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

作者： Markus Kirchweger Manfred Scheucher Stefan Szeider Algorithms and Complexity Group TU Wien Austria Institut för Mathematik Technische Universität Berlin Germany

ISBN: (纸本)9783959772860

To test a graph's planarity in SAT-based graph generation we develop SAT encodings with dynamic symmetry breaking as facilitated in the SAT modulo Symmetry (SMS) framework. We implement and compare encodings based on three planarity criteria. In particular, we consider two eager encodings utilizing order-based and universal-set-based planarity criteria, and a lazy encoding based on Kuratowski's theorem. The performance and scalability of these encodings are compared on two prominent problems from combinatorics: The computation of planar Turán numbers and the Earth-Moon problem. We further showcase the power of SMS equipped with a planarity encoding by verifying and extending several integer sequences from the Online Encyclopedia of Integer Sequences (OEIS) related to planar graph enumeration. Furthermore, we extend the SMS framework to directed graphs which might be of independent interest. © 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.

关键词： Moon

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Patterns and outlier analysis of traffic flow using data signatures via iDIRBrG method and vector fusion visualization

Patterns and outlier analysis of traffic flow using data sig...

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2010 3rd International Conference on Human-Centric Computing, HumanCom 2010

作者： Malinao, Jasmine A. Juayong, Richelle Ann B. Becerral, Jona G. Cabreros, Karmina Rosette C. Remaneses, Ken Marvi B. Khaw, Jason G. Wuysang, Danny F. Corpuz, Francis James O. Hernandez, Nestine Hope S. Yap, Jan Michael C. Adorna, Henry N. Algorithms and Complexity Laboratory Department of Computer Science University of Philippines Velasquez Ave. Diliman Quezon City 1101 Philippines

ISBN: (纸本)9781424475704

In this paper, we used X-Means clustering algorithm, incorporated data images from a so-called Iterative Data Image Rotated Bar Graph (iDIRBrG) method (formerly referred as BC method) and used Vector Fusion Visualization to achieve better traffic data analysis results compared to our previous work by improving how data signatures are constructed from the raw data set. By doing so, we effectively identify more patterns, extracted known as well as unexpected outliers, and novel information from the data set. These results were validated by experts from the NCTS. Furthermore, we also show more simplistic frequency-domain 2D visualizations of the entire data set. These successfully expose the internal structure and relationship of each individual point as well as the clusters obtained from it. Hence, using the methods above, we provide an effective and efficient time series traffic analysis. © 2010 IEEE.

关键词： Power spectrum

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Lossy kernels for hitting subgraphs 42

Lossy kernels for hitting subgraphs

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42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017

作者： Eiben, Eduard Hermelin, Danny Ramanujan, M.S. Algorithms and Complexity Group TU Wien Vienna Austria Industrial Engineering and Management Ben Gurion University Be'er Scheva Israel

ISBN: (纸本)9783959770460

In this paper, we study the Connected H-hitting Set and Dominating Set problems from the perspective of approximate kernelization, a framework recently introduced by Lokshtanov et al. [STOC 2017]. For the Connected H-hitting set problem, we obtain an -approximate kernel for every > 1 and complement it with a lower bound for the natural weighted version. We then perform a refined analysis of the tradeoff between the approximation factor and kernel size for the Dominating Set problem on d-degenerate graphs, and provide an interpolation of approximate kernels between the known d2-approximate kernel of constant size and 1-approximate kernel of size kO(d2). © Eduard Eiben, Danny Hermelin, and M. S. Ramanujan;licensed under Creative Commons License CC-BY.

关键词： Graph theory

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A quantitative analysis-based algorithm for optimal data signature construction of traffic data sets

A quantitative analysis-based algorithm for optimal data sig...

