Steiner Tree

教育

免费 · 专为 iPad 设计

This app computes Steiner trees using an evolutionary algorithm. You can place, drag, and delete points of your tree. The optimal number and position of Steiner points is computed. A minimal spanning tree (MST) connects a given set of points in a plane so that the sum of all edges is minimal. Often this sum of all edges can be reduced, if additional points are added. These points are called Steiner points, and the corresponding minimal spanning tree Steiner tree. If more than 3 points are given, it is a hard optimization problem to compute the optimal number and position of Steiner points. This app uses a simple evolutionary algorithm for demonstration purposes. It uses a population of individuals. Each individual represents a MST containing some Steiner points. The population develops towards the optimal Steiner tree in an evolutionary loop: Initially, each individual sets random Steiner points, and constructs the corresponding Steiner tree. The minimal length of the Steiner tree in the population is stored. Each individual has now a fitness value, which is the higher, the closer its Steiner tree length is to the minimal length in the population. Fitter individuals have more descendants by reproduction, and less fit individuals die out. In order to explore better solutions, reproduction does not create descendants that are identical to the parent individual, i.e. do not have their Steiner points at the same position. Rather these positions are shifted randomly by mutation, using a Gaussian distribution. How far they are shifted on average is determined also by their fitness: Good individuals shift their Steiner points less than worse individuals. How fast a good solution is found, depends thus on the population size, and the mutation strength.

评分及评论

  • 此 App 尚未收到足够的评分或评论，无法显示整体评分。

Minor internal update for newer iOS versions

版本 4.3

开发者“Reinhard MAENNER”已表明该 App 的隐私规范可能包括下述数据处理方式。更多相关信息，请参阅 开发者隐私政策 。

  • 未收集数据

    开发者不会从此 App 中收集任何数据。

    隐私规范可能因你使用的功能或你的年龄等因素而异。 进一步了解

    辅助功能

    开发者尚未表明此 App 支持哪些辅助功能。 进一步了解

    信息

    • 销售商
      • Reinhard MAENNER
    • 大小
      • 677.9 KB
    • 类别
      • 教育
    • 兼容性
      设备需装有 iOS 12.0 或更高版本。
      • iPhone
        设备需装有 iOS 12.0 或更高版本。
      • iPad
        设备需装有 iPadOS 12.0 或更高版本。
      • iPod touch
        设备需装有 iOS 12.0 或更高版本。
      • Mac
        需要 macOS 11.0 或更高版本以及装有 Apple M1 或更高版本芯片的 Mac。
      • Apple Vision
        设备需装有 visionOS 1.0 或更高版本。
    • 语言
      • 英语
    • 年龄分级
      4+
    • 版权
      • © zeh4soft
  • 隐私政策

    • 更多来自"Reinhard MAENNER"的 App

    你可能还喜欢