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Documents authored by Karrenbauer, Andreas

Document
DOI: 10.4230/LIPIcs.SEA.2025.10
Algorithm Engineering of SSSP with Negative Edge Weights

Authors: Alejandro Cassis, Andreas Karrenbauer, André Nusser, and Paolo Luigi Rinaldi

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
Computing shortest paths is one of the most fundamental algorithmic graph problems. It is known since decades that this problem can be solved in near-linear time if all weights are nonnegative. A recent break-through by [Aaron Bernstein et al., 2022] presented a randomized near-linear time algorithm for this problem. A subsequent improvement in [Karl Bringmann et al., 2023] significantly reduced the number of logarithmic factors and thereby also simplified the algorithm. It is surprising and exciting that both of these algorithms are combinatorial and do not contain any fundamental obstacles for being practical. We launch the, to the best of our knowledge, first extensive investigation towards a practical implementation of [Karl Bringmann et al., 2023]. To this end, we give an accessible overview of the algorithm and discuss what adaptions are necessary to obtain a fast algorithm in practice. We manifest these adaptions in an efficient implementation. We test our implementation on a benchmark data set that is adapted to be more difficult for our implementation in order to allow for a fair comparison. As in [Karl Bringmann et al., 2023] as well as in our implementation there are multiple parameters to tune, we empirically evaluate their effect and thereby determine the best choices. Our implementation is then extensively compared to one of the state-of-the-art algorithms for this problem [Andrew V. Goldberg and Tomasz Radzik, 1993]. On the hardest instance type, we are faster by up to almost two orders of magnitude.
Cite as

Alejandro Cassis, Andreas Karrenbauer, André Nusser, and Paolo Luigi Rinaldi. Algorithm Engineering of SSSP with Negative Edge Weights. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cassis_et_al:LIPIcs.SEA.2025.10,
  author =	{Cassis, Alejandro and Karrenbauer, Andreas and Nusser, Andr\'{e} and Rinaldi, Paolo Luigi},
  title =	{{Algorithm Engineering of SSSP with Negative Edge Weights}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.10},
  URN =		{urn:nbn:de:0030-drops-232486},
  doi =		{10.4230/LIPIcs.SEA.2025.10},
  annote =	{Keywords: Single Source Shortest Paths, Negative Weights, Near-Linear Time}
}
Document
DOI: 10.4230/LIPIcs.SEA.2025.18
Engineering Insights into Biclique Partitions and Fractional Binary Ranks of Matrices

Authors: Angikar Ghosal and Andreas Karrenbauer

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
We investigate structural properties of the binary rank of Kronecker powers of binary matrices, equivalently, the biclique partition numbers of the corresponding bipartite graphs. To this end, we engineer a Column Generation approach to solve linear optimization problems for the fractional biclique partition number of bipartite graphs, specifically examining the Domino graph and its Kronecker powers. We address the challenges posed by the double exponential growth of the number of bicliques in increasing Kronecker powers. We discuss various strategies to generate suitable initial sets of bicliques, including an inductive method for increasing Kronecker powers. We show how to manage the number of active bicliques to improve running time and to stay within memory limits. Our computational results reveal that the fractional binary rank is not multiplicative with respect to the Kronecker product. Hence, there are binary matrices, and bipartite graphs, respectively, such as the Domino, where the asymptotic fractional binary rank is strictly smaller than the fractional binary rank. While we used our algorithm to reduce the upper bound, we formally prove that the fractional biclique cover number is a lower bound, which is at least as good as the widely used isolating (or fooling set) bound. For the Domino, we obtain that the asymptotic fractional binary rank lies in the interval [2,2.373]. Since our computational resources are not sufficient to further reduce the upper bound, we encourage further exploration using more substantial computing resources or further mathematical engineering techniques to narrow the gap and advance our understanding of biclique partitions, particularly, to settle the open question whether binary rank and biclique partition number are multiplicative with respect to the Kronecker product.
Cite as

