Download or read book Approximation Algorithms for Network Design and Graph Partitioning Problems written by Konstantin Andreev and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation Algorithms for Network Design and Partitioning Problems written by and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop new approximation algorithms for three graph-theoretic optimization problems. Two of these problems arise in communication networks and the third comes up in the context of classification and labeling. Below we describe these problems and present an overview of our main results. Information Network Design: We develop a model for information networks with a cost structure that captures savings obtained by redundant-data elimination. This model presents an expressive and algorithmically interesting framework as it allows us to represent information flow and still maintain the tractable nature of classical network-design. We consider two problems within this framework and develop algorithms that achieve logarithmic and constant-factor approximation for them. Multi-Route Cuts: A fundamental problem in combinatorial optimization is to find a low-cost cut which disconnects the underlying graph. A natural generalization of finding small cuts is the multi-route cut problem where the goal is to determine a low-cost set of edges or nodes whose removal reduces the connectivity of the graph to below a certain threshold. This problem arises in the context of reliability of service in networks. We provide the first non-trivial approximations for variants of the problem. When the connectivity thresholds are either two or infinity, we obtain polylogarithmic approximations to cost. For arbitrary thresholds, we develop bicriteria approximation algorithms; in particular, we obtain approximations to cost while ensuring that the connectivity drops below a constant times the threshold. Packing Multiway Cuts: Problems involving classification and labeling of interconnected objects arise in many contexts such as machine learning and computational biology. An important class of labeling problems reduces to packing cuts in a graph where the goal is to determine nearly-disjoint cuts that satisfy containment constraints. We develop constant-factor approximation algorithms for the multiway cut packing problem; where, given a collection of subsets of vertices, the objective is to produce separating cuts (one for each subset) that are as edge disjoint as possible.

Download or read book Graph Theory Approximation Methods written by N.B. Singh and published by N.B. Singh. This book was released on with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the fascinating realm of graph theory through the lens of approximation methods in this comprehensive guide, Graph Theory: Approximation Methods . From fundamental concepts to advanced algorithms, this book delves into strategies for solving complex optimization problems in networks, offering insights and techniques essential for both students and researchers in the field. Discover practical applications, theoretical foundations, and cutting-edge developments that shape the future of graph theory and its computational applications.

Download or read book Approximation Algorithms for New Graph Partitioning and Facility Location Problems written by Zoya Svitkina and published by . This book was released on 2007 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In applications as diverse as data placement in peer-to-peer systems, control of epidemic outbreaks, and routing in sensor networks, the fundamental questions can be abstracted as problems in combinatorial optimization. However, many of these problems are NP-hard, which makes it unlikely that exact polynomial-time algorithms for them exist. Approximation algorithms are designed to circumvent this difficulty, by finding provably near-optimal solutions in polynomial time. This thesis introduces a number of new combinatorial optimization problems that arise from various applications and proposes approximation algorithms for them. These problems fall into two general areas: graph partitioning and facility location. The first problem that we introduce is the unbalanced graph cut problem. Here the goal is to find a graph cut, minimizing the size of one of the sides, while also respecting an upper bound on the number of edges cut. We develop two bicriteria approximation algorithms for this problem using the technique of Lagrangian relaxation, and a different algorithm for its maximization version. The other graph partitioning problem that we introduce and study is the min-max multiway cut problem. It aims to partition a graph into multiple components, minimizing the maximum number of edges coming out of any component. We present an approximation algorithm for this problem which uses unbalanced cuts as well as the greedy technique. In the second part of the thesis, we study two generalizations of the facility location problem, which aims to open facilities, assigning clients to them, in order to minimize the facility opening costs and the connection costs. In the facility location with hierarchical facility costs problem, the facility costs are more general, and depend on the set of assigned clients. Our algorithm, based on the local search technique, uses two new local improvement operations, achieving a constant-factor approximation guarantee. The second generalization is the load-balanced facility location problem, which specifies a lower bound for the number of clients assigned to an open facility. We give the first true constant-factor approximation algorithm, which uses a reduction to the capacitated facility location problem. The thesis is concluded with related open problems and directions for future research. (Abstract).

Download or read book Fast Approximation Algorithms for Graph Partitioning Using Spectral and Semidefinite Programming Techniques written by Lorenzo Orecchia and published by . This book was released on 2011 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph partitioning problems are a central topic of research in the study of approximation algorithms. They are of interest to theoretical computer scientists for their far-reaching connections to spectral graph theory, metric embeddings and inapproximability theory. And they are also important for many practitioners, as algorithms for graph partitioning are often fundamental primitives in the solution of other problems, such as image segmentation, clustering and social-network analysis. While many theoretical approximation algorithms exist for graph partitioning, they often rely on multicommodity-flow computations that run quadratic time in the worst case and are too time-consuming for the massive graphs that are prevalent in today's applications. In this thesis, we study the design of approximation algorithms that yield strong approximation ratios, while running in subquadratic time and relying on computational procedures that are often fast in practice. Our algorithms employ spectral and s-t flow operations to explore the cuts of a graph in a very efficient way. A crucial ingredient in their design is the usage of random walks that capture the sparse cuts of a graph better than single eigenvectors. The analysis of our methods is particularly simple, as it relies on a semidefinite programming formulation of the graph partitioning problem of choice. Indeed, we can develop our algorithms as primal-dual methods for solving a semidefinite program and show that certain random walks arise naturally from this approach.

