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29th International Conference on Principles and Practice of Constraint Programming, CP 2023

作者： Zhang, Tianwei Szeider, Stefan Algorithms and Complexity Group TU Wien Austria

ISBN: (纸本)9783959773003

A graph is induced k-universal if it contains all graphs of order k as an induced subgraph. For over half a century, the question of determining smallest k-universal graphs has been studied. A related question asks for a smallest k-universal tournament containing all tournaments of order k. This paper proposes and compares SAT-based methods for answering these questions exactly for small values of k. Our methods scale to values for which a generate-and-test approach isn't feasible;for instance, we show that an induced 7-universal graph has more than 16 vertices, whereas the number of all connected graphs on 16 vertices, modulo isomorphism, is a number with 23 decimal digits Our methods include static and dynamic symmetry breaking and lazy encodings, employing external subgraph isomorphism testing. © Tianwei Zhang and Stefan Szeider.

关键词： Directed graphs

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Minimizing Switches in Cased Graph Drawings 32

Minimizing Switches in Cased Graph Drawings

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32nd International Symposium on Graph Drawing and Network Visualization, GD 2024

作者： Ganian, Robert Nöllenburg, Martin Röder, Sebastian Algorithms and Complexity Group TU Wien Austria TU Wien Austria

ISBN: (纸本)9783959773430

In cased drawings of graphs, edges are drawn in front of others in order to decrease the negative impact of crossings on readability. In this context, a switch on an edge is defined as two consecutive crossings, where the edge is drawn in the front at one crossing and behind another edge at the next crossing. We investigate the problem of minimizing the maximum number of switches on any edge - both in a fixed drawing as well as for non-embedded graphs. We resolve an open question by Eppstein, van Kreveld, Mumford, and Speckmann (2009) by establishing the NP-hardness of minimizing the number of switches in a fixed drawing, provide a fixed-parameter algorithm for this problem, and obtain a full characterization of the problem for non-embedded graphs. © Robert Ganian, Martin Nöllenburg, and Sebastian Röder.

关键词： Graphic methods

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Separating Incremental and Non-Incremental Bottom-Up Compilation 26

Separating Incremental and Non-Incremental Bottom-Up Compila...

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26th International Conference on Theory and Applications of Satisfiability Testing, SAT 2023

作者： De Colnet, Alexis Algorithms and Complexity Group TU Wien Austria

ISBN: (纸本)9783959772860

The aim of a compiler is, given a function represented in some language, to generate an equivalent representation in a target language L. In bottom-up (BU) compilation of functions given as CNF formulas, constructing the new representation requires compiling several subformulas in L. The compiler starts by compiling the clauses in L and iteratively constructs representations for new subformulas using an "Apply" operator that performs conjunction in L, until all clauses are combined into one representation. In principle, BU compilation can generate representations for any subformulas and conjoin them in any way. But an attractive strategy from a practical point of view is to augment one main representation - which we call the core - by conjoining to it the clauses one at a time. We refer to this strategy as incremental BU compilation. We prove that, for known relevant languages L for BU compilation, there is a class of CNF formulas that admit BU compilations to L that generate only polynomial-size intermediate representations, while their incremental BU compilations all generate an exponential-size core. © 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： Program compilers

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Proven Optimally-Balanced Latin Rectangles with SAT 29

Proven Optimally-Balanced Latin Rectangles with SAT

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29th International Conference on Principles and Practice of Constraint Programming, CP 2023

作者： Ramaswamy, Vaidyanathan Peruvemba Szeider, Stefan Algorithms and Complexity Group TU Wien Austria

ISBN: (纸本)9783959773003

Motivated by applications from agronomic field experiments, Díaz, Le Bras, and Gomes [CPAIOR 2015] introduced Partially Balanced Latin Rectangles as a generalization of Spatially Balanced Latin Squares. They observed that the generation of Latin rectangles that are optimally balanced is a highly challenging computational problem. They computed, utilizing CSP and MIP encodings, Latin rectangles up to 12 × 12, some optimally balanced, some suboptimally balanced. In this paper, we develop a SAT encoding for generating balanced Latin rectangles. We compare experimentally encoding variants. Our results indicate that SAT encodings perform competitively with the MIP encoding, in some cases better. In some cases we could find Latin rectangles that are more balanced than previously known ones. This finding is significant, as there are many arithmetic constraints involved. The SAT approach offers the advantage that we can certify that Latin rectangles are optimally balanced through DRAT proofs that can be verified independently. © Vaidyanathan Peruvemba Ramaswamy and Stefan Szeider.

