Download or read book Degree constrained editing of small degree graphs written by Nichterlein, Andre and published by Universitätsverlag der TU Berlin. This book was released on 2015-07-03 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis deals with degree-constrained graph modification problems. In particular, we investigate the computational complexity of DAG Realization and Degree Anonymity. The DAG Realization problem is, given a multiset of positive integer pairs, to decide whether there is a realizing directed acyclic graph (DAG), that is, pairs are one-to-one assigned to vertices such that the indegree and the outdegree of every vertex coincides with the two integers of the assigned pair. The Degree Anonymity problem is, given an undirected graph G and two positive integers k and s, to decide whether at most s graph modification operations can be performed in G in order to obtain a k-anonymous graph, that is, a graph where for each vertex there are k − 1 other vertices with the same degree. We classify both problems as NP-complete, that is, there are presumably no polynomial-time algorithms that can solve every instance of these problems. Confronted with this worst-case intractability, we perform a parameterized complexity study in order to detect efficiently solvable special cases that are still practically relevant. The goal herein is to develop fixed-parameter algorithms where the seemingly unavoidable exponential dependency in the running time is confined to a parameter of the input. If the parameter is small, then the corresponding fixed-parameter algorithm is fast. The parameter thus measures some structure in the input whose exploitation makes the particular input tractable. Considering Degree Anonymity, two natural parameters provided with the input are anonymity level k and solution size s. However, we will show that Degree Anonymity is W[1]-hard with respect to the parameter s even if k = 2. This means that the existence of fixed-parameter algorithms for s and k is very unlikely. Thus, other parameters have to be considered. We will show that the parameter maximum vertex degree is very promising for both DAG Realization and Degree Anonymity. Herein, for Degree Anonymity, we consider the maximum degree of the input graph. Considering DAG Realization, we take the maximum degree in a realizing DAG. Due to the problem definition, we can easily determine the maximum degree by taking the maximum over all integers in the given multiset. We provide fixed-parameter algorithms with respect to the maximum degree for DAG Realization and for Anonym E-Ins. The later is the variant of Degree Anonymity when only edge insertions are allowed as modification operations. If we allow edge deletions or vertex deletions as graph modification operations, then we can show that the corresponding variants of Degree Anonymity—called Anonym V-Del and Anonym E-Del—are NP-complete even if the maximum vertex degree is seven. Moreover, we provide strong intractability results for Anonym E-Del and Anonym V-Del proving that they remain NP-complete in several restricted graph classes. Studying the approximability of natural optimization problems associated with Anonym E-Del or Anonym V-Del, we obtain negative results showing that none of the considered problems can be approximated in polynomial time better than within a factor of n^(1/2) where n denotes the number of vertices in the input. Furthermore, for the optimization variants where the solution size s is given and the task is to maximize the anonymity level k, this inapproximability even holds if we allow a running time that is exponential in s. Observe that DAG Realization also can be seen as degree-constrained graph modification problem where only arc insertions are allowed: Starting with an arcless graph, the task is to insert arcs to obtain a realizing DAG for the given multiset. The above classification with respect to the parameter maximum degree shows that in graphs with small maximum degree the modification operation edge respectively arc insertion is easier than vertex or edge deletion. There is a plausible explanation for this behavior: When the maximum degree is small, then there is a high freedom in inserting edges or arcs as for a given vertex almost all other vertices can be chosen as new neighbor. Observe that for DAG Realization the additional requirement that the directed graph shall be acyclic restricts this freedom. In Anonym E-Ins, we do not have restrictions on this freedom. In fact, exploiting this freedom in our implementation for Anonym E-Ins, we show that our theoretical ideas can be turned into successful heuristics and lower bounds. Experiments on several large-scale real-world datasets show that our implementation significantly improves on a recent heuristic and provides (provably) optimal solutions on about 21 % (56 of 260) of the real-world data.