Angikar Ghosal and Andreas Karrenbauer. Engineering Insights into Biclique Partitions and Fractional Binary Ranks of Matrices. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 18:1-18:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghosal_et_al:LIPIcs.SEA.2025.18,
  author =	{Ghosal, Angikar and Karrenbauer, Andreas},
  title =	{{Engineering Insights into Biclique Partitions and Fractional Binary Ranks of Matrices}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{18:1--18:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.18},
  URN =		{urn:nbn:de:0030-drops-232568},
  doi =		{10.4230/LIPIcs.SEA.2025.18},
  annote =	{Keywords: Asymptotic Binary Rank, Algorithm Engineering, Combinatorics of Bipartite Graphs, Linear Programming}
}
Document
DOI: 10.4230/LIPIcs.DISC.2017.7
Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming Models

Authors: Ruben Becker, Andreas Karrenbauer, Sebastian Krinninger, and Christoph Lenzen

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Abstract
We present a method for solving the shortest transshipment problem - also known as uncapacitated minimum cost flow - up to a multiplicative error of (1 + epsilon) in undirected graphs with non-negative integer edge weights using a tailored gradient descent algorithm. Our gradient descent algorithm takes epsilon^(-3) polylog(n) iterations, and in each iteration it needs to solve an instance of the transshipment problem up to a multiplicative error of polylog(n), where n is the number of nodes. In particular, this allows us to perform a single iteration by computing a solution on a sparse spanner of logarithmic stretch. Using a careful white-box analysis, we can further extend the method to finding approximate solutions for the single-source shortest paths (SSSP) problem. As a consequence, we improve prior work by obtaining the following results: (1) Broadcast CONGEST model: (1 + epsilon)-approximate SSSP using ~O((sqrt(n) + D) epsilon^(-O(1))) rounds, where D is the (hop) diameter of the network. (2) Broadcast congested clique model: (1 + epsilon)-approximate shortest transshipment and SSSP using ~O(epsilon^(-O(1))) rounds. (3) Multipass streaming model: (1 + epsilon)-approximate shortest transshipment and SSSP using ~O(n) space and ~O(epsilon^(-O(1))) passes. The previously fastest SSSP algorithms for these models leverage sparse hop sets. We bypass the hop set construction; computing a spanner is sufficient with our method. The above bounds assume non-negative integer edge weights that are polynomially bounded in n; for general non-negative weights, running times scale with the logarithm of the maximum ratio between non-zero weights. In case of asymmetric costs for traversing an edge in opposite directions, running times scale with the maximum ratio between the costs of both directions over all edges.
Cite as

Ruben Becker, Andreas Karrenbauer, Sebastian Krinninger, and Christoph Lenzen. Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming Models. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{becker_et_al:LIPIcs.DISC.2017.7,
  author =	{Becker, Ruben and Karrenbauer, Andreas and Krinninger, Sebastian and Lenzen, Christoph},
  title =	{{Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming Models}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.7},
  URN =		{urn:nbn:de:0030-drops-80031},
  doi =		{10.4230/LIPIcs.DISC.2017.7},
  annote =	{Keywords: Shortest Paths, Shortest Transshipment, Undirected Min-cost Flow, Gradient Descent, Spanner}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2016.11
On the Parameterized Complexity of Biclique Cover and Partition

