‫ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ‬
‫ﻓﺎﻃﻤﻪ ﺷﻴﺮﺯﺍﺩ‬
‫‪١‬‬
‫ﭼﮑﻴﺪﻩ ‪ .‬ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﻪ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﮐﻪ ﺷﺎﺧﻪ ﺍي ﺍﺯ ﻋﻠﻢ ﺍﻗﺘﺼﺎﺩ ﻭ ﻧﻈﺮﻳﻪ ﺑﺎﺯي ﻫﺎ ﺍﺳﺖ‪ ،‬ﺩﺭ ﺳﻴﺴﺘﻢ‬
‫ﻫﺎي ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﻪ ﺧﺼﻮﺹ ﺍﻳﻨﺘﺮﻧﺖ ﺗﻮﺟﻪ ﺩﺍﺭﺩ ﻭ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﺴﺎﺋﻞ ﺟﺪﻳﺪي ﮐﻪ ﻃﺮﺍﺡ ﻣﮑﺎﻧﻴﺰﻡ ﺑﺎ ﺁﻥ ﻫﺎ ﺩﺭ ﺍﻳﻦ ﻣﺤﻴﻂ ﻫﺎ ﻣﻮﺍﺟﻪ ﺍﺳﺖ‬
‫ﺍﺯ ﺟﻤﻠﻪ ﭘﻴﭽﻴﺪﮔﻲ ﺷﺒﮑﻪ ﺍي ﻭ ﺩﺳﺘﮑﺎﺭي ﻣﺤﺎﺳﺒﺎﺗﻲ‪ ،‬ﺳﻌﻲ ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎ ﻭ ﺍﻟﮕﻮﺭﻳﺘﻢ ﻫﺎﻳﻲ ﺩﺍﺭﺩ ﮐﻪ ﺑﻪ ﺍﻳﻦ ﻣﺸﮑﻼﺕ ﺟﺪﻳﺪ‬
‫ﻓﺎﺋﻖ ﺁﻳﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﺟﺎ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻋﻼﻭﻩ ﺑﺮ ﺍﻋﻼﻡ ﻣﻘﺎﺩﻳﺮ ﺧﺼﻮﺻﻲ ﺧﻮﺩ‪ ،‬ﻣﻮﻇﻒ ﺑﻪ ﺍﻧﺠﺎﻡ ﻣﺤﺎﺳﺒﺎﺕ ﻣﺮﺑﻮﻁ ﺑﻪ ﻣﮑﺎﻧﻴﺰﻡ ﻧﻴﺰ ﻫﺴﺘﻨﺪ‪ ،‬ﺑﺮ ﺧﻼﻑ‬
‫ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﮐﻪ ﺍﻧﺠﺎﻡ ﻣﺤﺎﺳﺒﺎﺕ ﺩﺭ ﺁﻥ ﺑﺮ ﻋﻬﺪﻩ ﻳﮏ ﻣﻮﺟﻮﺩﻳﺖ ﻣﺮﮐﺰي ﻭ ﻣﻌﺘﻤﺪ ﺍﺳﺖ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﺍﺳﺖ ﮐﻪ ﻣﺸﮑﻼﺕ‬
‫ﻭ ﻣﺴﺎﺋﻞ ﺟﺪﻳﺪي ﭘﻴﺶ ﺭﻭي ﻃﺮﺍﺡ ﻣﮑﺎﻧﻴﺰﻡ ﻭ ﺍﻟﮕﻮﺭﻳﺘﻢ ﺑﻪ ﻭﺟﻮﺩ ﻣﻲ ﺁﻳﺪ‪ .‬ﺩﺭ ﺍﻳﻦ ﻧﻮﺷﺘﻪ ﺳﻌﻲ ﺑﺮ ﺁﻥ ﺍﺳﺖ ﺍﻳﻦ ﻣﺴﺎﺋﻞ ﺭﺍ ﺷﺮﺡ ﺩﺍﺩﻩ ﻭ ﺭﺍﻩ‬
‫ﺣﻞ ﻫﺎﻳﻲ ﮐﻪ ﺗﺎ ﮐﻨﻮﻥ ﺍﺭﺍﺋﻪ ﺷﺪﻩ ﺍﻧﺪ ﺭﺍ ﺑﻪ ﻫﻤﺮﺍﻩ ﻧﻤﻮﻧﻪ ﻣﺴﺌﻠﻪ ﻫﺎﻳﻲ ﭘﻴﺶ ﺭﻭي ﺧﻮﺍﻧﻨﺪﻩ ﻗﺮﺍﺭ ﺩﻫﻴﻢ‪.‬‬
‫‪ ۱‬ﻣﻌﺮﻓﻲ‬
‫ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺑﻪ ﻋﻨﻮﺍﻥ ﺷﺎﺧﻪ ﺍي ﺍﺯ ﻧﻈﺮﻳﻪ ﺑﺎﺯي ﻫﺎ ﺑﻪ ﺗﻌﺮﻳﻒ ﻗﻮﺍﻋﺪي ﺑﺮﺍي ﻳﮏ ﺑﺎﺯي ﻣﻲ ﭘﺮﺩﺍﺯﺩ ﺗﺎ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺭﺍ ﻭﺍﺩﺍﺭ ﺑﻪ ﺍﻧﺠﺎﻡ ﺑﺎﺯي ﮐﻨﻨﺪ‬
‫ﮐﻪ ﻧﺘﻴﺠﻪ ﺁﻥ ﻣﻮﺭﺩ ﻧﻈﺮ ﻃﺮﺍﺡ ﻣﮑﺎﻧﻴﺰﻡ ﺍﺳﺖ‪ .‬ﻧﺘﺎﻳﺠﻲ ﮐﻪ ﺗﺎﮐﻨﻮﻥ ﺩﺭ ﺍﻳﻦ ﺯﻣﻴﻨﻪ ﺑﺪﺳﺖ ﺁﻣﺪﻩ ﻓﻘﻂ ﺳﻌﻲ ﮐﺮﺩﻩ ﺑﻪ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﻧﮕﻴﺰﻩ ﺑﺪﻫﺪ ﺗﺎ‬
‫ﻣﻄﺎﺑﻖ ﻣﻴﻞ ﻃﺮﺍﺡ ﺑﺎﺯي ﮐﻨﻨﺪ ﻭ ﺑﻪ ﭘﻴﭽﻴﺪﮔﻲ ﻣﺤﺎﺳﺒﺎﺗﻲ ﭘﻴﺎﺩﻩ ﺳﺎﺯي ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎي ﻃﺮﺍﺣﻲ ﺷﺪﻩ ﺗﻮﺟﻬﻲ ﻧﺪﺍﺷﺘﻪ ﺍﺳﺖ‪ .‬ﺑﺮﺍي ﭘﻴﺎﺩﻩ ﺳﺎﺯي ﺍﻳﻦ‬
‫ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎ ﺩﺭ ﮐﺎﻣﭙﻴﻮﺗﺮ ﻻﺯﻡ ﺍﺳﺖ ﺍﺯ ﻟﺤﺎﻅ ﭘﻴﭽﻴﺪﮔﻲ ﻣﺤﺎﺳﺒﺎﺗﻲ ﻗﺎﺑﻞ ﺍﺟﺮﺍ ﺑﺎﺷﻨﺪ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ‪ Nisan‬ﻭ ‪ Ronen‬ﺩﺭ ]‪ [1‬ﺷﺎﺧﻪ ﻃﺮﺍﺣﻲ‬
‫ﻣﮑﺎﻧﻴﺰﻡ ﺭﺍ ﮔﺴﺘﺮﺵ ﺩﺍﺩﻧﺪ ﻭ ﺑﺤﺚ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺭﺍ ﺑﻪ ﻭﺟﻮﺩ ﺁﻭﺭﺩﻧﺪ ﮐﻪ ﺩﺭ ﺁﻥ ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎﻳﻲ ﻃﺮﺍﺣﻲ ﻣﻲ ﺷﻮﻧﺪ ﮐﻪ ﺍﺯ ﭘﻴﭽﻴﺪﮔﻲ‬