Download or read book Classic graph problems made temporal a parameterized complexity analysis written by Molter, Hendrik and published by Universitätsverlag der TU Berlin. This book was released on 2020 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis investigates the parameterized computational complexity of six classic graph problems lifted to a temporal setting. More specifically, we consider problems defined on temporal graphs, that is, a graph where the edge set may change over a discrete time interval, while the vertex set remains unchanged. Temporal graphs are well-suited to model dynamic data and hence they are naturally motivated in contexts where dynamic changes or time-dependent interactions play an important role, such as, for example, communication networks, social networks, or physical proximity networks. The most important selection criteria for our problems was that they are well-motivated in the context of dynamic data analysis. Since temporal graphs are mathematically more complex than static graphs, it is maybe not surprising that all problems we consider in this thesis are NP-hard. We focus on the development of exact algorithms, where our goal is to obtain fixed-parameter tractability results, and refined computational hardness reductions that either show NP-hardness for very restricted input instances or parameterized hardness with respect to “large” parameters. In the context of temporal graphs, we mostly consider structural parameters of the underlying graph, that is, the graph obtained by ignoring all time information. However, we also consider parameters of other types, such as ones trying to measure how fast the temporal graph changes over time. In the following we briefly discuss the problem setting and the main results. Restless Temporal Paths. A path in a temporal graph has to respect causality, or time, which means that the edges used by a temporal path have to appear at non-decreasing times. We investigate temporal paths that additionally have a maximum waiting time in every vertex of the temporal graph. Our main contributions are establishing NP-hardness for the problem of finding restless temporal paths even in very restricted cases, and showing W[1]-hardness with respect to the feedback vertex number of the underlying graph. Temporal Separators. A temporal separator is a vertex set that, when removed from the temporal graph, destroys all temporal paths between two dedicated vertices. Our contribution here is twofold: Firstly, we investigate the computational complexity of finding temporal separators in temporal unit interval graphs, a generalization of unit interval graphs to the temporal setting. We show that the problem is NP-hard on temporal unit interval graphs but we identify an additional restriction which makes the problem solvable in polynomial time. We use the latter result to develop a fixed-parameter algorithm with a “distance-to-triviality” parameterization. Secondly, we show that finding temporal separators that destroy all restless temporal paths is Σ-P-2-hard. Temporal Matchings. We introduce a model for matchings in temporal graphs, where, if two vertices are matched at some point in time, then they have to “recharge” afterwards, meaning that they cannot be matched again for a certain number of time steps. In our main result we employ temporal line graphs to show that finding matchings is NP-hard even on instances where the underlying graph is a path. Temporal Coloring. We lift the classic graph coloring problem to the temporal setting. In our model, every edge has to be colored properly (that is,the endpoints are colored differently) at least once in every time interval of a certain length. We show that this problem is NP-hard in very restricted cases, even if we only have two colors. We present simple exponential-time algorithms to solve this problem. As a main contribution, we show that these algorithms presumably cannot be improved significantly. Temporal Cliques and s-Plexes. We propose a model for temporal s-plexes that is a canonical generalization of an existing model for temporal cliques. Our main contribution is a fixed-parameter algorithm that enumerates all maximal temporal s-plexes in a given temporal graph, where we use a temporal adaptation of degeneracy as a parameter. Temporal Cluster Editing. We present a model for cluster editing in temporal graphs, where we want to edit all “layers” of a temporal graph into cluster graphs that are sufficiently similar. Our main contribution is a fixed-parameter algorithm with respect to the parameter “number of edge modifications” plus the “measure of similarity” of the resulting clusterings. We further show that there is an efficient preprocessing procedure that can provably reduce the size of the input instance to be independent of the number of vertices of the original input instance.

Download or read book Parameterized Algorithms written by Marek Cygan and published by Springer. This book was released on 2015-07-20 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.

Download or read book Computer Science Theory and Applications written by Alexander S. Kulikov and published by Springer. This book was released on 2016-06-02 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 11th International Computer Science Symposium in Russia, CSR 2016, held in St. Petersburg, Russia, in June 2016. The 28 full papers presented in this volume were carefully reviewed and selected from 71 submissions. In addition the book contains 4 invited lectures. The scope of the proposed topics is quite broad and covers a wide range of areas such as: include, but are not limited to: algorithms and data structures; combinatorial optimization; constraint solving; computational complexity; cryptography; combinatorics in computer science; formal languages and automata; computational models and concepts; algorithms for concurrent and distributed systems, networks; proof theory and applications of logic to computer science; model checking; automated reasoning; and deductive methods.

Download or read book Mathematical Foundations of Computer Science 2014 written by Ersébet Csuhaj-Varjú and published by Springer. This book was released on 2014-08-12 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set LNCS 8634 and LNCS 8635 constitutes the refereed conference proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science, MFCS 2014, held in Budapest, Hungary, in August 2014. The 95 revised full papers presented together with 6 invited talks were carefully selected from 270 submissions. The focus of the conference was on following topics: Logic, Semantics, Automata, Theory of Programming, Algorithms, Complexity, Parallel and Distributed Computing, Quantum Computing, Automata, Grammars and Formal Languages, Combinatorics on Words, Trees and Games.

Download or read book Parameterized and Exact Computation written by Marek Cygan and published by Springer. This book was released on 2014-12-02 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Symposium on Parameterized and Exact Computation, IPEC 2014, in Wroclaw, Poland, in September 2014. The 27 revised full papers presented together with one invited paper were carefully reviewed and selected from 42 submissions. The topics addressed cover research in all aspects of parameterized/exact algorithms and complexity including but are not limited to new techniques for the design and analysis of parameterized and exact algorithms, fixed-parameter tractability results; parameterized complexity theory, relationship between parameterized complexity and traditional complexity classifications; applications of parameterized and exact exponential-time computation; and implementation issues of parameterized and exact exponential-time algorithms.

Download or read book Fundamentals of Parameterized Complexity written by Rodney G. Downey and published by Springer Science & Business Media. This book was released on 2013-12-03 with total page 765 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years.

