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Lossy Kernelization of Same-Size Clustering 1

17th International Computer Science Symposium in Russia, CSR 2022

作者： Bandyapadhyay, Sayan Fomin, Fedor V. Golovach, Petr A. Purohit, Nidhi Siminov, Kirill Department of Informatics University of Bergen Bergen Norway Algorithms and Complexity Group TU Wien Vienna Austria

ISBN: (数字)9783031095740

ISBN: (纸本)9783031095733

In this work, we study the k-median clustering problem with an additional equal-size constraint on the clusters, from the perspective of parameterized preprocessing. Our main result is the first lossy (2-approximate) polynomial kernel for this problem, parameterized by the cost of clustering. We complement this result by establishing lower bounds for the problem that eliminate the existences of an (exact) kernel of polynomial size and a PTAS. © 2022, Springer Nature Switzerland AG.

关键词： Parameterization

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A Tight Subexponential-Time Algorithm for Two-Page Book Embedding 51

A Tight Subexponential-Time Algorithm for Two-Page Book Embe...

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51st International Colloquium on Automata, Languages, and Programming, ICALP 2024

作者： Ganian, Robert Müller, Haiko Ordyniak, Sebastian Paesani, Giacomo Rychlicki, Mateusz Algorithms and Complexity Group TU Wien Austria School of Computing University of Leeds United Kingdom

ISBN: (纸本)9783959773225

A book embedding of a graph is a drawing that maps vertices onto a line and edges to simple pairwise non-crossing curves drawn into "pages", which are half-planes bounded by that line. Two-page book embeddings, i.e., book embeddings into 2 pages, are of special importance as they are both NP-hard to compute and have specific applications. We obtain a 2O(√n) algorithm for computing a book embedding of an n-vertex graph on two pages – a result which is asymptotically tight under the Exponential Time Hypothesis. As a key tool in our approach, we obtain a single-exponential fixed-parameter algorithm for the same problem when parameterized by the treewidth of the input graph. We conclude by establishing the fixed-parameter tractability of computing minimum-page book embeddings when parameterized by the feedback edge number, settling an open question arising from previous work on the problem. © Robert Ganian, Haiko Müller, Sebastian Ordyniak, Giacomo Paesani, and Mateusz Rychlicki.

关键词： Parameter estimation

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Path-contractions, edge deletions and connectivity preservation 25

Path-contractions, edge deletions and connectivity preservat...

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25th European Symposium on algorithms, ESA 2017

作者： Gutin, Gregory Ramanujan, M.S. Reidl, Felix Wahlström, Magnus Algorithms and Complexity Group TU Wien Vienna Austria Royal Holloway University Egham United Kingdom

ISBN: (纸本)9783959770491

We study several problems related to graph modification problems under connectivity constraints from the perspective of parameterized complexity: (Weighted) Biconnectivity Deletion, where we are tasked with deleting k edges while preserving biconnectivity in an undirected graph, Vertexdeletion Preserving Strong Connectivity, where we want to maintain strong connectivity of a digraph while deleting exactly k vertices, and Path-contraction Preserving Strong Connectivity, in which the operation of path contraction on arcs is used instead. The parameterized tractability of this last problem was posed in [Bang-Jensen and Yeo, Discrete Applied Math 2008] as an open question and we answer it here in the negative: both variants of preserving strong connectivity are W[1]-hard. Preserving biconnectivity, on the other hand, turns out to be fixed parameter tractable (FPT) and we provide an FPT algorithm that solves Weighted Biconnectivity Deletion. Further, we show that the unweighted case even admits a randomized polynomial kernel. All our results provide further interesting data points for the systematic study of connectivitypreservation constraints in the parameterized setting.

关键词： Undirected graphs

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Parameterised Partially-Predrawn Crossing Number 38

Parameterised Partially-Predrawn Crossing Number

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38th International Symposium on Computational Geometry, SoCG 2022

作者： Hamm, Thekla Hlinený, Petr Algorithms and Complexity Group TU Wien Austria Faculty of Informatics Masaryk University Brno Czech Republic

ISBN: (纸本)9783959772273

Inspired by the increasingly popular research on extending partial graph drawings, we propose a new perspective on the traditional and arguably most important geometric graph parameter, the crossing number. Specifically, we define the partially predrawn crossing number to be the smallest number of crossings in any drawing of a graph, part of which is prescribed on the input (not counting the prescribed crossings). Our main result - an FPT-algorithm to compute the partially predrawn crossing number - combines advanced ideas from research on the classical crossing number and so called partial planarity in a very natural but intricate way. Not only do our techniques generalise the known FPT-algorithm by Grohe for computing the standard crossing number, they also allow us to substantially improve a number of recent parameterised results for various drawing extension problems. © Thekla Hamm and Petr Hlinn;licensed under Creative Commons License CC-BY 4.0

关键词： Parameterization

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Foundations of evolutionary multi-objective optimization 11

Foundations of evolutionary multi-objective optimization

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13th Annual Genetic and Evolutionary Computation Conference - Companion Publication, GECCO 2011 Companion

作者： Friedrich, Tobias Neumann, Frank Algorithms and Complexity Max Planck Institute for Informatics Germany School of Computer Science University of Adelaide Australia

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Distributed evaluation of functional BSP programs

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Parallel Processing Letters 2001年第4期11卷 423-437页

作者： Loulergue, F. Lab. of Algorithms Complexity/Logic University of Paris 12 61 ave. du General de Gaulle F-94010 Créteil Cedex France

The BSλp-calculus is a calculus of functional bulk synchronous parallel (BSP) programs. It is the basis for the design of a bulk synchronous parallel ML language. For data-parallel languages, there are two points of view: the programming model where a program is seen as a sequence of operations on parallel vectors, and the execution model where the program is a parallel composition of programs run on each processor of the parallel machine. BSP algorithms are defined by data-parallel algorithms with explicit (physical) processes in order to allow their parallel execution time to be estimated. We present here a distributed evaluation minimally synchronous for BSP execution (which corresponds to the execution model). This distributed evaluation is correct w.r.t. the call-by-value strategy of the BSλp-calculus (which corresponds to the programming model).