‫ﻣﺤﺎﺳﺒﺎﺗﻲ ﺩﺭ ﺯﻣﺎﻥ ﭼﻨﺪ ﺟﻤﻠﻪ ﺍي ﻗﺎﺑﻞ ﺣﻞ ﺑﺎﺷﻨﺪ ﻭ ﻳﺎ ﺩﺭ ﻣﻮﺍﺭﺩي ﮐﻪ ﺍﻳﻦ ﺍﻣﮑﺎﻥ ﻭﺟﻮﺩ ﻧﺪﺍﺭﺩ‪ ،‬ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺭﻭﺵ ﻫﺎي ﺗﻘﺮﻳﺒﻲ ﻣﮑﺎﻧﻴﺰﻣﻲ‬
‫ﻃﺮﺍﺣﻲ ﺷﻮﺩ ﮐﻪ ﺩﺭ ﺯﻣﺎﻥ ﭼﻨﺪ ﺟﻤﻠﻪ ﺍي ﻗﺎﺑﻞ ﺍﺟﺮﺍ ﺑﺎﺷﺪ‪ .‬ﺍﻳﻦ ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎ ﺑﺮﺍي ﺑﺎﺯي ﺩﺭ ﻣﻮﺍﺭﺩي ﮐﻪ ﻳﮏ ﻣﻮﺟﻮﺩﻳﺖ ﻣﺮﮐﺰي ﻣﻌﺘﻤﺪ ﺑﺮﺍي ﺍﻧﺠﺎﻡ‬
‫ﻣﺤﺎﺳﺒﺎﺕ ﻣﺮﺑﻮﻁ ﺑﻪ ﺧﺮﻭﺟﻲ ﻭ ﻣﻘﺎﺩﻳﺮ ﭘﺮﺩﺍﺧﺘﻲ ﻣﮑﺎﻧﻴﺰﻡ ﻭﺟﻮﺩ ﺩﺍﺭﺩ ﻗﺎﺑﻞ ﻗﺒﻮﻝ ﺍﺳﺖ‪ ،‬ﺍﻣﺎ ﺑﺎ ﮔﺴﺘﺮﺵ ﺍﻳﻨﺘﺮﻧﺖ‪ ،‬ﻓﺮﺽ ﻭﺟﻮﺩ ﭼﻨﻴﻦ ﻣﻮﺟﻮﺩﻳﺖ‬
‫ﻣﺮﮐﺰي ﻭ ﻗﺎﺑﻞ ﺍﻋﺘﻤﺎﺩ ﺍﺯ ﺑﻴﻦ ﻣﻲ ﺭﻭﺩ‪ .‬ﺍﺯ ﻃﺮﻑ ﺩﻳﮕﺮ ﺑﻪ ﺩﻟﻴﻞ ﮔﺴﺘﺮﺵ ﺍﻳﻨﺘﺮﻧﺖ ﻭ ﺩﺭ ﻧﺘﻴﺠﻪ ﺑﺰﺭﮒ ﺷﺪﻥ ﺷﺒﮑﻪ‪ ،‬ﺍﻧﺠﺎﻡ ﻣﺤﺎﺳﺒﺎﺕ ﺯﻣﺎﻥ ﮔﻴﺮ‬
‫ﺧﻮﺍﻫﺪ ﺷﺪ‪ ،‬ﭘﺲ ﻃﺮﺍﺣﻲ ﻭ ﭘﻴﺎﺩﻩ ﺳﺎﺯي ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎﻳﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﺮﺍي ﺍﻧﺠﺎﻡ ﻣﺤﺎﺳﺒﺎﺕ ﻻﺯﻡ ﺍﺳﺖ‪ .‬ﺍﻳﻦ ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎ ﺗﻮﺳﻂ ﺧﻮﺩ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﻪ‬
‫ﺻﻮﺭﺕ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺍﻧﺠﺎﻡ ﻣﻲ ﺷﻮﺩ ﻭ ﻧﺘﺎﻳﺞ ﻣﺤﺎﺳﺒﺎﺗﻲ ﮐﻪ ﺑﺮ ﺩﻭﺵ ﻫﺮ ﺑﺎﺯﻳﮑﻦ ﺍﺳﺖ ﺑﻪ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﻳﮕﺮ ﺍﺯ ﻃﺮﻳﻖ ﭘﻴﺎﻡ ﻫﺎﻳﻲ ﺍﻃﻼﻉ ﺩﺍﺩﻩ ﻣﻲ ﺷﻮﺩ‬
‫ﺗﺎ ﺁﻥ ﻫﺎ ﻧﻴﺰ ﺑﻪ ﻧﻮﺑﻪ ﺧﻮﺩ ﻣﺤﺎﺳﺒﺎﺕ ﺭﺍ ﺍﻧﺠﺎﻡ ﺩﻫﻨﺪ ﻭ ﺍﻳﻦ ﮐﺎﺭ ﺑﻪ ﻃﻮﺭ ﺑﺎﺯﮔﺸﺘﻲ ﺩﺭ ﺷﺒﮑﻪ ﺍﺩﺍﻣﻪ ﻣﻲ ﻳﺎﺑﺪ ﺗﺎ ﺩﺭ ﻧﻬﺎﻳﺖ ﻧﺘﻴﺠﻪ ﺑﺪﺳﺖ ﺁﻳﺪ‪ .‬ﺍﻣﺎ‬
‫ﻣﺸﮑﻞ ﺟﺪﻳﺪي ﮐﻪ ﺑﺮﻭﺯ ﻣﻲ ﮐﻨﺪ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺍﻳﻦ ﺟﺎ ﺑﺮ ﺧﻼﻑ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺑﻪ ﺻﻮﺭﺕ ﻣﺘﻤﺮﮐﺰ ﮐﻪ ﻣﺸﮑﻞ ﺁﻥ ﻓﻘﻂ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ‬
‫ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﻣﮑﺎﻥ ﺩﺍﺭﺩ ﻣﻘﺎﺩﻳﺮ ﺧﺼﻮﺻﻲ ﺧﻮﺩ ﺭﺍ ﻏﻴﺮ ﻭﺍﻗﻌﻲ ﺑﻪ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻋﻼﻡ ﮐﻨﻨﺪ‪ ،‬ﻣﺸﮑﻞ ﺟﺪﻳﺪي ﻣﻄﺮﺡ ﻣﻲ ﺷﻮﺩ ﻭ ﺁﻥ ﺍﻳﻦ ﻣﺸﮑﻞ ﺍﺳﺖ ﮐﻪ‬
‫ﭼﻮﻥ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺧﻮﺩ ﻣﺴﺌﻮﻝ ﺍﻧﺠﺎﻡ ﻣﺤﺎﺳﺒﺎﺕ ﻫﺴﺘﻨﺪ‪ ،‬ﺣﺘﻲ ﺍﮔﺮ ﻓﺮﺽ ﮐﻨﻴﻢ ﻣﻘﺎﺩﻳﺮ ﺧﺼﻮﺻﻲ ﺧﻮﺩ ﺭﺍ ﺻﺎﺩﻗﺎﻧﻪ ﺍﻋﻼﻡ ﻣﻲ ﮐﻨﻨﺪ‪ ،‬ﺍﻣﮑﺎﻥ ﺩﺍﺭﺩ‬
‫ﻣﺤﺎﺳﺒﺎﺕ ﺭﺍ ﺻﺎﺩﻗﺎﻧﻪ ﺍﻧﺠﺎﻡ ﻧﺪﻫﻨﺪ ﻭ ﻳﺎ ﻧﺘﺎﻳﺞ ﺭﺍ ﺑﻪ ﺩﺭﻭﻍ ﺑﻪ ﻳﮑﺪﻳﮕﺮ ﺗﻮﺳﻂ ﭘﻴﺎﻡ ﻫﺎﻳﻲ ﮐﻪ ﺭﺩ ﻭ ﺑﺪﻝ ﻣﻲ ﮐﻨﻨﺪ ﻋﻼﻭﻩ ﺑﺮ ﺁﻥ ﭘﻴﭽﻴﺪﮔﻲ ﺷﺒﮑﻪ ﺍي‬
