3 Search Results for "Kurz, Denis"

Document
DOI: 10.4230/LIPIcs.SEA.2026.14
K-Hole Separation in PEO‑Based ILP Treewidth Formulation

Authors: Andrea D'Ascenzo

Published in: LIPIcs, Volume 371, 24th International Symposium on Experimental Algorithms (SEA 2026)

Abstract
In this paper, we introduce a family of valid inequalities for the strongest currently known integer programming formulation of treewidth based on perfect elimination orderings. These inequalities arise from the structure of induced chordless cycles (holes) and strengthen the canonical linear relaxation by enforcing constraints that every feasible chordal completion must satisfy. To handle the exponentially many such inequalities, we develop a dedicated separation routine capable of detecting violated k-hole constraints within a cutting-plane framework. Our computational results show that incorporating these inequalities substantially improves the quality of the lower bounds across a broad range of graph classes, in some cases nearly closing the integrality gap.
Cite as

Andrea D'Ascenzo. K-Hole Separation in PEO‑Based ILP Treewidth Formulation. In 24th International Symposium on Experimental Algorithms (SEA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 371, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dascenzo:LIPIcs.SEA.2026.14,
  author =	{D'Ascenzo, Andrea},
  title =	{{K-Hole Separation in PEO‑Based ILP Treewidth Formulation}},
  booktitle =	{24th International Symposium on Experimental Algorithms (SEA 2026)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-422-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{371},
  editor =	{Aum\"{u}ller, Martin and Finocchi, Irene},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2026.14},
  URN =		{urn:nbn:de:0030-drops-260186},
  doi =		{10.4230/LIPIcs.SEA.2026.14},
  annote =	{Keywords: Treewidth, Integer Linear Programming, Polyhedral Combinatorics, Chordal Completion, Induced Cycles}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2017.16
K-Best Solutions of MSO Problems on Tree-Decomposable Graphs

Authors: David Eppstein and Denis Kurz

Published in: LIPIcs, Volume 89, 12th International Symposium on Parameterized and Exact Computation (IPEC 2017)

Abstract
We show that, for any graph optimization problem in which the feasible solutions can be expressed by a formula in monadic second-order logic describing sets of vertices or edges and in which the goal is to minimize the sum of the weights in the selected sets, we can find the k best solution values for n-vertex graphs of bounded treewidth in time O(n + k log n). In particular, this applies to finding the k shortest simple paths between given vertices in directed graphs of bounded treewidth, giving an exponential speedup in the per-path cost over previous algorithms.
Cite as

David Eppstein and Denis Kurz. K-Best Solutions of MSO Problems on Tree-Decomposable Graphs. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{eppstein_et_al:LIPIcs.IPEC.2017.16,
  author =	{Eppstein, David and Kurz, Denis},
  title =	{{K-Best Solutions of MSO Problems on Tree-Decomposable Graphs}},
  booktitle =	{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
  pages =	{16:1--16:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-051-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{89},
  editor =	{Lokshtanov, Daniel and Nishimura, Naomi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2017.16},
  URN =		{urn:nbn:de:0030-drops-85494},
  doi =		{10.4230/LIPIcs.IPEC.2017.16},
  annote =	{Keywords: graph algorithm, k-best, monadic second-order logic, treewidth}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2016.49
A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph

Authors: Denis Kurz and Petra Mutzel

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

Abstract
We present an algorithm for the k shortest simple path problem on weighted directed graphs (kSSP) that is based on Eppstein’s algorithm for a similar problem in which paths are allowed to contain cycles. In contrast to most other algorithms for kSSP, ours is not based on Yen's algorithm [Networks, 1971] and does not solve replacement path problems. Its worst-case running time is on par with state-of-the-art algorithms for kSSP. Using our algorithm, one may find O(m) simple paths with a single shortest path tree computation and O(n+m) additional time per path in well-behaved cases, where n is the number of nodes and m is the number of edges. Our computational results show that on random graphs and large road networks, these well-behaved cases are quite common and our algorithm is faster than existing algorithms by an order of magnitude.
Cite as

Denis Kurz and Petra Mutzel. A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 49:1-49:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{kurz_et_al:LIPIcs.ISAAC.2016.49,
  author =	{Kurz, Denis and Mutzel, Petra},
  title =	{{A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{49:1--49:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.49},
  URN =		{urn:nbn:de:0030-drops-68199},
  doi =		{10.4230/LIPIcs.ISAAC.2016.49},
  annote =	{Keywords: directed graph, k-best, shortest path, simple path, weighted graph}
}
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