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Approximation Algorithms for Bus Routing on Printed Circuit Boards

Habibollahi, Mohammad Mahdi | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 55271 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Zarrabizadeh, Hamid
  7. Abstract:
  8. Since the amount of data is increasing, it is important to reduce the size of components and circuits. For instance, bus routing problem, rectangle scape problem, and minimizing number of layers are important problems in printed circuit boards. Rectangle scape problem can be used as an estimation for minimizing number of layers problem. To minimize number of layers in this problem, we are given some axis-parallel rectangles inside a axis-parallel rectangular region. The objective is to extend one of the four boundaries of each rectangle in a certain direction such that all rectangles can be placed without any conflict in minimum number of layers. In this thesis, we analyze a common greedy algorithm for minimizing number of layers problem in which we place the maximum number of possible rectangles in a layer at each step. We show that the approximation factor of this greedy algorithm is at most ln n for each input of n rectangles. We also prove that the approximation factor of this algorithm is at least 1/2 ln n. In the end, we provide an algorithm with constant approximation factor for minimizing number of layers problem
  9. Keywords:
  10. Bus Routing ; Minimization Number of Layers ; Approximate Algorithm ; Printed Circuit Board ; Rectangle Escape Problem

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