‫ﻧﻴﺰ ﻣﻄﺮﺡ ﻣﻲ ﺷﻮﺩ ﮐﻪ ﺁﻥ ﻣﺮﺑﻮﻁ ﺑﻪ ﺑﺎﺭي ﺍﺳﺖ ﮐﻪ ﭘﻴﺎﻡ ﻫﺎي ﻣﺒﺎﺩﻟﻪ ﺷﺪﻩ ﺑﻴﻦ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﺮ ﺷﺒﮑﻪ ﺗﺤﻤﻴﻞ ﻣﻲ ﮐﻨﻨﺪ‪.‬‬
‫ﺩﺭ ﺍﺩﺍﻣﻪ ﺍﺑﺘﺪﺍ ﺩﺭ ﺑﺨﺶ ‪ ۲‬ﺑﻪ ﻣﺸﺨﺺ ﮐﺮﺩﻥ ﻭ ﺩﺳﺘﻪ ﺑﻨﺪي ﻣﺸﮑﻼﺕ ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻣﻲ ﭘﺮﺩﺍﺯﻳﻢ‪ .‬ﺩﺭ‬
‫ﺑﺨﺶ ‪ ۳‬ﺑﻪ ﻃﻮﺭ ﺭﺳﻤﻲ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺷﺮﺡ ﺩﺍﺩﻩ ﻣﻲ ﺷﻮﺩ‪ .‬ﺑﺮﺍي ﺑﻬﺘﺮ ﺁﺷﻨﺎ ﺷﺪﻥ ﺑﺎ ﺭﻭﺵ ﻫﺎي ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ‬
‫‪ ١‬ﺩﺍﻧﺸﺠﻮي ﮐﺎﺭﺷﻨﺎﺳﻲ ﺍﺭﺷﺪ ﻣﻬﻨﺪﺳﻲ ﻓﻨﺎﻭﺭي ﺍﻃﻼﻋﺎﺕ ﺩﺍﻧﺸﮕﺎﻩ ﺻﻨﻌﺘﻲ ﺷﺮﻳﻒ‬
‫ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺍﺑﺘﺪﺍ ﺩﻭ ﻧﻤﻮﻧﻪ ﻣﺴﺌﻠﻪ ﮐﻪ ﺑﻪ ﺁﻥ ﻫﺎ ﺗﺎﮐﻨﻮﻥ ﭘﺮﺩﺍﺧﺘﻪ ﺷﺪﻩ ﺍﺳﺖ ﺩﺭ ﺑﺨﺶ ‪ ۴‬ﺑﻴﺎﻥ ﻣﻲ ﺷﻮﺩ‪ .‬ﺩﺭ ﻧﻬﺎﻳﺖ ﺑﺨﺶ ‪ ۵‬ﻧﺘﻴﺠﻪ‬
‫ﮔﻴﺮي ﺍﻳﻦ ﺗﺤﻘﻴﻖ ﺭﺍ ﺩﺭ ﺑﺮ ﻣﻲ ﮔﻴﺮﺩ‪.‬‬
‫‪ ۲‬ﻣﺴﺎﺋﻞ ﻣﻮﺭﺩ ﺗﻮﺟﻪ ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ‬
‫ﺩﻭ ﻭﻳﮋﮔﻲ ﻣﺸﺘﺮﮎ ﮐﻪ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﺎ ﻧﺴﺨﻪ ﻣﺘﻤﺮﮐﺰ ﺁﻥ ﻳﻌﻨﻲ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺩﺍﺭﺩ‪،‬‬
‫ﺳﺎﺯﮔﺎﺭي ﻣﺤﺮﮎ‪ ٢‬ﻭ ﺗﻮﺟﻪ ﺑﻪ ﭘﻴﭽﻴﺪﮔﻲ ﻣﺤﺎﺳﺒﺎﺗﻲ ﺍﺳﺖ‪ .‬ﻳﻌﻨﻲ ﺩﺭ ﻫﺮ ﺩﻭ ﻧﺴﺨﻪ ﺍﺯ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺑﺎﻳﺪ ﻣﮑﺎﻧﻴﺰﻣﻲ ﻓﺮﺍﻫﻢ ﺷﻮﺩ ﮐﻪ‬
‫ﺑﺎﺯﻳﮑﻨﺎﻥ ﺭﺍ ﻭﺍﺩﺍﺭ ﮐﻨﺪ ﺻﺎﺩﻗﺎﻧﻪ ﻣﻘﺎﺩﻳﺮ ﺧﺼﻮﺻﻲ)ﺍﻧﻮﺍﻉ‪ (٣‬ﺧﻮﺩ ﺭﺍ ﺩﺭ ﺑﺎﺯي ﺑﻪ ﮐﺎﺭ ﺑﺮﻧﺪ‪ .‬ﻭﻳﮋﮔﻲ ﺩﻭﻡ ﻧﻴﺰ ﺍﺯ ﺍﻳﻦ ﺣﮑﺎﻳﺖ ﺩﺍﺭﺩ ﮐﻪ ﻫﺮ ﺩﻭ‬
‫ﻧﺴﺨﻪ ﺍﺯ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺑﻪ ﻋﻤﻠﻲ ﺑﻮﺩﻥ ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎ ﺩﺭ ﮐﺎﻣﭙﻴﻮﺗﺮ ﻣﻲ ﺍﻧﺪﻳﺸﻨﺪ ﻭ ﺳﻌﻲ ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎﻳﻲ ﺩﺍﺭﻧﺪ ﮐﻪ ﺩﺭ ﺯﻣﺎﻥ‬
‫ﭼﻨﺪ ﺟﻤﻠﻪ ﺍي ﺩﺭ ﮐﺎﻣﭙﻴﻮﺗﺮ ﻗﺎﺑﻞ ﭘﻴﺎﺩﻩ ﺳﺎﺯي ﻭ ﺍﺟﺮﺍ ﺑﺎﺷﻨﺪ‪.‬‬
‫ﺍﻣﺎ ﺗﻔﺎﻭﺕ ﻫﺎي ﺍﻳﻦ ﺩﻭ ﻧﺴﺨﻪ ﺩﺭ ﺩﻭ ﻣﻮﺭﺩ ﺟﺪﻳﺪ ﺍﺳﺖ ﮐﻪ ﺑﻪ ﺁﻥ ﭘﻴﭽﻴﺪﮔﻲ ﺷﺒﮑﻪ ﺍي ﻭ ﺍﺟﺮﺍي ﻣﮑﺎﻧﻴﺰﻡ ﺑﻪ ﻃﻮﺭ ﻭﻓﺎﺩﺍﺭﺍﻧﻪ‬
‫‪٤‬‬
‫ﺍﺳﺖ‪ .‬ﭘﻴﭽﻴﺪﮔﻲ ﺷﺒﮑﻪ ﺍي‪ ٥‬ﮐﻪ ﻓﻘﻂ ﺑﺮﺍي ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﻪ ﮐﺎﺭ ﻣﻲ ﺭﻭﺩ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻣﺎﻫﻴﺖ ﺍﻳﻦ ﻧﻮﻉ ﺍﺯ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ‬
‫ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺁﻥ ﻧﻴﺎﺯ ﺑﻪ ﺍﺭﺳﺎﻝ ﻭ ﺩﺭﻳﺎﻓﺖ ﭘﻴﺎﻡ ﻣﻴﺎﻥ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﺷﺒﮑﻪ ﻣﻲ ﺑﺎﺷﺪ‪ .‬ﺩﺭ ﺑﺮﺭﺳﻲ ﭘﻴﭽﻴﺪﮔﻲ ﺷﺒﮑﻪ ﺍي ﺑﻪ ﻣﻮﺍﺭﺩي ﭼﻮﻥ‬
‫ﺗﻌﺪﺍﺩ ﮐﻞ ﭘﻴﺎﻡ ﻫﺎﻳﻲ ﮐﻪ ﺭﻭي ﺷﺒﮑﻪ ﺍﺭﺳﺎﻝ ﻣﻲ ﺷﻮﺩ‪ ،‬ﺑﻴﺸﻴﻨﻪ ﭘﻴﺎﻡ ﻫﺎﻳﻲ ﮐﻪ ﺭﻭي ﻳﮏ ﺍﺗﺼﺎﻝ ﺩﺭ ﺷﺒﮑﻪ ﺍﺭﺳﺎﻝ ﻣﻲ ﺷﻮﺩ‪ ،‬ﺑﻴﺸﻴﻨﻪ ﺍﻧﺪﺍﺯﻩ‬