Download or read book Approximation Algorithms for Problems in Sequencing Scheduling and Communication Network Design written by David Bernard Shmoys and published by . This book was released on 1984 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation and Online Algorithms written by Roberto Solis-Oba and published by Springer. This book was released on 2018-04-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed workshop post-proceedings of the 15th International Workshop on Approximation and Online Algorithms, WAOA 2017, held in Vienna, Austria, in September 2017 as part of ALGO 2017. The 23 revised full papers presented in this book were carefully reviewed and selected from 50 submissions. Topics of interest for WAOA 2017 were: graph algorithms; inapproximability results; network design; packing and covering; paradigms for the design and analysis of approximation and online algorithms; parameterized complexity; scheduling problems; algorithmic game theory; coloring and partitioning; competitive analysis; computational advertising; computational finance; cuts and connectivity; geometric problems; mechanism design; resource augmentation; and real-world applications.

Download or read book Approximation Algorithms for NP hard Problems written by Dorit S. Hochbaum and published by Course Technology. This book was released on 1997 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms. APPROXIMATION ALGORITHMS FOR NP-HARD PROBLEMS is intended for computer scientists and operations researchers interested in specific algorithm implementations, as well as design tools for algorithms. Among the techniques discussed: the use of linear programming, primal-dual techniques in worst-case analysis, semidefinite programming, computational geometry techniques, randomized algorithms, average-case analysis, probabilistically checkable proofs and inapproximability, and the Markov Chain Monte Carlo method. The text includes a variety of pedagogical features: definitions, exercises, open problems, glossary of problems, index, and notes on how best to use the book.

Download or read book Approximation and Online Algorithms written by Klaus Jansen and published by Springer. This book was released on 2017-01-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-workshop proceedings of the 14th International Workshop on Approximation and Online Algorithms, WAOA 2016, held in Aarhus, Denmark, in August 2016 as part of ALGO 2016. The 16 revised full papers presented together with 2 invited lectures were carefully reviewed and selected from 33 submissions. Topics of interest for WAOA 2016 were: coloring and partitioning, competitive analysis, network design, packing and covering, paradigms for design and analysis of approximation and online algorithms, randomization techniques, real world applications, and scheduling problems.

Download or read book Approximation Algorithms for Network Design and Orienteering written by Nitish J. Korula and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents approximation algorithms for some NP-Hard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widely-believed complexity-theoretic assumption that P is not equal to NP, there are no efficient (i.e., polynomial-time) algorithms that solve these problems exactly. Hence, if one desires efficient algorithms for such problems, it is necessary to consider approximate solutions: An approximation algorithm for an NP-Hard problem is a polynomial time algorithm which, for any instance of the problem, finds a solution whose value is guaranteed to be within a multiplicative factor of the value of an optimal solution to that instance. We attempt to design algorithms for which this factor, referred to as the approximation ratio of the algorithm, is as small as possible. The field of Network Design comprises a large class of problems that deal with constructing networks of low cost and/or high capacity, routing data through existing networks, and many related issues. In this thesis, we focus chiefly on designing fault-tolerant networks. Two vertices u,v in a network are said to be k-edge-connected if deleting any set of k 8́2 1 edges leaves u and v connected; similarly, they are k-vertex connected if deleting any set of k 8́2 1 other vertices or edges leaves u and v connected. We focus on building networks that are highly connected, meaning that even if a small number of edges and nodes fail, the remaining nodes will still be able to communicate. A brief description of some of our results is given below. We study the problem of building 2-vertex-connected networks that are large and have low cost. Given an n-node graph with costs on its edges and any integer k, we give an O(log n log k) approximation for the problem of finding a minimum-cost 2-vertex-connected subgraph containing at least k nodes. We also give an algorithm of similar approximation ratio for maximizing the number of nodes in a 2-vertex-connected subgraph subject to a budget constraint on the total cost of its edges. Our algorithms are based on a pruning process that, given a 2-vertex-connected graph, finds a 2-vertex-connected subgraph of any desired size and of density comparable to the input graph, where the density of a graph is the ratio of its cost to the number of vertices it contains. This pruning algorithm is simple and efficient, and is likely to find additional applications. Recent breakthroughs on vertex-connectivity have made use of algorithms for element-connectivity problems. We develop an algorithm that, given a graph with some vertices marked as terminals, significantly simplifies the graph while preserving the pairwise element-connectivity of all terminals; in fact, the resulting graph is bipartite. We believe that our simplification/reduction algorithm will be a useful tool in many settings. We illustrate its applicability by giving algorithms to find many trees that each span a given terminal set, while being disjoint on edges and non-terminal vertices; such problems have applications in VLSI design and other areas. We also use this reduction algorithm to analyze simple algorithms for single-sink network design problems with high vertex-connectivity requirements; we give an O(k log n)-approximation for the problem of k-connecting a given set of terminals to a common sink. We study similar problems in which different types of links, of varying capacities and costs, can be used to connect nodes; assuming there are economies of scale, we give algorithms to construct low-cost networks with sufficient capacity or bandwidth to simultaneously support flow from each terminal to the common sink along many vertex-disjoint paths. We further investigate capacitated network design, where edges may have arbitrary costs and capacities. Given a connectivity requirement R_uv for each pair of vertices u,v, the goal is to find a low-cost network which, for each uv, can support a flow of R_uv units of traffic between u and v. We study several special cases of this problem, giving both algorithmic and hardness results. In addition to Network Design, we consider certain Traveling Salesperson-like problems, where the goal is to find short walks that visit many distinct vertices. We give a (2 + epsilon)-approximation for Orienteering in undirected graphs, achieving the best known approximation ratio, and the first approximation algorithm for Orienteering in directed graphs. We also give improved algorithms for Orienteering with time windows, in which vertices must be visited between specified release times and deadlines, and other related problems. These problems are motivated by applications in the fields of vehicle routing, delivery and transportation of goods, and robot path planning.