关键词： Parallel processing systems

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Discovering Archipelagos of Tractability for Constraint Satisfaction and Counting 16

Discovering Archipelagos of Tractability for Constraint Sati...

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Annual ACM-Society for Industrial and Applied Mathmatics Symposium on Discrete algorithms

作者： Robert Ganian M. S. Ramanujan Stefan Szeider Algorithms and Complexity Group

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. (IJCAI 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 constitutes an archipela

关键词： chip scale packaging communicating sequential processes phosphocellulose Language islands constraint satisfaction problems archipelagoes Constraint Polynomial time

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Deterministic Constrained Multilinear Detection 48

Deterministic Constrained Multilinear Detection

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48th International Symposium on Mathematical Foundations of Computer Science, MFCS 2023

作者： Brand, Cornelius Korchemna, Viktoriia Skotnica, Michael Algorithms and Complexity Group TU Wien Austria Department of Applied Mathematics Charles University Prague Czech Republic

ISBN: (纸本)9783959772921

We extend the algebraic techniques of Brand and Pratt (ICALP’21) for deterministic detection of k-multilinear monomials in a given polynomial with non-negative coefficients to the more general situation of detecting colored k-multilinear monomials that satisfy additional constraints on the multiplicities of the colors appearing in them. Our techniques can be viewed as a characteristic-zero generalization of the algebraic tools developed by Guillemot and Sikora (MFCS’10) and Björklund, Kaski and Kowalik (STACS’13) As applications, we recover the state-of-the-art deterministic algorithms for the Graph Motif problem due to Pinter, Schachnai and Zehavi (MFCS’14), and give new deterministic algorithms for generalizations of certain questions on colored directed spanning trees or bipartite planar matchings running in deterministic time O∗(4k), studied originally by Gutin, Reidl, Wahlström and Zehavi (J. Comp. Sys. Sci. 95,’18). Finally, we give improved randomized algorithms for intersecting three and four matroids of rank k in characteristic zero, improving the record bounds of Brand and Pratt (ICALP’21) from O∗(64k) and O∗(256k), respectively, to O∗(4k). © Cornelius Brand, Viktoriia Korchemna, and Michael Skotnica

关键词： Trees (mathematics)

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Twin-Width Meets Feedback Edges and Vertex Integrity 19

Twin-Width Meets Feedback Edges and Vertex Integrity

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19th International Symposium on Parameterized and Exact Computation, IPEC 2024

作者： Balabán, Jakub Ganian, Robert Rocton, Mathis Faculty of Informatics Masaryk University Brno Czech Republic Algorithms and Complexity Group TU Wien Vienna Austria

ISBN: (纸本)9783959773539

The approximate computation of twin-width has attracted significant attention already since the moment the parameter was introduced. A recently proposed approach (STACS 2024) towards obtaining a better understanding of this question is to consider the approximability of twin-width via fixed-parameter algorithms whose running time depends not on twin-width itself, but rather on parameters which impose stronger restrictions on the input graph. The first step that article made in this direction is to establish the fixed-parameter approximability of twin-width (with an additive error of 1) when the runtime parameter is the feedback edge number. Here, we make several new steps in this research direction and obtain: An asymptotically tight bound between twin-width and the feedback edge number;A significantly improved fixed-parameter approximation algorithm for twin-width under the same runtime parameter (i.e., the feedback edge number) which circumvents many of the technicalities of the original result and simultaneously avoids its formerly non-elementary runtime dependency;An entirely new fixed-parameter approximation algorithm for twin-width when the runtime parameter is the vertex integrity of the graph. © Jakub Balabán, Robert Ganian, and Mathis Rocton.

关键词： Approximation algorithms

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On evolution-communication P systems with energy having bounded and unbounded communication 18th

On evolution-communication P systems with energy having boun...

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18th International Conference on Membrane Computing, CMC 1018

作者： Juayong, Richelle Ann B. Hernandez, Nestine Hope S. Cabarle, Francis George C. Buño, Kelvin C. Adorna, Henry N. Algorithms and Complexity Lab Department of Computer Science University of the Philippines Diliman Diliman Quezon City1101 Philippines

ISBN: (纸本)9783319733586

We explore the computing power of Evolution-Communication P systems with energy (ECPe systems) considering dynamical communication measures, ComN, ComR and ComW. These measures consider the number of communication steps, communication rules and total energy used per communication step, respectively. In this paper, we address a previous conjecture that states that only semilinear sets can be generated with bounded ComX, X∈ { N, R, W}. Our result on bounded ComW seems to support such conjecture while the conjecture is not true for bounded ComN and ComR. We also show that the class of recursively enumerable sets can be computed using ECPe systems with two membranes. This improves a previous result that makes use of four membranes to show computational completeness. © 2018, Springer International Publishing AG.

关键词： Artificial intelligence

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