‫ﭘﻴﺎﻡ‪ ،‬ﺑﺎﺭ ﻣﺤﺎﺳﺒﺎﺗﻲ ﺩﺭ ﻫﺮ ﮔﺮﻩ‪ ،‬ﻭ ﻓﻀﺎي ﻻﺯﻡ ﺩﺭ ﻫﺮ ﮔﺮﻩ ﺍﺳﺖ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﭘﻴﭽﻴﺪﮔﻲ ﺷﺒﮑﻪ ﺍي ﺑﻪ ﮔﻮﻧﻪ ﺍي ﭘﻴﭽﻴﺪﮔﻲ ﻣﺤﺎﺳﺒﺎﺗﻲ‬
‫ﺭﺍ ﻧﻴﺰ ﺩﺭ ﺑﺮ ﺩﺍﺭﺩ‪.‬‬
‫ﺗﻔﺎﻭﺕ ﺩﻳﮕﺮي ﮐﻪ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﺎ ﻧﻮﻉ ﻣﺘﻤﺮﮐﺰ ﺩﺍﺭﺩ‪ ،‬ﻭﺟﻮﺩ ﻣﺴﺌﻠﻪ ﺟﺪﻳﺪ ﺑﻪ ﻧﺎﻡ ﺍﺟﺮﺍي ﻣﮑﺎﻧﻴﺰﻡ ﺑﻪ ﺻﻮﺭﺕ‬
‫ﻭﻓﺎﺩﺍﺭﺍﻧﻪ ﺍﺳﺖ‪ .‬ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻳﮏ ﺍﻣﮑﺎﻥ ﺟﺪﻳﺪ ﻭﺟﻮﺩ ﺩﺍﺭﺩ ﮐﻪ ﺁﻥ ﺍﻣﮑﺎﻥ ﺩﺳﺘﮑﺎﺭي ﺩﺭ ﻣﺤﺎﺳﺒﺎﺕ ﺗﻮﺳﻂ‬
‫ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﺳﺖ ﺩﺭ ﺣﺎﻟﻲ ﮐﻪ ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﻣﺴﺌﻠﻪ ﻓﻘﻂ ﺍﻣﮑﺎﻥ ﺍﺳﺘﺮﺍﺗﮋﻳﮏ ﺭﻓﺘﺎﺭ ﮐﺮﺩﻥ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﺁﺷﮑﺎﺭﺳﺎﺯي ﺍﻧﻮﺍﻉ‬
‫ﺧﺼﻮﺻﻲ ﺧﻮﺩ ﺑﻮﺩ‪ .‬ﮐﺎﺭﻫﺎﻳﻲ ﮐﻪ ﮔﺮﻩ ﺩﺭ ﺳﻴﺴﺘﻢ ﻫﺎي ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻣﻲ ﺗﻮﺍﻧﺪ ﺍﻧﺠﺎﻡ ﺩﻫﺪ ﻏﻴﺮ ﻭﺍﻗﻌﻲ ﺟﻠﻮﻩ ﺩﺍﺩﻥ ﻧﺘﺎﻳﺞ ﻣﺤﺎﺳﺒﺎﺕ ﻣﺤﻠﻲ‬
‫ﺧﻮﺩ ﺑﻪ ﻫﻤﺴﺎﻳﻪ ﻭ ﻳﺎ ﺍﺭﺳﺎﻝ ﻧﮑﺮﺩﻥ ﻧﺘﺎﻳﺞ ﺑﻪ ﮔﺮﻩ ﻫﻤﺴﺎﻳﻪ ﺍﺳﺖ ﺗﺎ ﺍﻭ ﺭﺍ ﺍﺯ ﺑﺎﺯي ﺣﺬﻑ ﮐﻨﺪ‪ .‬ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ‬
‫ﺗﻼﺵ ﺑﺮ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﺑﻪ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﻧﮕﻴﺰﻩ ﮐﺎﻓﻲ ﺩﺍﺩﻩ ﺷﻮﺩ ﺗﺎ ﺑﺪﺍﻧﻨﺪ ﺑﻬﺘﺮﻳﻦ ﮐﺎﺭي ﮐﻪ ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﺍﻧﺠﺎﻡ ﺩﻫﻨﺪ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﺑﻪ ﺩﺭﺳﺘﻲ‬
‫ﻣﺤﺎﺳﺒﺎﺕ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺭﺍ ﺍﻧﺠﺎﻡ ﺩﺍﺩﻩ ﻭ ﺍﺭﺗﺒﺎﻃﺎﺕ ﺭﺍ ﺑﺮﻗﺮﺍﺭ ﮐﻨﻨﺪ‪ .‬ﺩﺭ ﻭﺍﻗﻊ ﺗﻌﺪﺍﺩ ﻋﻤﻞ‪ ٦‬ﻫﺎﻳﻲ ﮐﻪ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﺳﻴﺴﺘﻢ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺍﻧﺠﺎﻡ‬
‫ﻣﻲ ﺩﻫﻨﺪ ﻧﺴﺒﺖ ﺑﻪ ﻧﻮﻉ ﻣﺘﻤﺮﮐﺰ ﺍﻓﺰﺍﻳﺶ ﻳﺎﻓﺘﻪ ﺍﺳﺖ‪ .‬ﺩﺭ ﻧﻮﻉ ﻣﺘﻤﺮﮐﺰ ﺗﻨﻬﺎ ﻋﻤﻞ ﻳﮏ ﺑﺎﺯﻳﮑﻦ ﺁﺷﮑﺎﺭﺳﺎﺯي ﻣﻘﺎﺩﻳﺮ ﺧﺼﻮﺻﻲ ﺧﻮﺩ ﺑﻮﺩ‬
‫ﺩﺭ ﺣﺎﻟﻲ ﮐﻪ ﺩﺭ ﻧﻮﻉ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻋﻼﻭﻩ ﺑﺮ ﺁﻥ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﻣﺤﺎﺳﺒﺎﺕ ﺭﺍ ﻏﻴﺮ ﺍﺯ ﻭﺍﻗﻌﻴﺖ ﺍﻧﺠﺎﻡ ﺩﻫﻨﺪ‪ ،‬ﻧﺘﻴﺠﻪ ﺭﺍ ﺑﻪ ﺩﺭﻭﻍ ﺍﻋﻼﻡ‬
‫ﮐﻨﻨﺪ‪ ،‬ﭘﻴﺎﻡ ﻫﺎﻳﻲ ﮐﻪ ﺍﺯ ﺩﻳﮕﺮﺍﻥ ﺑﺮﺍي ﺩﻳﮕﺮ ﮔﺮﻩ ﻫﺎ ﺭﺳﻴﺪﻩ ﺭﺍ ﺑﻪ ﺩﺭﺳﺘﻲ ﺍﻧﺘﻘﺎﻝ ﻧﺪﻫﻨﺪ‪.‬‬
‫ﺩﺭ ﺍﻳﻦ ﺟﺎ ﻧﻴﺰ ﻓﺮﺽ ﺑﺮ ﻋﺎﻗﻞ ﺑﻮﺩﻥ‪ ،‬ﺧﻮﺩ ﻣﺨﺘﺎﺭ ﺑﻮﺩﻥ‪ ،‬ﻭ ﺧﻮﺩﺧﻮﺍﻩ ﺑﻮﺩﻥ ﮔﺮﻩ ﻫﺎ ﺍﺳﺖ‪ .‬ﺩﺭ ﺍﺩﺍﻣﻪ ﻳﮏ ﺑﻴﺎﻥ ﺭﺳﻤﻲ ﺍﺯ‬