关键词： Encoding (symbols)

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A SAT Solver's Opinion on the Erdos-Faber-Lovász Conjecture 26

A SAT Solver's Opinion on the Erdos-Faber-Lovász Conjecture

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26th International Conference on Theory and Applications of Satisfiability Testing, SAT 2023

作者： Kirchweger, Markus Peitl, Tomas Szeider, Stefan Algorithms and Complexity Group TU Wien Austria

ISBN: (纸本)9783959772860

In 1972, Paul Erdos, Vance Faber, and Lászlo Lovász asked whether every linear hypergraph with n vertices can be edge-colored with n colors, a statement that has come to be known as the EFL conjecture. Erdos himself considered the conjecture as one of his three favorite open problems, and offered increasing money prizes for its solution on several occasions. A proof of the conjecture was recently announced, for all but a finite number of hypergraphs. In this paper we look at some of the cases not covered by this proof. We use SAT solvers, and in particular the SAT Modulo Symmetries (SMS) framework, to generate non-colorable linear hypergraphs with a fixed number of vertices and hyperedges modulo isomorphisms. Since hypergraph colorability is NP-hard, we cannot directly express in a propositional formula that we want only non-colorable hypergraphs. Instead, we use one SAT (SMS) solver to generate candidate hypergraphs modulo isomorphisms, and another to reject them by finding a coloring. Each successive candidate is required to defeat all previous colorings, whereby we avoid having to generate and test all linear hypergraphs. Computational methods have previously been used to verify the EFL conjecture for small hypergraphs. We verify and extend these results to larger values and discuss challenges and directions. Ours is the first computational approach to the EFL conjecture that allows producing independently verifiable, DRAT proofs. © 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： Set theory

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Block Crossings in One-Sided Tanglegrams 18th

Block Crossings in One-Sided Tanglegrams

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18th International Symposium on algorithms and Data Structures, WADS 2023

作者： Dobler, Alexander Nöllenburg, Martin Algorithms and Complexity Group TU Wien Vienna Austria

ISBN: (纸本)9783031389054

Tanglegrams are drawings of two rooted binary phylogenetic trees and a matching between their leaf sets. The trees are drawn crossing-free on opposite sides with their leaf sets facing each other on two vertical lines. Instead of minimizing the number of pairwise edge crossings, we consider the problem of minimizing the number of block crossings, that is, two bundles of lines crossing each other locally. With one tree fixed, the leaves of the second tree can be permuted according to its tree structure. We give a complete picture of the algorithmic complexity of minimizing block crossings in one-sided tanglegrams by showing NP -completeness, constant-factor approximations, and a fixed-parameter algorithm. We also state first results for non-binary trees. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

关键词： Binary trees

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Constrained Boundary Labeling 35

Constrained Boundary Labeling

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35th International Symposium on algorithms and Computation, ISAAC 2024

作者： Depian, Thomas Nöllenburg, Martin Terziadis, Soeren Wallinger, Markus Algorithms and Complexity Group TU Wien Austria Algorithms cluster TU Eindhoven Netherlands Technical University of Munich Germany

ISBN: (纸本)9783959773546

Boundary labeling is a technique in computational geometry used to label dense sets of feature points in an illustration. It involves placing labels along an axis-aligned bounding box and connecting each label with its corresponding feature point using non-crossing leader lines. Although boundary labeling is well-studied, semantic constraints on the labels have not been investigated thoroughly. In this paper, we introduce grouping and ordering constraints in boundary labeling: grouping constraints enforce that all labels in a group are placed consecutively on the boundary, and ordering constraints enforce a partial order over the labels. We show that it is NP-hard to find a labeling for arbitrarily sized labels with unrestricted positions along one side of the boundary. However, we obtain polynomial-time algorithms if we restrict this problem either to uniform-height labels or to a finite set of candidate positions. Finally, we show that finding a labeling on two opposite sides of the boundary is NP-complete, even for uniform-height labels and finite label positions. © Thomas Depian, Martin Nöllenburg, Soeren Terziadis, and Markus Wallinger.