Authors: Sunil Chandran, Davis Issac, and Andreas Karrenbauer

Published in: LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Abstract
Given a bipartite graph G, we consider the decision problem called BicliqueCover for a fixed positive integer parameter k where we are asked whether the edges of G can be covered with at most k complete bipartite subgraphs (a.k.a. bicliques). In the BicliquePartition problem, we have the additional constraint that each edge should appear in exactly one of the k bicliques. These problems are both known to be NP-complete but fixed parameter tractable. However, the known FPT algorithms have a running time that is doubly exponential in k, and the best known kernel for both problems is exponential in k. We build on this kernel and improve the running time for BicliquePartition to O*(2^{2k^2+k*log(k)+k}) by exploiting a linear algebraic view on this problem. On the other hand, we show that no such improvement is possible for BicliqueCover unless the Exponential Time Hypothesis (ETH) is false by proving a doubly exponential lower bound on the running time. We achieve this by giving a reduction from 3SAT on n variables to an instance of BicliqueCover with k=O(log(n)). As a further consequence of this reduction, we show that there is no subexponential kernel for BicliqueCover unless P=NP. Finally, we point out the significance of the exponential kernel mentioned above for the design of polynomial-time approximation algorithms for the optimization versions of both problems. That is, we show that it is possible to obtain approximation factors of n/log(n) for both problems, whereas the previous best approximation factor was n/sqrt(log(n)).
Cite as

Sunil Chandran, Davis Issac, and Andreas Karrenbauer. On the Parameterized Complexity of Biclique Cover and Partition. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 11:1-11:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chandran_et_al:LIPIcs.IPEC.2016.11,
  author =	{Chandran, Sunil and Issac, Davis and Karrenbauer, Andreas},
  title =	{{On the Parameterized Complexity of Biclique Cover and Partition}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{11:1--11:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Guo, Jiong and Hermelin, Danny},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.11},
  URN =		{urn:nbn:de:0030-drops-69293},
  doi =		{10.4230/LIPIcs.IPEC.2016.11},
  annote =	{Keywords: Biclique Cover/Partition, Linear algebra in finite fields, Lower bound}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.1
On Guillotine Cutting Sequences

Authors: Fidaa Abed, Parinya Chalermsook, José Correa, Andreas Karrenbauer, Pablo Pérez-Lantero, José A. Soto, and Andreas Wiese

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

Abstract
Imagine a wooden plate with a set of non-overlapping geometric objects painted on it. How many of them can a carpenter cut out using a panel saw making guillotine cuts, i.e., only moving forward through the material along a straight line until it is split into two pieces? Already fifteen years ago, Pach and Tardos investigated whether one can always cut out a constant fraction if all objects are axis-parallel rectangles. However, even for the case of axis-parallel squares this question is still open. In this paper, we answer the latter affirmatively. Our result is constructive and holds even in a more general setting where the squares have weights and the goal is to save as much weight as possible. We further show that when solving the more general question for rectangles affirmatively with only axis-parallel cuts, this would yield a combinatorial O(1)-approximation algorithm for the Maximum Independent Set of Rectangles problem, and would thus solve a long-standing open problem. In practical applications, like the mentioned carpentry and many other settings, we can usually place the items freely that we want to cut out, which gives rise to the two-dimensional guillotine knapsack problem: Given a collection of axis-parallel rectangles without presumed coordinates, our goal is to place as many of them as possible in a square-shaped knapsack respecting the constraint that the placed objects can be separated by a sequence of guillotine cuts. Our main result for this problem is a quasi-PTAS, assuming the input data to be quasi-polynomially bounded integers. This factor matches the best known (quasi-polynomial time) result for (non-guillotine) two-dimensional knapsack.
Cite as

Fidaa Abed, Parinya Chalermsook, José Correa, Andreas Karrenbauer, Pablo Pérez-Lantero, José A. Soto, and Andreas Wiese. On Guillotine Cutting Sequences. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{abed_et_al:LIPIcs.APPROX-RANDOM.2015.1,
  author =	{Abed, Fidaa and Chalermsook, Parinya and Correa, Jos\'{e} and Karrenbauer, Andreas and P\'{e}rez-Lantero, Pablo and Soto, Jos\'{e} A. and Wiese, Andreas},
  title =	{{On Guillotine Cutting Sequences}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{1--19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.1},
  URN =		{urn:nbn:de:0030-drops-52917},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.1},
  annote =	{Keywords: Guillotine cuts, Rectangles, Squares, Independent Sets, Packing}
}
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