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34th International Symposium on Computational Geometry, SoCG 2018

作者： Klute, Fabian Nöllenburg, Martin Algorithms and Complexity Group TU Wien Vienna Austria

ISBN: (纸本)9783959770668

Circular layouts are a popular graph drawing style, where vertices are placed on a circle and edges are drawn as straight chords. Crossing minimization in circular layouts is NP-hard. One way to allow for fewer crossings in practice are two-sided layouts that draw some edges as curves in the exterior of the circle. In fact, one- and two-sided circular layouts are equivalent to one-page and two-page book drawings, i.e., graph layouts with all vertices placed on a line (the spine) and edges drawn in one or two distinct half-planes (the pages) bounded by the spine. In this paper we study the problem of minimizing the crossings for a fixed cyclic vertex order by computing an optimal k-plane set of exteriorly drawn edges for k > 1, extending the previously studied case k = 0. We show that this relates to finding bounded-degree maximum-weight induced subgraphs of circle graphs, which is a graph-theoretic problem of independent interest. We show NP-hardness for arbitrary k, present an efficient algorithm for k = 1, and generalize it to an explicit XP-time algorithm for any fixed k. For the practically interesting case k = 1 we implemented our algorithm and present experimental results that confirm the applicability of our algorithm. © Fabian Klute and Martin Nöllenburg;licensed under Creative Commons License CC-BY 34th Symposium on Computational Geometry (SoCG 2018).

关键词： Drawing (graphics)

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The Parameterized complexity of Extending Stack Layouts

arXiv

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arXiv 2024年

作者： Depian, Thomas Fink, Simon D. Ganian, Robert Nöllenburg, Martin Algorithms and Complexity Group TU Wien Vienna Austria

An -page stack layout (also known as an -page book embedding) of a graph is a linear order of the vertex set together with a partition of the edge set into stacks (or pages), such that the endpoints of no two edges on the same stack alternate. We study the problem of extending a given partial -page stack layout into a complete one, which can be seen as a natural generalization of the classical NP-hard problem of computing a stack layout of an input graph from scratch. Given the inherent intractability of the problem, we focus on identifying tractable fragments through the refined lens of parameterized complexity analysis. Our results paint a detailed and surprisingly rich complexitytheoretic landscape of the problem which includes the identification of paraNP-hard, W[1]-hard and XP-tractable, as well as fixed-parameter tractable fragments of stack layout extension via a natural sequence of parameterizations. © 2024, CC BY.

关键词： Graph embeddings

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Mixed Linear Layouts: complexity, Heuristics, and Experiments

arXiv

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arXiv 2019年

作者： de Col, Philipp Klute, Fabian Nöllenburg, Martin Algorithms and Complexity Group TU Wien Vienna Austria

A k-page linear graph layout of a graph G = (V, E) draws all vertices along a line and each edge in one of k disjoint halfplanes called pages, which are bounded by . We consider two types of pages. In a stack page no two edges should cross and in a queue page no edge should be nested by another edge. A crossing (nesting) in a stack (queue) page is called a conflict. The algorithmic problem is twofold and requires to compute (i) a vertex ordering and (ii) a page assignment of the edges such that the resulting layout is either conflict-free or conflict-minimal. While linear layouts with only stack or only queue pages are well-studied, mixed s-stack q-queue layouts for s, q ≥ 1 have received less attention. We show NP-completeness results on the recognition problem of certain mixed linear layouts and present a new heuristic for minimizing conflicts. In a computational experiment for the case s, q = 1 we show that the new heuristic is an improvement over previous heuristics for linear layouts. Copyright © 2019, The Authors. All rights reserved.

关键词： Queueing theory

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Meta-kernelization using well-structured modulators 10

Meta-kernelization using well-structured modulators

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10th International Symposium on Parameterized and Exact Computation, IPEC 2015

作者： Eiben, Eduard Ganian, Robert Szeider, Stefan Algorithms and Complexity Group TU Wien Vienna Austria

ISBN: (纸本)9783939897927

Kernelization investigates exact preprocessing algorithms with performance guarantees. The most prevalent type of parameters used in kernelization is the solution size for optimization problems;however, also structural parameters have been successfully used to obtain polynomial kernels for a wide range of problems. Many of these parameters can be defined as the size of a smallest modulator of the given graph into a fixed graph class (i.e., a set of vertices whose deletion puts the graph into the graph class). Such parameters admit the construction of polynomial kernels even when the solution size is large or not applicable. This work follows up on the research on meta-kernelization frameworks in terms of structural parameters. We develop a class of parameters which are based on a more general view on modulators: instead of size, the parameters employ a combination of rank-width and split decompositions to measure structure inside the modulator. This allows us to lift kernelization results from modulator-size to more general parameters, hence providing smaller kernels. We show (i) how such large but well-structured modulators can be efficiently approximated, (ii) how they can be used to obtain polynomial kernels for any graph problem expressible in Monadic Second Order logic, and (iii) how they allow the extension of previous results in the area of structural metakernelization. © Eduard Eiben, Robert Ganian, and Stefan Szeider;.