关键词： Computational geometry

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Self-organized transport in noisy dynamic networks

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Physical Review E 2024年第4期110卷 044310页

作者： Frederic Folz Kurt Mehlhorn Giovanna Morigi Theoretische Physik Algorithms and Complexity Group

We present a numerical study of multicommodity transport in a noisy, nonlinear network. The nonlinearity determines the dynamics of the edge capacities, which can be amplified or suppressed depending on the local current flowing across an edge. We consider network self-organization for three different nonlinear functions: For all three we identify parameter regimes where noise leads to self-organization into more robust topologies, that are not found by the sole noiseless dynamics. Moreover, the interplay between noise and specific functional behavior of the nonlinearity gives rise to different features, such as (i) continuous or discontinuous responses to the demand strength and (ii) either single or multistable solutions. Our study shows the crucial role of the activation function on noise-assisted phenomena.

关键词： Dynamics of networks Biological networks Stochastic dynamical systems Stochastic networks

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GdMetriX - A NetworkX Extension For Graph Drawing Metrics 32

GdMetriX - A NetworkX Extension For Graph Drawing Metrics

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32nd International Symposium on Graph Drawing and Network Visualization, GD 2024

作者： Nöllenburg, Martin Röder, Sebastian Wallinger, Markus Algorithms and Complexity Group TU Wien Austria TU Wien Austria Chair for Efficient Algorithms Technical University of Munich Germany

ISBN: (纸本)9783959773430

networkX is a well-established Python library for network analysis. With gdMetriX, we aim to extend the functionality of networkX and provide common quality metrics used in the field of graph drawing, such as the number of crossings or the angular resolution. In addition, the package provides easy-to-use access to the graph datasets provided by the 'Graph Layout Benchmark Datasets' project from the Northeastern University Visualization Lab. © Martin Nöllenburg, Sebastian Röder, and Markus Wallinger.

关键词： Data visualization

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SAT Backdoors: Depth Beats Size 30

SAT Backdoors: Depth Beats Size

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30th Annual European Symposium on algorithms, ESA 2022

作者： Dreier, Jan Ordyniak, Sebastian Szeider, Stefan Algorithms and Complexity Group TU Wien Austria Algorithms and Complexity Group University of Leeds United Kingdom

ISBN: (纸本)9783959772471

For several decades, much effort has been put into identifying classes of CNF formulas whose satisfiability can be decided in polynomial time. Classic results are the linear-time tractability of Horn formulas (Aspvall, Plass, and Tarjan, 1979) and Krom (i.e., 2CNF) formulas (Dowling and Gallier, 1984). Backdoors, introduced by Williams, Gomes and Selman (2003), gradually extend such a tractable class to all formulas of bounded distance to the class. Backdoor size provides a natural but rather crude distance measure between a formula and a tractable class. Backdoor depth, introduced by Mählmann, Siebertz, and Vigny (2021), is a more refined distance measure, which admits the utilization of different backdoor variables in parallel. Bounded backdoor size implies bounded backdoor depth, but there are formulas of constant backdoor depth and arbitrarily large backdoor size. We propose FPT approximation algorithms to compute backdoor depth into the classes Horn and Krom. This leads to a linear-time algorithm for deciding the satisfiability of formulas of bounded backdoor depth into these classes. We base our FPT approximation algorithm on a sophisticated notion of obstructions, extending Mählmann et al.'s obstruction trees in various ways, including the addition of separator obstructions. We develop the algorithm through a new game-theoretic framework that simplifies the reasoning about backdoors. Finally, we show that bounded backdoor depth captures tractable classes of CNF formulas not captured by any known method. © 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： Approximation algorithms

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