Download or read book Approximation and Online Algorithms written by Laura Sanità and published by Springer. This book was released on 2016-01-12 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-workshop proceedings of the 13th International Workshop on Approximation and Online Algorithms, WAOA 2015, held in Patras, Greece, in September 2015 as part of ALGO 2015. The 17 revised full papers presented were carefully reviewed and selected from 40 submissions. Topics of interest for WAOA 2015 were: algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, geometric problems, graph algorithms, inapproximability, mechanism design, natural algorithms, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, parameterized complexity, scheduling problems,and real-world applications.

Download or read book Approximation Algorithms for Network Design Problems written by Adam W. Meyerson and published by . This book was released on 2002 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximation Algorithms for Combinatorial Optimization written by Klaus Jansen and published by Springer. This book was released on 2003-07-31 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2000, held in Saarbrcken, Germany in September 2000. The 22 revised full papers presented together with four invited contributions were carefully reviewed and selected from 68 submissions. The topics dealt with include design and analysis of approximation algorithms, inapproximibility results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and various applications.

Download or read book Approximation and Online Algorithms written by Christos Kaklamanis and published by Springer Nature. This book was released on 2021-07-05 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed workshop post-proceedings of the 18th International Workshop on Approximation and Online Algorithms, WAOA 2019, held virtually in September 2020 as part of ALGO 2020. The 15 revised full papers presented this book were carefully reviewed and selected from 40 submissions. Topics of interest for WAOA 2018 were graph algorithms, inapproximability results, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, parameterized complexity, scheduling problems, algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational -finance, cuts and connectivity, geometric problems, mechanism design, resource augmentation, real-world applications. Chapter "Explorable Uncertainty in Scheduling with Non-Uniform Testing Times" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Download or read book Approximation Algorithms for Combinatorial Optimization written by Klaus Jansen and published by Springer. This book was released on 2003-06-30 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002, held in Rome, Italy in September 2002. The 20 revised full papers presented were carefully reviewed and selected from 54 submissions. Among the topics addressed are design and analysis of approximation algorithms, inapproximability results, online problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and applications to game theory and other fields.

Download or read book Approximation and Online Algorithms written by Giuseppe Persiano and published by Springer. This book was released on 2005-02-09 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd Workshop on Approximation and Online Algorithms (WAOA 2004) focused on the design and analysis of algorithms for online and computationally hard problems. Both kinds of problems have a large number of applications arising from a variety of ?elds. WAOA 2004 took place in Bergen, Norway, from September 14 to September 16, 2004. The workshop was part of the ALGO 2004 event which also hosted ESA, WABI, IWPEC, and ATMOS. TopicsofinterestsforWAOA2004were:applicationstogametheory,appr- imation classes, coloring and partitioning, competitive analysis, computational ?nance, cuts and connectivity, geometric problems, inapproximability results, mechanism design, network design, routing, packing and covering, paradigms, randomization techniques, and scheduling problems. In response to our call we received 47 submissions. Each submission was reviewed by at least 3 referees, who judged the paper on originality, quality, and consistency with the topics of the conference. Based on the reviews, the Program Committee selected 21 papers. This volume contains the 21 selected papers and the two invited talks given by Yossi Azar and Klaus Jansen. We thank all the authors who submitted papers to the workshop and we also kindly thank the local organizers of ALGO 2004.

Download or read book Approximation Randomization and Combinatorial Optimization Algorithms and Techniques written by Moses Charikar and published by Springer Science & Business Media. This book was released on 2007-08-07 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and the 11th International Workshop on Randomization and Computation, RANDOM 2007, held in Princeton, NJ, USA, in August 2007. The 44 revised full papers presented were carefully reviewed and selected from 99 submissions. Topics of interest covered by the papers are design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, geometric problems, game theory and applications, network design and routing, packing and covering, scheduling, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and embeddings, error-correcting codes, average-case analysis, property testing, computational learning theory, and other applications of approximation and randomness.