6 Search Results for "Venzin, Moritz"

Document
DOI: 10.4230/LIPIcs.STACS.2026.16
To Buy or Not to Buy: Online Rent-Or-Buy on Node-Weighted Graphs

Authors: Sander Borst and Moritz Venzin

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study the rent-or-buy variant of the online Steiner forest problem on node- and edge-weighted graphs. For n-node graphs with at most ̄{n} nodes of non-zero weight, and at most k̃ different arriving terminal pairs, we obtain the following: - A deterministic, O(log n log ̄{n})-competitive algorithm against adaptive adversaries. This improves on the previous best, O(log⁴ n)-competitive algorithm obtained by the black-box reduction from [Yair Bartal et al., 2001] combined with the previously best deterministic algorithms for the simpler "buy-only" setting. - A deterministic, O(̄{n}log k̃)-competitive algorithm against adaptive adversaries. This generalizes the O(log k̃)-competitive algorithm for the purely edge-weighted setting from [Seeun Umboh, 2015]. - A randomized, O(log k̃ log ̄{n})-competitive algorithm against oblivious adversaries. All previous approaches were based on the randomized, black-box reduction from [Awerbuch et al., 2004] that achieves a O(log k̃ log n)-competitive ratio when combined with an algorithm for the "buy-only" setting. Our key technical ingredient is a novel charging scheme to an instance of online prize-collecting set cover. This allows us to extend the witness-technique of [Seeun Umboh, 2015] to the node-weighted setting and obtain refined guarantees with respect to ̄{n}, already in the much simpler "buy-only" setting.
Cite as

Sander Borst and Moritz Venzin. To Buy or Not to Buy: Online Rent-Or-Buy on Node-Weighted Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{borst_et_al:LIPIcs.STACS.2026.16,
  author =	{Borst, Sander and Venzin, Moritz},
  title =	{{To Buy or Not to Buy: Online Rent-Or-Buy on Node-Weighted Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{16:1--16:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.16},
  URN =		{urn:nbn:de:0030-drops-255054},
  doi =		{10.4230/LIPIcs.STACS.2026.16},
  annote =	{Keywords: online network design, node-weighted Steiner forest, derandomization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.IPEC.2025.1
A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk)

Authors: Martin Koutecký

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Integer Programming (IP) is a fundamental but computationally hard problem. Still, certain efficiently solvable subclasses have been identified over time, most notably totally unimodular IPs in the 1950s, and fixed-dimension IPs in the 1980s. Starting around the year 2000, a stream of research has identified block-structured IPs as yet another tractable subclass. In this paper, we give a brief and incomplete review of this history, with a focus on several of the author’s contributions.
Cite as

Martin Koutecký. A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk). In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koutecky:LIPIcs.IPEC.2025.1,
  author =	{Kouteck\'{y}, Martin},
  title =	{{A Brief History of Parameterized Algorithms for Block-Structured Integer Programs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.1},
  URN =		{urn:nbn:de:0030-drops-251338},
  doi =		{10.4230/LIPIcs.IPEC.2025.1},
  annote =	{Keywords: Integer Programming, Parameterized Algorithm, Graver Basis, Treedepth, n-fold, tree-fold, 2-stage stochastic, multistage stochastic, Mixed-Integer Programming}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.15
New Algorithm for Combinatorial n-Folds and Applications

Authors: Klaus Jansen, Kai Kahler, Lis Pirotton, and Malte Tutas

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address n-fold ILPs where the matrix 𝒜 has a specific structure, i.e., where the blocks in the lower part of 𝒜 consist only of the row vectors (1,… ,1). In this paper, we propose an approach tailored to exactly these combinatorial n-folds. We utilize a divide and conquer approach to separate the original problem such that the right-hand side iteratively decreases in size. We show that this decrease in size can be calculated such that we only need to consider a bounded amount of possible right-hand sides. This, in turn, lets us efficiently combine solutions of the smaller right-hand sides to solve the original problem. We can decide the feasibility of, and also optimally solve, such problems in time (n r Δ)^O(r) log(‖b‖_∞), where n is the number of blocks, r the number of rows in the upper blocks and Δ = ‖A‖_∞. We complement the algorithm by discussing applications of the n-fold ILPs with the specific structure we require. We consider the problems of (i) scheduling on uniform machines, (ii) closest string and (iii) (graph) imbalance. Regarding (i), our algorithm results in running times of p_max^O(d)|I|^O(1), matching a lower bound derived via ETH. For (ii) we achieve running times matching the current state-of-the-art in the general case. In contrast to the state-of-the-art, our result can leverage a bounded number of column-types to yield an improved running time. For (iii), we improve the parameter dependency on the size of the vertex cover.
Cite as

Klaus Jansen, Kai Kahler, Lis Pirotton, and Malte Tutas. New Algorithm for Combinatorial n-Folds and Applications. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.IPEC.2025.15,
  author =	{Jansen, Klaus and Kahler, Kai and Pirotton, Lis and Tutas, Malte},
  title =	{{New Algorithm for Combinatorial n-Folds and Applications}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.15},
  URN =		{urn:nbn:de:0030-drops-251472},
  doi =		{10.4230/LIPIcs.IPEC.2025.15},
  annote =	{Keywords: integer linear programming, n-fold, parameterized complexity, scheduling, uniform machines}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.48
Farthest-Point Voronoi Diagrams in the Hilbert Metric

