Linear Programming}
}
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