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International Association for Computer and Information Science/JNU International Conference on Computers, Networks, Systems and Industrial Engineering

作者： Malinao, Jasmine A. Juayong, Richelle Ann B. Oquendo, Erlo Robert F. Tadlas, Rona May U. Lee, John Boaz T. Clemente, Jhoirene B. Gaabucayan-Napalang, Ma. Sheilah Regidor, Jose Regin F. Adorna, Henry N. Department of Computer Science Algorithms and Complexity Laboratory University of the Philippines Velasquez Ave. Quezon City 1101 Metro Manila Philippines

ISBN: (纸本)9780769544175

In this paper, a new set of data signatures is derived to obtain better Vector Fusion 2D visualizations of a time series and periodic nD traffic data set as compared with previous work. The latter had used the entire Power Spectrum components for visualization purposes to produce 2D representations of each subset of the data. With the feasibility of obtaining a smaller representation of the data set in obtaining better cluster models compared to using the original n-dimensions, we now explore this feasibility for visualization purposes. We propose an algorithm that determines, in quantitative terms, how good the selected set of signatures represents the nD data set in 2 dimensions. We use the Vector Fusion visualization algorithm in transforming each signature from its n dimensions into 2 dimensions. An improved set of qualitative criterion is drawn to measure the goodness of the 2D data signature-based visual representation of the original nD data set. Finally, we provide empirical testing and discuss the results. © 2011 IEEE.

关键词： Power spectrum

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Splitting Plane Graphs to Outerplanarity

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Journal of Graph algorithms and Applications 2024年第3期28卷 31-48页

作者： Gronemann, Martin Nöllenburg, Martin Villedieu, Anaïs Algorithms and Complexity Group TU Wien Vienna Austria

Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often planarity, for which the problem is NP-hard. Here we study how to minimize the number of splits to turn a plane graph into an outerplane one. We tackle this problem by establishing a direct connection between splitting a plane graph to outerplanarity, finding a connected face cover, and finding a feedback vertex set in its dual. We prove NP-completeness for plane biconnected graphs, while we show that a polynomial-time algorithm exists for maximal planar graphs. Additionally, we show upper and lower bounds for certain families of maximal planar graphs. Finally, we provide a SAT formulation for the problem, and evaluate it on a small benchmark. © 2024, Brown University. All rights reserved.

关键词： Polynomial approximation

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Motivo: Fast motif counting via succinct color coding and adaptive sampling 45th

Motivo: Fast motif counting via succinct color coding and ad...

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45th International Conference on Very Large Data Bases, VLDB 2019

作者： Bressan, Marco Leucci, Stefano Panconesi, Alessandro Dipartimento di Informatica Sapienza Università di Roma Italy Department of Algorithms and Complexity Max Planck Institute for Informatics Germany

The randomized technique of color coding is behind state-ofthe-art algorithms for estimating graph motif counts. Those algorithms, however, are not yet capable of scaling well to very large graphs with billions of edges. In this paper we develop novel tools for the "motif counting via color coding" framework. As a result, our new algorithm, motivo, scales to much larger graphs while at the same time providing more accurate motif counts than ever before. This is achieved thanks to two types of improvements. First, we design new succinct data structures for fast color coding operations, and a biased coloring trick that trades accuracy versus resource usage. These optimizations drastically reduce the resource requirements of color coding. Second, we develop an adaptive motif sampling strategy, based on a fractional set cover problem, that breaks the additive approximation barrier of standard sampling. This gives multiplicative approximations for all motifs at once, allowing us to count not only the most frequent motifs but also extremely rare ones. To give an idea of the improvements, in 40 minutes motivo counts 7-nodes motifs on a graph with 65M nodes and 1.8B edges;this is 30 and 500 times larger than the state of the art, respectively in terms of nodes and edges. On the accuracy side, in one hour motivo produces accurate counts of ≈ 10.000 distinct 8-node motifs on graphs where state-of-the-art algorithms fail even to find the second most frequent motif. Our method requires just a high-end desktop machine. These results show how color coding can bring motif mining to the realm of truly massive graphs using only ordinary hardware. © 2019, is held by the owner/author(s).

关键词： Color

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A linear-Time parameterized algorithm for node unique label cover 25

A linear-Time parameterized algorithm for node unique label ...