‫ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻣﻄﺮﺡ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫ﺑﺮﺍي ﺩﻳﺪ ﺑﻬﺘﺮ ﻧﺴﺒﺖ ﺑﻪ ﻣﻄﺎﻟﺐ ﺍﻳﻦ ﺑﺨﺶ ﺑﻪ ]‪ [2‬ﻭ ]‪ [3‬ﻭ ]‪ [6‬ﻣﺮﺍﺟﻌﻪ ﻧﻤﺎﻳﻴﺪ‪.‬‬
‫‪ ۳‬ﺑﻴﺎﻥ ﺭﺳﻤﻲ‬
‫‪Incentive compatible ٢‬‬
‫‪type ٣‬‬
‫‪faithful mechanism execution ٤‬‬
‫‪network complexity ٥‬‬
‫‪action ٦‬‬
‫ﻃﺒﻖ ﺗﻌﺮﻳﻔﻲ ﮐﻪ ﺩﺭ ]‪ [4‬ﺁﻣﺪﻩ ﺍﺳﺖ ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻳﮏ ﻓﻀﺎي ﺍﺳﺘﺮﺍﺗﮋي‬
‫∑‬
‫…‬
‫∑( =∑ ﺩﺍﺭﻳﻢ ﮐﻪ ﺷﺎﻣﻞ‬
‫ﺍﺳﺘﺮﺍﺗﮋي ﻫﺎي ﻣﻤﮑﻦ ﺑﺮﺍي ﻫﺮ ﺑﺎﺯﻳﮑﻦ ‪ i‬ﺍﺳﺖ ﮐﻪ ﺑﺎﺯﻳﮑﻦ ﺍﺯ ﻣﻴﺎﻥ ﺁﻧﻬﺎ ﺍﺳﺘﺮﺍﺗﮋي ﺧﻮﺩ ﺭﺍ ﺍﻧﺘﺨﺎﺏ ﻣﻲ ﮐﻨﺪ‪ .‬ﺑﺮﺍي ﻫﺮ ﺑﺎﺯﻳﮑﻦ ﻳﮏ‬
‫‪ ٧‬ﻣﻲ ﻧﺎﻣﻴﻢ‪ .‬ﺍﻳﻦ ﺍﺳﺘﺮﺍﺗﮋي ﻫﻤﺎﻥ ﺍﺳﺘﺮﺍﺗﮋي ﺍﺳﺖ ﮐﻪ ﻃﺮﺍﺡ ﻣﺎﻳﻞ ﺍﺳﺖ‬
‫ﺍﺳﺘﺮﺍﺗﮋي ﺩﻟﺨﻮﺍﻩ ﻃﺮﺍﺡ ﻭﺟﻮﺩ ﺩﺍﺭﺩ ﮐﻪ ﺁﻥ ﺭﺍ ∑‬
‫ﺑﺎﺯﻳﮑﻨﺎﻥ ﺁﻥ ﺭﺍ ﺍﻧﺠﺎﻡ ﺩﻫﻨﺪ ﺩﺭ ﻭﺍﻗﻊ ﻣﻲ ﺗﻮﺍﻥ ﺁﻥ ﻫﻤﺎﻥ ﺍﻟﮕﻮﺭﻳﺘﻢ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺍي ﺗﻌﺒﻴﺮ ﮐﺮﺩ ﮐﻪ ﻃﺮﺍﺡ ﻣﺎﻳﻞ ﺍﺳﺖ ﺩﺭ ﻫﺮ ﮔﺮﻩ ﺩﺭ ﺷﺒﮑﻪ‬
‫ﺍﻧﺠﺎﻡ ﺷﻮﺩ ﻭ ﮔﺮﻩ ﻫﺎ ﺍﺯ ﺁﻥ ﺗﺨﻄﻲ ﻧﮑﻨﻨﺪ‪ .‬ﻳﮏ ﺧﺮﻭﺟﻲ‬
‫‪,…,‬‬
‫ﻧﺘﻴﺠﻪ ﺑﺎﺯي ﺍﺳﺖ ﻭ ﺑﺮﺩﺍﺭ‬
‫ﺑﺮﺍي ﺑﺎﺯي ﺑﻪ ﺻﻮﺭﺕ ﺯﻭﺝ )‪ o=(a,p‬ﺗﻌﺮﻳﻒ ﻣﻲ ﺷﻮﺩ‪ ،‬ﮐﻪ ‪ a‬ﻫﻤﺎﻥ‬
‫∑ ‪ :‬ﺍﺳﺖ‬
‫ﭘﺮﺩﺍﺧﺘﻲ ﻫﺎي ﻫﺮ ﺑﺎﺯﻳﮑﻦ ﺍﺳﺖ‪ .‬ﻗﺎﻧﻮﻥ ﺧﺮﻭﺟﻲ ‪ g‬ﻳﮏ ﺗﺎﺑﻊ‬
‫ﮐﻪ ﺧﺮﻭﺟﻲ ﺭﺍ ﺑﺮ ﺍﺳﺎﺱ ﺍﺳﺘﺮﺍﺗﮋي ﻫﺎي ﺍﻧﺘﺨﺎﺑﻲ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺗﻌﻴﻴﻦ ﻣﻲ ﮐﻨﺪ‪.‬‬
‫ﺑﺮ ﺍﺳﺎﺱ ﺁﻧﭽﻪ ﺩﺭ ﺑﻨﺪ ﻗﺒﻞ ﮔﻔﺘﻪ ﺷﺪ‪ ،‬ﺣﺎﻝ ﺑﻪ ﺗﻌﺮﻳﻒ ﺭﺳﻤﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻣﻲ ﭘﺮﺩﺍﺯﻳﻢ‪.‬‬
‫ﺗﻌﺮﻳﻒ ‪ .۱‬ﻳﮏ ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ‪ M‬ﺑﺎ ﺗﻌﺪﺍﺩ ‪ n‬ﺑﺎﺯﻳﮑﻦ ﻳﮏ ﺳﻪ ﺗﺎﻳﻲ ﺑﻪ ﺻﻮﺭﺕ‬
‫•‬
‫∑‬
‫•‬
‫•‬
‫…‬
‫‪, ∑,‬‬
‫ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺁﻥ‪:‬‬
‫∑( =∑ ﻣﺠﻤﻮﻋﻪ ﺍﺳﺘﺮﺍﺗﮋي ﻫﺎي ﻣﻤﮑﻦ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺍﺳﺖ‪.‬‬
‫∑ ‪ :‬ﺗﺎﺑﻊ ﺧﺮﻭﺟﻲ ﺍﺳﺖ ﮐﻪ ﺗﻮﺳﻂ ﻣﮑﺎﻧﻴﺰﻡ ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫‪s ,…,s‬‬
‫ﺍﺳﺘﺮﺍﺗﮋي ﺗﻮﺻﻴﻪ ﺷﺪﻩ ﻭ ﻣﻮﺭﺩ ﺩﻟﺨﻮﺍﻩ ﻃﺮﺍﺡ ﺍﺳﺖ‪.‬‬
‫ﻫﺪﻑ ﻃﺮﺍﺡ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﺍﺳﺘﺮﺍﺗﮋي ﻫﺎي ﺍﻧﺘﺨﺎﺑﻲ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﻳﮏ ﺗﻌﺎﺩﻟﻲ ﻗﺮﺍﺭ ﺑﮕﻴﺮﻧﺪ ﮐﻪ ﺍﻧﺤﺮﺍﻑ ﻫﺮ ﺑﺎﺯﻳﮑﻦ ﺍﺯ ﺁﻥ ﺗﻌﺎﺩﻝ ﻧﺘﻴﺠﻪ‬
‫ﺑﻬﺘﺮي ﺑﺮﺍي ﺍﻭ ﻧﺪﺍﺷﺘﻪ ﺑﺎﺷﺪ‪ .‬ﭘﺲ ﺍﮔﺮ‬
‫ﻳﮏ ﻧﻘﻄﻪ ﺗﻌﺎﺩﻝ ﺑﺎﺷﺪ ﻣﮑﺎﻧﻴﺰﻡ ﻳﮏ ﭘﻴﺎﺩﻩ ﺳﺎﺯي ﻭﻓﺎﺩﺍﺭﺍﻧﻪ ﺍﺯ ﺗﺎﺑﻊ ﺍﻧﺘﺨﺎﺏ ﺍﺟﺘﻤﺎﻋﻲ‬
‫‪٨‬‬
‫ﺧﻮﺍﻫﺪ ﺑﻮﺩ‪.‬‬
‫ﺗﻌﺮﻳﻒ ‪ .۲‬ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ‬
‫‪, ∑,‬‬
