3 Search Results for "Hespe, Demian"


Document
Pareto Sums of Pareto Sets

Authors: Demian Hespe, Peter Sanders, Sabine Storandt, and Carina Truschel

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
In bi-criteria optimization problems, the goal is typically to compute the set of Pareto-optimal solutions. Many algorithms for these types of problems rely on efficient merging or combining of partial solutions and filtering of dominated solutions in the resulting sets. In this paper, we consider the task of computing the Pareto sum of two given Pareto sets A, B of size n. The Pareto sum contains all non-dominated points of the Minkowski sum M = {a+b|a ∈ A, b ∈ B}. Since the Minkowski sum has a size of n², but the Pareto sum C can be much smaller, the goal is to compute C without having to compute and store all of M. We present several new algorithms for efficient Pareto sum computation, including an output-sensitive one with a running time of 𝒪(n log n + nk) and a space consumption of 𝒪(n+k) for k = |C|. We also describe suitable engineering techniques to improve the practical running times of our algorithms and provide a comparative experimental study. As one showcase application, we consider preprocessing-based methods for bi-criteria route planning in road networks. Pareto sum computation is a frequent task in the preprocessing phase. We show that using our algorithms with an output-sensitive space consumption allows to tackle larger instances and reduces the preprocessing time compared to algorithms that fully store M.

Cite as

Demian Hespe, Peter Sanders, Sabine Storandt, and Carina Truschel. Pareto Sums of Pareto Sets. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 60:1-60:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{hespe_et_al:LIPIcs.ESA.2023.60,
  author =	{Hespe, Demian and Sanders, Peter and Storandt, Sabine and Truschel, Carina},
  title =	{{Pareto Sums of Pareto Sets}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{60:1--60:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. 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.2023.60},
  URN =		{urn:nbn:de:0030-drops-187132},
  doi =		{10.4230/LIPIcs.ESA.2023.60},
  annote =	{Keywords: Minkowski sum, Skyline, Successive Algorithm}
}
Document
Targeted Branching for the Maximum Independent Set Problem

Authors: Demian Hespe, Sebastian Lamm, and Christian Schorr

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)


Abstract
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. In recent years, some of the most successful algorithms for solving this problem are based on the branch-and-bound or branch-and-reduce paradigms. In particular, branch-and-reduce algorithms, which combine branch-and-bound with reduction rules, have been able to achieve substantial results, solving many previously infeasible real-world instances. These results were to a large part achieved by developing new, more practical reduction rules. However, other components that have been shown to have a significant impact on the performance of these algorithms have not received as much attention. One of these is the branching strategy, which determines what vertex is included or excluded in a potential solution. Even now, the most commonly used strategy selects vertices solely based on their degree and does not take into account other factors that contribute to the performance of the algorithm. In this work, we develop and evaluate several novel branching strategies for both branch-and-bound and branch-and-reduce algorithms. Our strategies are based on one of two approaches which are motivated by existing research. They either (1) aim to decompose the graph into two or more connected components which can then be solved independently, or (2) try to remove vertices that hinder the application of a reduction rule which can lead to smaller graphs. Our experimental evaluation on a large set of real-world instances indicates that our strategies are able to improve the performance of the state-of-the-art branch-and-reduce algorithm by Akiba and Iwata. To be more specific, our reduction-based packing branching rule is able to outperform the default branching strategy of selecting a vertex of highest degree on 65% of all instances tested. Furthermore, our decomposition-based strategy based on edge cuts is able to achieve a speedup of 2.29 on sparse networks (1.22 on all instances).

Cite as

Demian Hespe, Sebastian Lamm, and Christian Schorr. Targeted Branching for the Maximum Independent Set Problem. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{hespe_et_al:LIPIcs.SEA.2021.17,
  author =	{Hespe, Demian and Lamm, Sebastian and Schorr, Christian},
  title =	{{Targeted Branching for the Maximum Independent Set Problem}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{17:1--17:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.17},
  URN =		{urn:nbn:de:0030-drops-137893},
  doi =		{10.4230/LIPIcs.SEA.2021.17},
  annote =	{Keywords: Graphs, Combinatorial Optimization, Independent Set, Vertex Cover, Clique, Branch-and-Reduce, Branch-and-Bound, Data Reduction}
}
Document
More Hierarchy in Route Planning Using Edge Hierarchies

Authors: Demian Hespe and Peter Sanders

Published in: OASIcs, Volume 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)


Abstract
A highly successful approach to route planning in networks (particularly road networks) is to identify a hierarchy in the network that allows faster queries after some preprocessing that basically inserts additional "shortcut"-edges into a graph. In the past there has been a succession of techniques that infer a more and more fine grained hierarchy enabling increasingly more efficient queries. This appeared to culminate in contraction hierarchies that assign one hierarchy level to each vertex. In this paper we show how to identify an even more fine grained hierarchy that assigns one level to each edge of the network. Our findings indicate that this can lead to considerably smaller search spaces in terms of visited edges. Currently, this rarely implies improved query times so that it remains an open question whether edge hierarchies can lead to consistently improved performance. However, we believe that the technique as such is a noteworthy enrichment of the portfolio of available techniques that might prove useful in the future.

Cite as

Demian Hespe and Peter Sanders. More Hierarchy in Route Planning Using Edge Hierarchies. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{hespe_et_al:OASIcs.ATMOS.2019.10,
  author =	{Hespe, Demian and Sanders, Peter},
  title =	{{More Hierarchy in Route Planning Using Edge Hierarchies}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{10:1--10:14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-128-3},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{75},
  editor =	{Cacchiani, Valentina and Marchetti-Spaccamela, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.10},
  URN =		{urn:nbn:de:0030-drops-114228},
  doi =		{10.4230/OASIcs.ATMOS.2019.10},
  annote =	{Keywords: shortest path, hierarchy, road networks, preprocessing}
}
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