rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Shortest Connectivity
    sub title: An Introduction with Applications in Phylogeny
  name:
    name part: Cieslik, Dietmar.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2005
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: IX, 268 p. online resource.
  abstract: The problem of "Shortest Connectivity" has a long and convoluted history: given a finite set of points in a metric space, search for a network that connects these points with the shortest possible length. This shortest network must be a tree and may contain vertices different from the points which are to be connected. Over the years more and more real-life problems are given, which use this problem or one of its relatives as an application, as a subproblem or a model. This volume is an introduction to the theory of "Shortest Connectivity", as the core of the so-called "Geometric Network Design Problems", where the general problem can be stated as follows: given a configuration of vertices and/or edges, find a network which contains these objects, satisfies some predetermined requirements, and which minimizes a given objective function that depends on several distance measures. A new application of shortest connectivity is also discussed, namely to create trees which reflect the evolutionary history of "living entities". The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology. .
  table of contents: Two Classical Optimization Problems -- Gauss’ Question -- What Does Solution Mean? -- Network Design Problems -- A New Challenge: The Phylogeny -- An Analysis of Steiner’s Problem in Phylogenetic Spaces -- Tree Building Algorithms.
  note: by Dietmar Cieslik.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical models
  subject:
    topic: Mathematical optimization
  subject:
    topic: Operations research
  subject:
    topic: Management science
  subject:
    topic: Biomathematics
  subject:
    topic: Mathematics
  subject:
    topic: Operations Research, Management Science
  subject:
    topic: Optimization
  subject:
    topic: Mathematical Modeling and Industrial Mathematics
  subject:
    topic: Mathematical and Computational Biology
  classification: QA402-402.37
  classification: T57.6-57.97
  classification: 519.6
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Combinatorial Optimization, 17
  identifier: 9780387235394
  identifier: http://dx.doi.org/10.1007/b101778
  record info:
    record creation date: 100301
    record change date: 20151204155959.0
    record identifier: 978-0-387-23539-4