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25th European Symposium on algorithms, ESA 2017

作者： Lokshtanov, Daniel Ramanujan, M.S. Saurabh, Saket University of Bergen Bergen Norway Algorithms and Complexity Group TU Wien Vienna Austria Institute of Mathematical Sciences Chennai India

ISBN: (纸本)9783959770491

The optimization version of the Unique Label Cover problem is at the heart of the Unique Games Conjecture which has played an important role in the proof of several tight inapproximability results. In recent years, this problem has been also studied extensively from the point of view of parameterized complexity. Chitnis et al. [FOCS 2012, SICOMP 2016] proved that this problem is fixed-parameter tractable (FPT) and Wahlström [SODA 2014] gave an FPT algorithm with an improved parameter dependence. Subsequently, Iwata, Wahlström and Yoshida [SICOMP 2016] proved that the edge version of Unique Label Cover can be solved in linear FPT-Time, and they left open the existence of such an algorithm for the node version of the problem. In this paper, we resolve this question by presenting the first linear-Time FPT algorithm for Node Unique Label Cover.

关键词： Parameter estimation

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Fixed-Parameter algorithms for Computing Bend-Restricted RAC Drawings of Graphs

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Journal of Graph algorithms and Applications 2024年第2期28卷 131-150页

作者： Brand, Cornelius Ganian, Robert Röder, Sebastian Schager, Florian Algorithms and Complexity Group TU Wien Vienna Austria

In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly 90◦, where the number of bends on such polylines is typically restricted in some way. While structural and topological properties of RAC drawings have been the focus of extensive research and particular attention has been paid to RAC drawings with at most 0, 1, 2 and 3 bends per edge, little was known about the boundaries of tractability for computing such drawings. In this paper, we initiate the study of bend-restricted RAC drawings from the viewpoint of parameterized complexity. In particular, we establish that computing a RAC drawing of an input graph G with at most b bends where each edge e has a prescribed upper-bound 0 ≤ β(e) ≤ 3 on the number of bends it can support (or determining that none exists) is: • fixed-parameter tractable parameterized by the feedback edge number of G, and • fixed-parameter tractable parameterized by b plus the vertex cover number of G. © 2024, Brown University. All rights reserved.

关键词： Graph algorithms

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Backdoor Dnfs

SSRN

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SSRN 2023年

作者： Ordyniak, Sebastian Schidler, Andre Szeider, Stefan Algorithms and Complexity Group TU Wien Vienna Austria Algorithms and Complexity Group University of Leeds United Kingdom

We introduce backdoor DNFs, as a tool to measure the theoretical hardness of CNF formulas. Like backdoor sets and backdoor trees, backdoor DNFs are defined relative to a tractable class of CNF formulas. Each conjunctive term of a backdoor DNF defines a partial assignment that moves the input CNF formula into the base class. Backdoor DNFs are more expressive and potentially smaller than their predecessors backdoor sets and backdoor trees. We establish the fixed-parameter tractability of the backdoor DNF detection problem. Our results hold for the fundamental base classes Horn and 2CNF, and their combination. We complement our theoretical findings by an empirical study. Our experiments show that backdoor DNFs provide a significant improvement over their predecessors. © 2023, The Authors. All rights reserved.

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Parameterized study of steiner tree on unit disk graphs 17

Parameterized study of steiner tree on unit disk graphs

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17th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2020

作者： Bhore, Sujoy Carmi, Paz Kolay, Sudeshna Zehavi, Meirav Algorithms and Complexity Group TU Wien Austria Ben-Gurion University of the Negev Beersheba Israel Indian Institute of Technology Kharagpur India

ISBN: (纸本)9783959771504

We study the Steiner Tree problem on unit disk graphs. Given a n vertex unit disk graph G, a subset R ⊆ V(G) of t vertices and a positive integer k, the objective is to decide if there exists a tree T in G that spans over all vertices of R and uses at most k vertices from V \R. The vertices of R are referred to as terminals and the vertices of V(G) \R as Steiner vertices. First, we show that the problem is NP-hard. Next, we prove that the Steiner Tree problem on unit disk graphs can be solved in nO(√t+k) time. We also show that the Steiner Tree problem on unit disk graphs parameterized by k has an FPT algorithm with running time 2O(k)nO(1). In fact, the algorithms are designed for a more general class of graphs, called clique-grid graphs [16]. We mention that the algorithmic results can be made to work for Steiner Tree on disk graphs with bounded aspect ratio. Finally, we prove that Steiner Tree on disk graphs parameterized by k is W[1]-hard. © Sujoy Bhore, Paz Carmi, Sudeshna Kolay, and Meirav Zehavi;licensed under Creative Commons License CC-BY

关键词： Aspect ratio

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