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.

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.

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)