Download or read book Parameterized and Exact Computation written by Gregory Gutin and published by Springer. This book was released on 2013-11-19 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Symposium on Parameterized and Exact Computation, IPEC 2013, in Sophia Antipolis, France, in September 2013. The 29 revised full papers presented were carefully reviewed and selected from 58 submissions. The topics addressed cover research in all aspects of parameterized/exact algorithms and complexity including but are not limited to new techniques for the design and analysis of parameterized and exact algorithms, fixed-parameter tractability results, parameterized complexity theory, relationship between parameterized complexity and traditional complexity classifications, applications of parameterized and exact computation, and implementation issues of parameterized and exact algorithms.

Download or read book Algorithm Theory SWAT 2014 written by Inge Li Gørtz and published by Springer. This book was released on 2014-06-25 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 14th International Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2014, held in Copenhagen, Denmark, in July 2014. The 33 papers were carefully reviewed and selected from a total of 134 submissions. The papers present original research and cover a wide range of topics in the field of design and analysis of algorithms and data structures including but not limited to approximation algorithms, parameterized algorithms, computational biology, computational geometry and topology, distributed algorithms, external-memory algorithms, exponential algorithms, graph algorithms, online algorithms, optimization algorithms, randomized algorithms, streaming algorithms, string algorithms, sublinear algorithms and algorithmic game theory.

Download or read book LATIN 2016 Theoretical Informatics written by Evangelos Kranakis and published by Springer. This book was released on 2016-03-21 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th Latin American Symposium on Theoretical Informatics, LATIN 2016, held in Ensenada, Mexico, in April 2016. The 52 papers presented together with 5 abstracts were carefully reviewed and selected from 131 submissions. The papers address a variety of topics in theoretical computer science with a certain focus on algorithms (approximation, online, randomized, algorithmic game theory, etc.), analytic combinatorics and analysis of algorithms, automata theory and formal languages, coding theory and data compression, combinatorial algorithms, combinatorial optimization, combinatorics and graph theory, complexity theory, computational algebra, computational biology, computational geometry, computational number theory, cryptology, databases and information retrieval, data structures, formal methods and security, Internet and the web, parallel and distributed computing, pattern matching, programming language theory, and random structures.

Download or read book Theory and Applications of Models of Computation written by Xujin Chen and published by Springer Nature. This book was released on with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parameterized Algorithmics for Network Analysis Clustering Querying written by Christian Komusiewicz and published by Univerlagtuberlin. This book was released on 2011 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Combinatorial Optimization and Applications written by Donghyun Kim and published by Springer. This book was released on 2018-12-06 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference proceeding LNCS 11346 constitutes the refereed proceedings of the 12th International Conference on Combinatorial Optimization and Applications, COCOA 2018, held in Atlanta, GA, USA, in December 2018. The 50 full papers presented were carefully reviewed and selected from 106 submissions. The papers cover most aspects of t graph algorithms, routing and network design problems, scheduling algorithms, network optimization, combinatorial algorithms, approximation algorithms, paths and connectivity problems and much more.

Download or read book Computing and Combinatorics written by Bin Fu and published by Springer. This book was released on 2011-07-18 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th Annual International Conference on Computing and Combinatorics, held in Dallas, TX, USA, in August 2011. The 54 revised full papers presented were carefully reviewed and selected from 136 submissions. Topics covered are algorithms and data structures; algorithmic game theory and online algorithms; automata, languages, logic, and computability; combinatorics related to algorithms and complexity; complexity theory; computational learning theory and knowledge discovery; cryptography, reliability and security, and database theory; computational biology and bioinformatics; computational algebra, geometry, and number theory; graph drawing and information visualization; graph theory, communication networks, and optimization; parallel and distributed computing.

Download or read book Computer Science Theory and Applications written by Lev D. Beklemishev and published by Springer. This book was released on 2015-06-22 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 10th International Computer Science Symposium in Russia, CSR 2015, held in Listvyanka, Russia, in July 2015. The 25 full papers presented in this volume were carefully reviewed and selected from 61 submissions. In addition the book contains 4 invited lectures. The scope of the proposed topics is quite broad and covers a wide range of areas in theoretical computer science and its applications.

Download or read book Combinatorial Optimization and Applications written by Xiaofeng Gao and published by Springer. This book was released on 2017-12-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 10627 and 10628 constitutes the refereed proceedings of the 11th International Conference on Combinatorial Optimization and Applications, COCOA 2017, held in Shanghai, China, in December 2017. The 59 full papers and 19 short papers presented were carefully reviewed and selected from 145 submissions. The papers cover most aspects of theoretical computer science and combinatorics related to computing, including classic combinatorial optimization, geometric optimization, complexity and data structures, and graph theory. They are organized in topical sections on network, approximation algorithm and graph theory, combinatorial optimization, game theory, and applications.

Download or read book Combinatorial Optimization and Applications written by Boting Yang and published by Springer. This book was released on 2008-08-20 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Combinatorial Optimization and Applications, COCOA 2008, held in St. John's, Canada, in August 2008. The 44 revised full papers were carefully reviewed and selected from 84 submissions. The papers feature original research in the areas of combinatorial optimization -- both theoretical issues and and applications motivated by real-world problems thus showing convincingly the usefulness and efficiency of the algorithms discussed in a practical setting.