‫ﻳﮏ ﭘﻴﺎﺩﻩ ﺳﺎﺯي ﻭﻓﺎﺩﺍﺭﺍﻧﻪ )ﺍﮐﺲ ﭘﺴﺖ‪ (٩‬ﺍﺯ ﺗﺎﺑﻊ ﺍﻧﺘﺨﺎﺏ ﺍﺟﺘﻤﺎﻋﻲ‬
‫ﺍﺳﺖ ﺍﮔﺮ ﭘﺮﻭﻓﺎﻳﻞ ﺍﺳﺘﺮﺍﺗﮋي ﺗﻮﺻﻴﻪ ﺷﺪﻩ‬
‫ﻳﮏ ﺗﻌﺎﺩﻝ ﺑﺮﺍي ﺑﺎﺯي ﺑﺎﺷﺪ‪.‬‬
‫ﭘﻴﺎﺩﻩ ﺳﺎﺯي ﻭﻓﺎﺩﺍﺭﺍﻧﻪ ﻋﻼﻭﻩ ﺑﺮ ﺷﺎﻣﻞ ﺷﺪﻥ ﺳﺎﺯﮔﺎﺭي ﻣﺤﺮﮎ ﺑﺮﺍي ﺁﺷﮑﺎﺭﺳﺎﺯي ﺍﻃﻼﻋﺎﺕ‪ ،‬ﻭﻳﮋﮔﻲ ﻫﺎي ﺳﺎﺯﮔﺎﺭي ﺍﺭﺗﺒﺎﻃﻲ ﺑﺮﺍي ﻋﻤﻞ‬
‫ﻫﺎي ﮔﺬﺭ ﭘﻴﺎﻡ ﺑﺎﺯﻳﮑﻨﺎﻥ‪ ،‬ﻭ ﺳﺎﺯﮔﺎﺭي ﺍﻟﮕﻮﺭﻳﺘﻤﻲ ﺑﺮﺍي ﻋﻤﻞ ﻫﺎي ﻣﺤﺎﺳﺒﺎﺗﻲ ﺭﺍ ﻧﻴﺰ ﺷﺎﻣﻞ ﻣﻲ ﺷﻮﺩ‪ .‬ﺑﺮﺍي ﻫﺮ ﮐﺪﺍﻡ ﺍﺯ ﺍﻳﻨﻬﺎ ﺗﻌﺮﻳﻔﻲ ﺑﻪ‬
‫ﺻﻮﺭﺕ ﺯﻳﺮ ﺩﺍﺭﻳﻢ‪:‬‬
‫ﺗﻌﺮﻳﻒ ‪ .۳‬ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ‪ M‬ﺳﺎﺯﮔﺎي ﺍﻟﮕﻮﺭﻳﺘﻤﻲ)‪ )(AC‬ﺑﻪ ﺗﺮﺗﻴﺐ ﺳﺎﺯﮔﺎﺭي ﺍﺭﺗﺒﺎﻃﻲ)‪ ،(CC‬ﺳﺎﺯﮔﺎﺭي ﻣﺤﺮﮎ)‪ ((IC‬ﺭﺍ ﺩﺍﺭﺩ‬
‫ﺍﮔﺮ ﻳﮏ ﺑﺎﺯﻳﮑﻦ ﻧﺘﻮﺍﻧﺪ ﺑﻪ ﺳﻮﺩ ﺑﻴﺸﺘﺮي ﺑﺎ ﺍﻧﺤﺮﺍﻑ ﺍﺯ ﻋﻤﻞ ﻫﺎي ﻣﺤﺎﺳﺒﺎﺗﻲ)ﺑﻪ ﺗﺮﺗﻴﺐ ﮔﺬﺭ ﭘﻴﺎﻡ‪ ،‬ﺁﺷﮑﺎﺭﺳﺎﺯي ﺍﻃﻼﻋﺎﺕ( ﺗﻮﺻﻴﻪ ﺷﺪﻩ‬
‫ﺩﺭ ﺗﻌﺎﺩﻝ ﺩﺳﺖ ﻳﺎﺑﺪ‪.‬‬
‫ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﻋﻤﻞ ﻫﺎي ﻣﺨﺘﻠﻔﻲ ﮐﻪ ﻫﺮ ﺑﺎﺯﻳﮑﻦ ﺩﺭ ﻣﺤﻴﻂ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻣﻲ ﺗﻮﺍﻧﺪ ﺍﻧﺠﺎﻡ ﺩﻫﺪ‪،‬‬
‫ﺑﻪ ﺻﻮﺭﺕ‬
‫‪,‬‬
‫‪,‬‬
‫ﺗﻌﺮﻳﻒ ﻣﻲ ﺷﻮﺩ‪ .‬ﮐﻪ ﺍﺯ ﭼﭗ ﺑﻪ ﺭﺍﺳﺖ ﻋﻤﻞ ﻫﺎي ﺁﺷﮑﺎﺭ ﺳﺎﺯي‪ ،‬ﮔﺬﺭ ﭘﻴﺎﻡ‪ ،‬ﻭ ﺍﺭﺗﺒﺎﻃﻲ ﺭﺍ ﻧﺸﺎﻥ ﻣﻲ ﺩﻫﻨﺪ‪ .‬ﺩﺭ ﻭﺍﻗﻊ ﺍﻳﻦ ﻋﻤﻞ ﻫﺎ ﺑﻪ ﻃﻮﺭ‬
‫ﻫﻤﺰﻣﺎﻥ ﺗﻮﺳﻂ ﺑﺎﺯﻳﮑﻦ ﺩﺭ ﻫﺮ ﻣﺮﺣﻠﻪ ﺍﻧﺠﺎﻡ ﻧﻤﻲ ﮔﻴﺮﺩ‪ .‬ﺯﻳﺮﺍ ﺑﺎﺯﻳﮑﻦ ﺩﺭ ﻫﺮ ﻣﺮﺣﻠﻪ ﻳﺎ ﺩﺭ ﺣﺎﻝ ﻋﻤﻞ ﻣﺮﺑﻮﻁ ﺑﻪ ﺁﺷﮑﺎﺭﺳﺎﺯي‪ ،‬ﻳﺎ ﮔﺬﺭ‬
‫ﭘﻴﺎﻡ‪ ،‬ﻭ ﻳﺎ ﺍﺭﺗﺒﺎﻃﻲ ﺍﺳﺖ‪.‬‬
‫‪ ٧‬ﺣﺮﻑ ‪ m‬ﺗﻮﺳﻂ ﻧﻮﻳﺴﻨﺪﮔﺎﻥ ]‪ [4‬ﻣﺸﺨﺺ ﻧﺸﺪﻩ ﺍﺳﺖ ﻣﺮﺑﻮﻁ ﺑﻪ ﭼﻪ ﭼﻴﺰي ﺍﺳﺖ‪ .‬ﻣﻲ ﺗﻮﺍﻥ ﺁﻥ ﺭﺍ ﻣﺮﺑﻮﻁ ﺑﻪ ﮐﻠﻤﻪ ﻣﮑﺎﻧﻴﺰﻡ ﺩﺍﻧﺴﺖ‪.‬‬
‫‪social choice function ٨‬‬
‫‪ex post ٩‬‬
‫‪ ۴‬ﻧﻤﻮﻧﻪ ﻣﺴﺎﺋﻞ‬
‫ﺩﺭ ﺍﻳﻦ ﺑﺨﺶ ﺩﻭ ﻧﻤﻮﻧﻪ ﻣﺴﺌﻠﻪ ﻭي ﺳﻲ ﺟﻲ‪ ١٠‬ﺗﻮﺯﻳﻊ ﺷﺪﻩ‪ ،‬ﻣﺴﻴﺮﻳﺎﺑﻲ ﻣﻴﺎﻥ ﻧﺎﺣﻴﻪ ﺍي ﺑﻴﺎﻥ ﻣﻲ ﺷﻮﺩ‪ .‬ﻫﻤﺎﻥ ﻃﻮﺭ ﮐﻪ ﺩﺭ ﺑﺨﺶ ‪ ۲‬ﺫﮐﺮ‬
‫ﺷﺪ ﺩﻭ ﻣﺴﺌﻠﻪ ﺍي ﮐﻪ ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﺎ ﺁﻥ ﻣﻮﺍﺟﻪ ﻫﺴﺘﻴﻢ ﭘﻴﭽﻴﺪﮔﻲ ﺷﺒﮑﻪ ﻭ ﭘﻴﺎﺩﻩ ﺳﺎﺯي ﻭﻓﺎﺩﺍﺭﺍﻧﻪ ﻣﮑﺎﻧﻴﺰﻡ ﺍﺳﺖ‪ .‬ﺩﺭ‬
‫ﺍﻳﻦ ﺟﺎ ﺍﺑﺘﺪﺍ ﻭي ﺳﻲ ﺟﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﺮﺭﺳﻲ ﻣﻲ ﺷﻮﺩ ﻭ ﺩﺭ ﺁﻥ ﻓﻘﻂ ﺑﻪ ﭘﻴﺎﺩﻩ ﺳﺎﺯي ﻭﻓﺎﺩﺍﺭﺍﻧﻪ ﺗﻮﺟﻪ ﻣﻲ ﺷﻮﺩ ﻭ ﺑﺎ ﭘﻴﭽﻴﺪﮔﻲ ﺷﺒﮑﻪ‬
‫ﮐﺎﺭي ﻧﺪﺍﺭﻳﻢ‪ .‬ﺩﺭ ﻣﺴﺌﻠﻪ ﺩﻭﻡ ﮐﻪ ﻣﺴﻴﺮﻳﺎﺑﻲ ﺑﻴﻦ ﻧﺎﺣﻴﻪ ﺍي ﺍﺳﺖ ﻓﺮﺽ ﻣﻲ ﺷﻮﺩ ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺳﻂ ﮔﺮﻩ ﻫﺎ ﺑﻪ ﺩﺭﺳﺘﻲ ﺍﺟﺮﺍ ﻣﻲ ﺷﻮﺩ‪ ،‬ﻭ‬
‫ﻓﻘﻂ ﻓﺮﺽ ﻣﻲ ﺷﻮﺩ ﻣﻮﺟﻮﺩﻳﺖ ﻣﺮﮐﺰي ﺑﺮﺍي ﺍﻧﺠﺎﻡ ﻣﮑﺎﻧﻴﺰﻡ ﻭﺟﻮﺩ ﻧﺪﺍﺭﺩ‪ ،‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﺑﻪ ﺟﻨﺒﻪ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﮐﺮﺩﻥ ﺭﺍﻩ ﺣﻞ ﺗﻮﺟﻪ ﻣﻲ‬