关键词： Polynomials

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The Power of Collaboration: Learning Large Bayesian Networks at Scale 36

The Power of Collaboration: Learning Large Bayesian Networks...

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36th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2024

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

ISBN: (纸本)9798331527235

We present a novel approach to learn the structure of large Bayesian Networks (BNs) of bounded treewidth. Our approach combines the complementary strengths of heuristic and MaxSAT-based methods. Both methods operate in parallel and cooperate in a mutually advantageous way to improve the quality of the learned BN structures. Our work utilizes an approach proposed by Peruvemba Ramaswamy and Szeider (AAAI'21, NeurIPS'21, UAI'22), which continually applies a MaxSAT-based algorithm to a BN obtained from heuristic search. We create a continuous and dynamic refinement process by allowing the heuristic and the MaxSAT-based technique to cooperate and repeatedly share their work. Our rigorous experiments show that the collaboration between the two methods is a powerful strategy for increasing the score of the learned BN structure. Moreover, the rate at which the score increases is significantly higher than that of the individual methods by themselves. Our results provide a strong argument for combining complementary approaches to learn treewidth-bounded BNs in a collaborative way. © 2024 IEEE.

关键词： Bayesian networks

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A Structural complexity Analysis of Hierarchical Task Network Planning

arXiv

引用

arXiv 2024年

作者： Brand, Cornelius Ganian, Robert Inerney, Fion Mc Wietheger, Simon Algorithms & Complexity Theory Group Regensburg University Germany Algorithms and Complexity Group TU Wien Austria Telefónica Scientific Research Barcelona Spain

We perform a refined complexity-theoretic analysis of three classical problems in the context of Hierarchical Task Network Planning: the verification of a provided plan, whether an executable plan exists, and whether a given state can be reached. Our focus lies on identifying structural properties which yield tractability. We obtain new polynomial algorithms for all three problems on a natural class of primitive networks, along with corresponding lower bounds. We also obtain an algorithmic meta-theorem for lifting polynomial-time solvability from primitive to general task networks, and prove that its preconditions are tight. Finally, we analyze the parameterized complexity of the three problems. Copyright © 2024, The Authors. All rights reserved.

关键词： Complex networks

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On structural parameterizations of the edge disjoint paths problem 28

On structural parameterizations of the edge disjoint paths p...

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28th International Symposium on algorithms and Computation, ISAAC 2017

作者： Ganian, Robert Ordyniak, Sebastian Sridharan, Ramanujan Algorithms and Complexity Group TU Wien Vienna Austria

ISBN: (纸本)9783959770545

In this paper we revisit the classical Edge Disjoint Paths (EDP) problem, where one is given an undirected graph G and a set of terminal pairs P and asks whether G contains a set of pairwise edge-disjoint paths connecting every terminal pair in P. Our focus lies on structural parameterizations for the problem that allow for efficient (polynomial-Time or fpt) algorithms. As our first result, we answer an open question stated in Fleszar, Mnich, and Spoerhase (2016), by showing that the problem can be solved in polynomial time if the input graph has a feedback vertex set of size one. We also show that EDP parameterized by the treewidth and the maximum degree of the input graph is fixed-parameter tractable. Having developed two novel algorithms for EDP using structural restrictions on the input graph, we then turn our attention towards the augmented graph, i.e., the graph obtained from the input graph after adding one edge between every terminal pair. In constrast to the input graph, where EDP is known to remain NP-hard even for treewidth two, a result by Zhou et al. (2000) shows that EDP can be solved in non-uniform polynomial time if the augmented graph has constant treewidth;we note that the possible improvement of this result to an fpt-Algorithm has remained open since then. We show that this is highly unlikely by establishing the W[1]-hardness of the problem parameterized by the treewidth (and even feedback vertex set) of the augmented graph. Finally, we develop an fpt-Algorithm for EDP by exploiting a novel structural parameter of the augmented graph.

关键词： Parameterization

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On the parameterized complexity of simultaneous deletion problems 37

On the parameterized complexity of simultaneous deletion pro...