Authors: Minju Song, Mook Kwon Jung, and Hee-Kap Ahn

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
The Hilbert metric, introduced by David Hilbert in 1895, is a projective metric defined on a bounded convex domain in a Euclidean space. For a convex polygon with m vertices and n point sites lying inside the polygon in the plane, it is shown that the nearest-point Voronoi diagram in the Hilbert metric has combinatorial complexity of O(mn) [Gezalyan and Mount, SoCG 2023]. In this paper, we show that the farthest-point Voronoi diagram in the Hilbert metric has combinatorial complexity O(m), which is independent of the number of sites. Also, we present an efficient algorithm to compute the farthest-point Voronoi diagram.
Cite as

Minju Song, Mook Kwon Jung, and Hee-Kap Ahn. Farthest-Point Voronoi Diagrams in the Hilbert Metric. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 48:1-48:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{song_et_al:LIPIcs.WADS.2025.48,
  author =	{Song, Minju and Jung, Mook Kwon and Ahn, Hee-Kap},
  title =	{{Farthest-Point Voronoi Diagrams in the Hilbert Metric}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{48:1--48:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.48},
  URN =		{urn:nbn:de:0030-drops-242797},
  doi =		{10.4230/LIPIcs.WADS.2025.48},
  annote =	{Keywords: Farthest-point Voronoi diagram, Hilbert metric, Complexity, Algorithm}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.33
Efficient Sequential and Parallel Algorithms for Multistage Stochastic Integer Programming Using Proximity

Authors: Jana Cslovjecsek, Friedrich Eisenbrand, Michał Pilipczuk, Moritz Venzin, and Robert Weismantel

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We consider the problem of solving integer programs of the form min {c^⊺ x : Ax = b, x ∈ ℤ_{⩾ 0}}, where A is a multistage stochastic matrix in the following sense: the primal treedepth of A is bounded by a parameter d, which means that the columns of A can be organized into a rooted forest of depth at most d so that columns not bound by the ancestor/descendant relation do not have non-zero entries in the same row. We give an algorithm that solves this problem in fixed-parameter time f(d,‖A‖_{∞})⋅ nlog^{𝒪(2^d)} n, where f is a computable function and n is the number of rows of A. The algorithm works in the strong model, where the running time only measures unit arithmetic operations on the input numbers and does not depend on their bitlength. This is the first fpt algorithm for multistage stochastic integer programming to achieve almost linear running time in the strong sense. For two-stage stochastic integer programs, our algorithm works in time 2^{((r+s)‖A‖_∞)^{𝒪(r(r+s))}}⋅ nlog^{𝒪(rs)} n, which improves over previous methods both in terms of the polynomial factor and in terms of the dependence on r and s. In fact, for r = 1 the dependence on s is asymptotically almost tight assuming the Exponential Time Hypothesis. Our algorithm can be also parallelized: we give an implementation in the PRAM model that achieves running time f(d,‖A‖_{∞})⋅ log^{𝒪(2^d)} n using n processors. The main conceptual ingredient in our algorithms is a new proximity result for multistage stochastic integer programs. We prove that if we consider an integer program P, say with a constraint matrix A, then for every optimum solution to the linear relaxation of P there exists an optimum (integral) solution to P that lies, in the 𝓁_{∞}-norm, within distance bounded by a function of ‖A‖_{∞} and the primal treedepth of A. On the way to achieve this result, we prove a generalization and considerable improvement of a structural result of Klein for multistage stochastic integer programs. Once the proximity results are established, this allows us to apply a treedepth-based branching strategy guided by an optimum solution to the linear relaxation.
Cite as

Jana Cslovjecsek, Friedrich Eisenbrand, Michał Pilipczuk, Moritz Venzin, and Robert Weismantel. Efficient Sequential and Parallel Algorithms for Multistage Stochastic Integer Programming Using Proximity. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 33:1-33:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cslovjecsek_et_al:LIPIcs.ESA.2021.33,
  author =	{Cslovjecsek, Jana and Eisenbrand, Friedrich and Pilipczuk, Micha{\l} and Venzin, Moritz and Weismantel, Robert},
  title =	{{Efficient Sequential and Parallel Algorithms for Multistage Stochastic Integer Programming Using Proximity}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{33:1--33:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus 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.2021.33},
  URN =		{urn:nbn:de:0030-drops-146146},
  doi =		{10.4230/LIPIcs.ESA.2021.33},
  annote =	{Keywords: parameterized algorithm, multistage stochastic programming, proximity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.43
Approximate CVP_p in Time 2^{0.802 n}

Authors: Friedrich Eisenbrand and Moritz Venzin

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

Abstract
We show that a constant factor approximation of the shortest and closest lattice vector problem w.r.t. any 𝓁_p-norm can be computed in time 2^{(0.802 +ε) n}. This matches the currently fastest constant factor approximation algorithm for the shortest vector problem w.r.t. 𝓁₂. To obtain our result, we combine the latter algorithm w.r.t. 𝓁₂ with geometric insights related to coverings.
Cite as

Friedrich Eisenbrand and Moritz Venzin. Approximate CVP_p in Time 2^{0.802 n}. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{eisenbrand_et_al:LIPIcs.ESA.2020.43,
  author =	{Eisenbrand, Friedrich and Venzin, Moritz},
  title =	{{Approximate CVP\underlinep in Time 2^\{0.802 n\}}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{43:1--43:15},
  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.2020.43},
  URN =		{urn:nbn:de:0030-drops-129097},
  doi =		{10.4230/LIPIcs.ESA.2020.43},
  annote =	{Keywords: Shortest and closest vector problem, approximation algorithm, sieving, covering convex bodies}
}
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