‫ﺷﻮﺩ‪..‬‬
‫‪۱.۴‬‬
‫ﻭي ﺳﻲ ﺟﻲ ﺗﻮﺯﻳﻊ ﺷﺪﻩ‬
‫ﻭي ﺳﻲ ﺟﻲ ﻳﮏ ﻧﺘﻴﺠﻪ ﺍﻣﻴﺪ ﺑﺨﺶ ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺍﺳﺖ ﮐﻪ ﺩﺭ ﺁﻥ ﺧﺮﻭﺟﻲ ﺑﺮ ﺍﺳﺎﺱ ﺑﻴﺸﻴﻨﻪ ﮐﺮﺩﻥ ﺗﺎﺑﻊ ﺭﻓﺎﻩ ﺍﺟﺘﻤﺎﻋﻲ ﺗﻌﻴﻴﻦ‬
‫ﻣﻲ ﺷﻮﺩ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ‪:‬‬
‫∑‬
‫‪W v o‬‬
‫)‪( ۱‬‬
‫)‪( ۲‬‬
‫ﺩﺭ ﻓﺮﻣﻮﻝ ‪۱‬‬
‫ﻭ‬
‫ﻣﻘﺪﺍﺭ ﺍﺭﺯﺷﻲ ﺍﺳﺖ ﮐﻪ ﺧﺮﻭﺟﻲ ‪ o‬ﺑﺮﺍي ‪ i‬ﺩﺍﺭﺩ ﻭ ﺩﺭ ﻓﺮﻣﻮﻝ ‪ W ،۲‬ﻣﻘﺪﺍﺭ ﮐﻞ ﻣﻘﺪﺍﺭ ﺭﻓﺎﻩ ﺍﺟﺘﻤﺎﻋﻲ ﺑﻴﺸﻴﻨﻪ ﺍﺳﺖ‬
‫ﻣﻘﺪﺍﺭي ﺭﻓﺎﻩ ﺍﺟﺘﻤﺎﻋﻲ ﺑﻴﺸﻴﻨﻪ ﺑﺮﺍي ﺳﺎﻳﺮ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﺻﻮﺭﺕ ﻧﺒﻮﺩ ﺑﺎﺯﻳﮑﻦ ‪ i‬ﺍﺳﺖ‪.‬‬
‫ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﺮﺍي ﺍﻳﻦ ﻣﺴﺌﻠﻪ‪ ،‬ﺑﺎﺯﻳﮑﻦ ﺩﻭ ﻋﻤﻞ ﺩﺍﺭﺩ‪ ،‬ﻳﮑﻲ ﻣﺮﺑﻮﻁ ﺑﻪ ﺁﺷﮑﺎﺭﺳﺎﺯي ﻣﻘﺎﺩﻳﺮ ﺍﺭﺯﺵ ﮔﺬﺍﺭي‬
‫ﻫﺎ ﻭ ﺩﻳﮕﺮي ﺍﻧﺠﺎﻡ ﻣﺤﺎﺳﺒﺎﺕ ﻣﺮﺑﻮﻁ ﺑﻪ‬
‫ﻭ‪W‬ﻭ‬
‫ﺍﺳﺖ ﮐﻪ ﺑﻪ ﺩﻭﻣﻴﻦ ﻋﻤﻞ ﺩﺳﺘﮑﺎﺭي ﻣﺤﺎﺳﺒﺎﺗﻲ ﻣﻲ ﮔﻮﻳﻴﻢ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ‬
‫ﺑﺎﺯﻳﮑﻨﺎﻥ ﻣﻲ ﺗﻮﺍﻧﻨﺪ ﺍﻳﻦ ﻣﻘﺎﺩﻳﺮ ﺭﺍ ﻏﻴﺮ ﻭﺍﻗﻌﻲ ﺟﻠﻮﻩ ﺩﻫﻨﺪ ﺗﺎ ﺳﻮﺩ ﺑﺒﺮﻧﺪ‪ .‬ﺑﺮﺍي ﻣﺜﺎﻝ ﺩﺭ ﻣﺰﺍﻳﺪﻩ ﻗﻴﻤﺖ ﺩﻭﻡ ﮐﻪ ﺣﺎﻟﺖ ﺧﺎﺻﻲ ﺍﺯ ﻣﮑﺎﻧﻴﺰﻡ‬
‫ﻭي ﺳﻲ ﺟﻲ ﺍﺳﺖ‪ ،‬ﻓﺮﺽ ﮐﻨﻴﺪ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﻳﮏ ﺷﺒﮑﻪ ﺑﺎ ﺗﻮﭘﻮﻟﻮﮊي ﺣﻠﻘﻪ ﺍي ﻫﺴﺘﻨﺪ ﻭ ﻣﮑﺎﻧﻴﺰﻡ ﺑﺎ ﺍﺭﺳﺎﻝ ﺩﻭ ﻗﻴﻤﺖ ﺑﺎﻻ ﺑﻪ ﻫﻤﺴﺎﻳﮕﺎﻥ‬
‫ﺧﻮﺩ ﺍﻧﺠﺎﻡ ﻣﻲ ﺩﻫﻨﺪ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﻳﮏ ﺑﺎﺯﻳﮑﻦ ﻣﻲ ﺗﻮﺍﻧﺪ ﺑﺎ ﻏﻴﺮ ﻭﺍﻗﻌﻲ ﺟﻠﻮﻩ ﺩﺍﺩﻥ ﻣﻘﺎﺩﻳﺮ ﺍﺭﺯﺵ ﮔﺬﺍﺭي ﺧﻮﺩ ﺑﻪ ﺩﻳﮕﺮﺍﻥ ﻭ ﻫﻤﭽﻨﻴﻦ‬
‫ﻏﻴﺮ ﻭﺍﻗﻌﻲ ﺟﻠﻮﻩ ﺩﺍﺩﻥ ﺩﻭ ﻣﻘﺪﺍﺭ ﺑﺎﻻ ﺩﺭ ﻣﺰﺍﻳﺪﻩ‪ ،‬ﻣﻘﺪﺍﺭ ﺧﻮﺩ ﺭﺍ ﺑﺎﻻﺗﺮ ﺍﺯ ﻫﻤﻪ ﻗﺮﺍﺭ ﺩﻫﺪ ﻭ ﺩﻭﻣﻴﻦ ﻣﻘﺪﺍﺭ ﺭﺍ ﺁﻥ ﻗﺪﺭ ﭘﺎﻳﻴﻦ ﻧﺸﺎﻥ ﺩﻫﺪ ﺗﺎ‬
‫ﺑﻪ ﺳﻮﺩ ﺑﻴﺸﺘﺮي ﺑﺮﺳﺪ‪.‬‬
‫ﺭﺍﻫﻲ ﮐﻪ ﺑﺮﺍي ﺟﻠﻮﮔﻴﺮي ﺩﺳﺘﮑﺎﺭي ﻣﺤﺎﺳﺒﺎﺗﻲ ﭘﻴﺸﻨﻬﺎﺩ ﻣﻲ ﺷﻮﺩ ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ ﺍﺯ ﺗﮑﺮﺍﺭ ﺍﺳﺖ‪ .‬ﺩﺭ ﺍﻳﻦ ﺭﺍﻩ ﺣﻞ‪ ،‬ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﻪ‬
‫ﺩﻭ ﮔﺮﻭﻩ ﺷﮑﺴﺘﻪ ﻣﻲ ﺷﻮﻧﺪ‪ .‬ﺩﺭ ﻫﺮ ﮔﺮﻭﻩ ﻣﺤﺎﺳﺒﺎﺕ‬
‫ﻭ‬
‫ﺍﻧﺠﺎﻡ ﻣﻲ ﺷﻮﺩ ﻭ ﻧﺘﻴﺠﻪ ﺑﻪ ﻳﮏ ﻣﺮﮐﺰ ﮔﺰﺍﺭﺵ ﻣﻲ ﺷﻮﺩ) ﻓﺮﺽ ﻣﺲ ﺷﻮﺩ‬
‫ﻳﮏ ﻣﺮﮐﺰ ﺩﺍﺭﻳﻢ ﺍﻣﺎ ﺳﻌﻲ ﻣﻲ ﺷﻮﺩ ﻧﻘﺶ ﺁﻥ ﺭﺍ ﺗﺎ ﺁﻥ ﺟﺎ ﮐﻪ ﻣﻤﮑﻦ ﺍﺳﺖ ﺩﺭ ﺍﺟﺮﺍي ﻣﮑﺎﻧﻴﺰﻡ ﮐﻢ ﮐﻨﻴﻢ(‪ .‬ﺍﮔﺮ ﻣﻘﺎﺩﻳﺮ ﺑﺎ ﻫﻢ ﻣﻐﺎﻳﺮﺕ‬
‫ﺩﺍﺷﺖ ﻳﮏ ﺗﻨﺒﻴﻪ ﺑﺰﺭﮒ ﺑﺮﺍي ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﻣﻲ ﺷﻮﺩ ﻭ ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﺳﻮﺩ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺑﻪ ﺷﺪﺕ ﮐﺎﻫﺶ ﻣﻲ ﻳﺎﺑﺪ‪ .‬ﺑﻪ ﺍﻳﻦ‬