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37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017

作者： Agrawal, Akanksha Krithika, R. Lokshtanov, Daniel Mouawad, Amer E. Ramanujan, M.S. Department of Informatics University of Bergen Bergen Norway Institute of Mathematical Sciences HBNI Chennai India Algorithms and Complexity Group Vienna University of Technology Vienna Austria

ISBN: (纸本)9783959770552

For a family of graphs F, an n-vertex graph G, and a positive integer k, the F-Deletion problem asks whether we can delete at most k vertices from G to obtain a graph in F. F-Deletion generalizes many classical graph problems such as Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. A (multi) graph G = (V, ?ai=1Ei), where the edge set of G is partitioned into a color classes, is called an a-edge-colored graph. A natural extension of the F-Deletion problem to edge-colored graphs is the Simultaneous (F1, . . ., Fa)-Deletion problem. In the latter problem, we are given an a-edge-colored graph G and the goal is to find a set S of at most k vertices such that each graph Gi - S, where Gi = (V, Ei) and 1 = i = a, is in Fi. Recently, a subset of the authors considered the aforementioned problem with F1 = . . . = Fa being the family of all forests. They showed that the problem is fixed-parameter tractable when parameterized by k and a and can be solved in O(2O(ak)) time1. In this work, we initiate the investigation of the complexity of Simultaneous (F1, . . ., Fa)-Deletion with di erent families of graphs. In the process, we obtain a complete characterization of the parameterized complexity of this problem when one or more of the Fis is the class of bipartite graphs and the rest (if any) are forests. We show that if F1 is the family of all bipartite graphs and each of F2 = F3 = . . . = Fa is the family of all forests then the problem is fixed-parameter tractable parameterized by k and a. However, even when F1 and F2 are both the family of all bipartite graphs, then the Simultaneous (F1, F2)-Deletion problem itself is already W[1]-hard. © Akanksha Agrawal, R. Krithika, Daniel Lokshtanov, Amer E. Mouawad, and M. S. Ramanujan.

关键词： Graphic methods

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ASP-QRAT: a Conditionally Optimal Dual Proof System for ASP 21

ASP-QRAT: a Conditionally Optimal Dual Proof System for ASP

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21st International Conference on Principles of Knowledge Representation and Reasoning, KR 2024

作者： Chew, Leroy de Colnet, Alexis Szeider, Stefan Algorithms and Complexity Group TU Wien Vienna Austria

ISBN: (纸本)9781956792058

Answer Set Programming (ASP) is a declarative programming approach that captures many problems in knowledge representation and reasoning. To certify an ASP solver’s decision, whether the program is consistent or inconsistent, we need a certificate or proof that can be independently verified. This paper proposes the dual proof system ASP-QRAT that certifies consistent and inconsistent ASPs. ASP-QRAT is based on a translation of ASP to QBF (Quantified Boolean Formulas) and the QBF proof system QRAT as a checking format. We show that ASP-QRAT p-simulates ASP-DRUPE, an existing refutation system for inconsistent disjunctive ASPs. We show that ASP-QRAT is conditionally optimal for consistent and inconsistent ASPs, i.e., any super-polynomial lower bound on the shortest proof size of ASP-QRAT implies a major breakthrough in theoretical computer science. The case for consistent ASPs is remarkable because no analog exists in the QBF case. © 2024 Proceedings of the International Conference on Knowledge Representation and Reasoning. All rights reserved.

关键词： Knowledge representation

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Discovering archipelagos of tractability for constraint satisfaction and counting 27

Discovering archipelagos of tractability for constraint sati...

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27th Annual ACM-SIAM Symposium on Discrete algorithms, SODA 2016

作者： Ganian, Robert Ramanujan, M.S. Szeider, Stefan Algorithms and Complexity Group TU Wien Vienna Austria

ISBN: (纸本)9781510819672

The Constraint Satisfaction Problem (CSP) is a central and generic computational problem which provides a common framework for many theoretical and practical applications. A central line of research is concerned with the identification of classes of instances for which CSP can be solved in polynomial time;such classes are often called "islands of tractability." A prominent way of defining islands of tractability for CSP is to restrict the relations that may occur in the constraints to a fixed set, called a constraint language, whereas a constraint language is conservative if it contains all unary relations. Schaefer's famous Dichotomy Theorem (STOC 1978) identifies all islands of tractability in terms of tractable constraint languages over a Boolean domain of values. Since then many extensions and generalizations of this result have been obtained. Recently, Bulatov (TOCL 2011, JACM 2013) gave a full characterization of all islands of tractability for CSP and the counting version #CSP that are defined in terms of conservative constraint languages. This paper addresses the general limit of the mentioned tractability results for CSP and #CSP, that they only apply to instances where all constraints belong to a single tractable language (in general, the union of two tractable languages isn't tractable). We show that we can overcome this limitation as long as we keep some control of how constraints over the various considered tractable languages interact with each other. For this purpose we utilize the notion of a strong backdoor of a CSP instance, as introduced by Williams et al. (DCAI 2003), which is a set of variables that when instantiated moves the instance to an island of tractability, i.e., to a tractable class of instances. We consider strong backdoors into scattered classes, consisting of CSP instances where each connected component belongs entirely to some class from a list of tractable classes. Figuratively speaking, a scattered class constitutesan archipelago

关键词： Constraint satisfaction problems

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