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Sequential Competitive Facility Location In Continuous Geometric Space

Lavasani, Ali Mohammad | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51204 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Abam, Mohammad Ali
  7. Abstract:
  8. Abstract The problem of competetive facility location can be defined as follows: There are a number of customers in the form of points in space, and two players arrange a number of facilities in the form of points in space, given some limitations, respectively. Each customer’s connection to each facility has a cost for the customer and an advantage for the facility, and each customer wants to be connected to at most one of the facilities which has the lowest cost for him. The goal is to find the strategy of placing the facilities and determining the cost which the facility receives from the customer, in such a way that the player’s profit is maximised.In this thesis, we first sought to resolve this version of the problem: each customer is connected to the closest facility and has a steady profit for the players. The first player places his facility on the page so that if the second player chooses anywhere else from the page, earns less than the first player. In the process of solving, we find the problem of finding a convex polygon of maximum weight, although it is not related to the title of the thesis, but it is important in terms of theoretical and practical value
  9. Keywords:
  10. Computational Geometry ; Geometric Space ; Plurality Point ; Competitive Facility Location

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  • مقدمه
    • تعریف مسائل
      • تعادل نش در قیمت گذاری تسهیلات Maximum-Weight Convex Polygon
      • نقطه‌ی قطبی وزن‌دار
      • چندوجهی محدب بیشینه وزن Maximum-Weight Convex Polygon
    • اهمیت موضوعات
      • تعادل نش در قیمت‌گذاری تسهیلات
      • نقطه‌ی قطبی وزن‌دار
      • چندوجهی محدب بیشینه وزن
    • ادبیات موضوع
    • اهداف تحقیق
    • ساختار پایان‌نامه
  • مفاهیم اولیه
    • تعادل نش Nash Equilibrium
    • نمودار ورونوی Voronoi Diagram
    • بازی ورونوی Voronoi Game
    • مسئله‌ی اندازه‌ی کلی Klee's measure problem
  • کارهای پیشین
    • نقطه‌ی قطبی وزن‌دار
      • نقطه‌ی قطبی
      • مجموعه‌ی بدون نقطه‌ی قطبی
    • چند وجهی محدب بیشینه وزن
      • جعبه‌ی بیشینه وزنMaximum-Weight Box
      • عمق وزن‌دار
      • جعبه‌ی بیشینه اختلاف دو رنگی Maximum Bichromatic Discrepancy Box
      • جعبه‌ی بیشینهMaximum Box
  • نتایج جدید
    • نقطه‌ی قطبی وزن‌دار
      • خواص نقطه‌ی قطبی وزن‌دار
      • پیدا کردن نقطه‌ی قطبی
      • دیگر قضیه‌ها
    • چندوجهی محدب بیشینه وزن
  • نتیجه گیری
    • نتایج به دست آمده
      • نقطه‌ی قطبی وزن‌دار
      • چندوجهی محدب بیشینه وزن
    • کار‌های آتی
      • نقطه‌ی قطبی وزن‌دار
      • چندوجهی محدب بیشینه وزن
  • مطالب تکمیلی
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