Degree Based Spanning Tree Optimization

We consider several spanning tree optimization problems all having a measure function which depends only on the degrees of the resulting spanning tree. In addition, all investigated problems are generalizations of the Hamiltonian Path problem and so are NP-hard. As we cannot expect exact polynomial-time solutions, we use the approach of approximation algorithms. We look for a suboptimal solution in polynomial time and prove that it is not farther from the optimal one than a given approximation factor. Beside algorithmic aspects, we also consider the number of spanning tree leaves from a bit more theoretical point of view. We investigate how different graph vulnerability parameters, namely scattering number and cut-asymmetry, are related to the number of spanning tree leaves and that of independent spanning tree leaves. Some of our results are applied for the analysis of the Maximum Internal Spanning Tree problem, while some others give connection to the theory of hamiltonicity. In particular, we give a sufficient condition for the existence of a Hamiltonian path by means of cut-asymmetry.

The design of approximation algorithms for spanning tree problems has become an exciting and important area of theoretical computer science and also plays a significant role in emerging fields such as biological sequence alignments and evolutionary tree construction. While work in this field remains quite active, the time has come to collect under

This paper presents two algorithms to construct minimum weight spanning trees with approximately minimum degree. The first method gives a spanning tree whose maximum degree is $O(\delta[superscript]{*} + logn)$ where $\delta[superscript]{*}$ is the minimum possible, and $n$ is the number of vertices. The second method gives a spanning tree of degree no more than $k \cdot (\delta[superscript]{*} + 1)$, where $k$ is the number of distinct weights in the graph. Finding the exact minimum is NP-hard.

Im Mittelpunkt dieses Buches steht eines der wichtigsten Optimierungsverfahren der industriellen Ingenieurtechnik: Mit Hilfe genetischer Algorithmen lassen sich Qualität, Design und Zuverlässigkeit von Produkten entscheidend verbessern. Das Verfahren beruht auf der Wahrscheinlichkeitstheorie und lehnt sich an die Prinzipien der biologischen Vererbung an: Die Eigenschaften des Produkts werden, unter Beachtung der äußeren Randbedingungen, schrittweise optimiert. Ein hochaktueller Band international anerkannter Autoren. (03/00)

This book constitutes the proceedings of the 10th International Workshop on Frontiers in Algorithmics, FAW 2016, held in Qingdao, China, in June/July 2016. The 25 full papers presented in this volume were carefully reviewed and selected from 54 submissions. They deal with algorithm, complexity, problem, reduction, NP-complete, graph, approximation, linear programming, local search, integer programming, semidefinite programming, parameterized algorithm, fixed parameter, tractability, randomness, computational geometry.

With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.

This book constitutes the refereed proceedings of the 14th Algorithms and Data Structures Symposium, WADS 2015, held in Victoria, BC, Canada, August 2015. The 54 revised full papers presented in this volume were carefully reviewed and selected from 148 submissions. The Algorithms and Data Structures Symposium - WADS (formerly Workshop on Algorithms And Data Structures), which alternates with the Scandinavian Workshop on Algorithm Theory, is intended as a forum for researchers in the area of design and analysis of algorithms and data structures. WADS includes papers presenting original research on algorithms and data structures in all areas, including bioinformatics, combinatorics, computational geometry, databases, graphics, and parallel and distributed computing.

This book constitutes the refereed proceedings of the 25th International Symposium on Algorithms and Computation, ISAAC 2014, held in Jeonju, Korea, in December 2014. The 60 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 171 submissions for inclusion in the book. The focus of the volume in on the following topics: computational geometry, combinatorial optimization, graph algorithms: enumeration, matching and assignment, data structures and algorithms, fixed-parameter tractable algorithms, scheduling algorithms, computational complexity, computational complexity, approximation algorithms, graph theory and algorithms, online and approximation algorithms, and network and scheduling algorithms.

This book constitutes the refereed proceedings of the 18th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2016, held in Liège, Belgium, in June 2016. The 33 full papers presented were carefully reviewed and selected from 125 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.