‫ﺗﺮﺗﻴﺐ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻣﺤﺎﺳﺒﺎﺕ ﺭﺍ ﺑﻪ ﺩﺭﺳﺘﻲ ﺍﻧﺠﺎﻡ ﺧﻮﺍﻫﻨﺪ ﺩﺍﺩ ﻭ ﮔﺰﺍﺭﺵ ﺧﻮﺍﻫﻨﺪ ﮐﺮﺩ‪.‬‬
‫ﺍﺯ ﻃﺮﻑ ﺩﻳﮕﺮ ﭼﻮﻥ ﻭي ﺳﻲ ﺟﻲ‪ ،‬ﺧﻮﺩ ﻳﮏ ﻣﮑﺎﻧﻴﺰﻡ ﺿﺪ ﺍﺳﺘﺮﺍﺗﮋي‪ ١١‬ﺍﺳﺖ‪ ،‬ﻣﻘﺎﺩﻳﺮ ﻧﻴﺰ ﺑﻪ ﺩﺭﺳﺘﻲ ﺁﺷﮑﺎﺭﺳﺎﺯي ﺧﻮﺍﻫﻨﺪ‬
‫ﮐﺮﺩ ﻭ ﺑﺎ ﺍﻋﻤﺎﻝ ﺭﺍﻩ ﺣﻞ ﺗﮑﺮﺍﺭ ﺩﺭ ﮐﻞ ﻣﺤﺎﺳﺒﺎﺕ ﺑﻪ ﻃﻮﺭ ﺻﺎﺩﻗﺎﻧﻪ ﺍﻧﺠﺎﻡ ﻭ ﮔﺰﺍﺭﺵ ﺧﻮﺍﻫﺪ ﺷﺪ‪ .‬ﭘﺲ ﺩﺭ ﮐﻞ ﻫﺮ ﺩﻭ ﻋﻤﻞ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻣﻮﺭﺩ‬
‫ﺗﻮﺟﻪ ﻗﺮﺍﺭ ﮔﺮﻓﺖ ﻭ ﺭﺍﻩ ﺣﻠﻲ ﺑﺮﺍي ﻣﻘﺎﺑﻠﻪ ﺑﺎ ﺭﻓﺘﺎﺭ ﺧﻮﺩﺧﻮﺍﻫﺎﻧﻪ ﺍﺭﺍﺋﻪ ﺷﺪ‪.‬‬
‫‪VCG ١٠‬‬
‫‪strategy‐proof ١١‬‬
‫ﺍﻟﺒﺘﻪ ﻣﺤﺎﺳﺒﻪ ﺻﺎﺩﻗﺎﻧﻪ ﮐﻪ ﺩﺭ ﺍﻳﻦ ﺟﺎ ﻣﻄﺮﺡ ﺷﺪ ﻳﮏ ﺍﺳﺘﺮﺍﺗﮋي ﺣﮑﻤﻔﺮﻣﺎ‪ ١٢‬ﻧﻴﺴﺖ‪ ،‬ﭼﻮﻥ ﺍﮔﺮ ﺳﺎﻳﺮ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻏﻴﺮ ﺍﺯ ﺑﺎﺯﻳﮑﻦ‬
‫‪ i‬ﺗﺼﻤﻴﻢ ﺑﻪ ﻳﮏ ﺧﺮﻭﺟﻲ ﻏﻴﺮ ﺑﻬﻴﻨﻪ ﻣﺸﺘﺮﮎ ﺑﮕﻴﺮﻧﺪ‪ ،‬ﺑﻬﺘﺮﻳﻦ ﮐﺎﺭ ﺑﺮﺍي ﺑﺎﺯﻳﮑﻦ ‪ i‬ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﺍﻭ ﻧﻴﺰ ﺗﺼﻤﻴﻢ ﺑﻪ ﻫﻤﺎﻥ ﺧﺮﻭﺟﻲ ﻏﻴﺮ‬
‫ﺑﻬﻴﻨﻪ ﺑﮕﻴﺮﺩ ﺗﺎ ﺍﺯ ﺗﻨﺒﻴﻪ ﻧﺎﺷﻲ ﺍﺯ ﻧﺎﻫﻤﺎﻫﻨﮕﻲ ﻧﺘﺎﻳﺞ ﺑﻪ ﺩﻭﺭ ﺑﺎﺷﺪ‪ .‬ﭘﺲ ﺩﺭ ﻣﻮﺭﺩ ﻣﺴﺌﻠﻪ ﺩﺳﺘﮑﺎﺭي ﻣﺤﺎﺳﺒﺎﺗﻲ ﮐﻪ ﺩﺭ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ‬
‫ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻣﻄﺮﺡ ﻣﻲ ﺷﻮﺩ‪ ،‬ﺑﻪ ﺟﺎي ﺗﻌﺎﺩﻝ ﻣﺮﻭﺑﻂ ﺑﻪ ﺍﺳﺘﺮﺍﺗﮋي ﺣﮑﻤﻔﺮﻣﺎ ﺍﺯ ﺗﻌﺎﺩﻝ ﻧﺶ ﺍﮐﺲ ﭘﺴﺖ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﺷﻮﺩ‪ .‬ﺍﻟﺒﺘﻪ ﺑﺎﻳﺪ‬
‫ﺩﺍﻧﺴﺖ ﮐﻪ ﺍﻳﻦ ﺗﻌﺎﺩﻝ ﺑﺎ ﺁﻧﮑﻪ ﺍﺯ ﺗﻌﺎﺩﻝ ﺣﮑﻤﻔﺮﻣﺎ ﺿﻌﻴﻔﺘﺮ ﺍﺳﺖ ﺍﻣﺎ ﺍﺯ ﻣﻐﻬﻮﻡ ﺗﻌﺎﺩﻝ ﻧﺶ ﻣﻌﻤﻮﻟﻲ ﻗﻮي ﺗﺮ ﺍﺳﺖ‪ ،‬ﺯﻳﺮﺍ ﺩﺭ ﺍﻳﻦ ﺟﺎ‬
‫ﺑﺎﺯﻳﮑﻨﺎﻥ ﻧﻴﺎﺯ ﻧﺪﺍﺭﻧﺪ ﮐﻪ ﻣﻘﺎﺩﻳﺮ ﺧﺼﻮﺻﻲ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺩﻳﮕﺮ ﺭﺍ ﺑﺪﺍﻧﻨﺪ‪.‬‬
‫‪۲.۴‬‬
‫ﻣﺴﻴﺮﻳﺎﺑﻲ ﻣﻴﺎﻥ ﻧﺎﺣﻴﻪ ﺍي‬
‫ﺩﺭ ﺍﻳﻦ ﻣﺴﺌﻠﻪ ﺷﺒﮑﻪ ﺍﺯ ﻧﺎﺣﻴﻪ ﻫﺎي ﻣﺨﺘﻠﻒ ﺩﺭﺳﺖ ﺷﺪﻩ ﺍﺳﺖ ﮐﻪ ﻫﺮ ﻧﺎﺣﻴﻪ ﻳﮏ ﺳﻴﺴﺘﻢ ﺧﻮﺩ ﻣﺨﺘﺎﺭ‪ ١٣‬ﻳﺎ ﺑﻪ ﺍﺧﺘﺼﺎﺭ ‪ AS‬ﻧﺎﻡ ﺩﺍﺭﺩ‪.‬‬
‫ﻫﺮ ‪ AS‬ﻳﮏ ﺑﺎﺯﻳﮑﻦ ﺩﺭ ﺷﺒﮑﻪ ﺍﺳﺖ ﻭ ﺍﻫﺪﺍﻑ ﻣﻨﻔﻌﺖ ﻃﻠﺒﺎﻧﻪ ﺧﻮﺩ ﺭﺍ ﺩﺍﺭﺩ‪ .‬ﻣﺴﺌﻠﻪ ﻣﺮﺑﻮﻁ ﺑﻪ ﻣﺴﻴﺮ ﻳﺎﺑﻲ ﺑﻴﻦ ﺍﻳﻦ ‪ AS‬ﻫﺎ ﺍﺳﺖ ﻭ‬
‫ﻣﺴﻴﺮﻳﺎﺑﻲ ﺩﺍﺧﻞ ﻫﺮ ‪ AS‬ﻣﻄﺮﺡ ﻧﻴﺴﺖ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﻣﻲ ﺗﻮﺍﻥ ﺷﺒﮑﻪ ﺭﺍ ﺑﻪ ﺻﻮﺭﺕ ﻳﮏ ﮔﺮﺍﻑ )‪ G(N,L‬ﻣﺪﻝ ﮐﺮﺩ ﮐﻪ ﺩﺭ ﺁﻥ ‪N‬‬
‫ﻣﺠﻤﻮﻋﻪ ﮔﺮﻩ ﻫﺎ ﻳﺎ ﻫﻤﺎﻥ ‪ AS‬ﻫﺎ ﺍﺳﺖ ﻭ ‪ L‬ﻣﺠﻤﻮﻋﻪ ﻳﺎﻝ ﻫﺎ ﺍﺳﺖ ﮐﻪ ﻫﺮ ﻳﺎﻝ ﻧﺸﺎﻥ ﺩﻫﻨﺪﻩ ﺍﺗﺼﺎﻝ ﺑﻴﻦ ﺩﻭ ﮔﺮﻩ ﻣﺨﺘﻠﻒ ﺍﺳﺖ‪ .‬ﺩﺭ ﺍﻳﻦ‬
‫ﺟﺎ ﭼﻮﻥ ﻫﺮ ﮔﺮﻩ ﻧﻤﻲ ﺧﻮﺍﻫﺪ ﺍﻃﻼﻋﺎﺕ ﺧﻮﺩ ﺭﺍ ﺩﺭ ﺍﺧﺘﻴﺎﺭ ﻣﺮﮐﺰ ﻗﺮﺍﺭ ﺩﻫﺪ‪ ،‬ﻧﻤﻲ ﺗﻮﺍﻥ ﺍﺯ ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎي ﻣﺘﻤﺮﮐﺰ ﺍﺳﺘﻔﺎﺩﻩ ﮐﺮﺩ‪ .‬ﺧﻮﺩ ﮔﺮﻩ‬
‫ﻫﺎ ﻫﺴﺘﻨﺪ ﮐﻪ ﺑﺎﻳﺪ ﻣﺴﻴﺮ ﺑﻴﻦ ﺩﻭ ﮔﺮﻩ ﺭﺍ ﻣﺤﺎﺳﺒﻪ ﮐﻨﻨﺪ‪ .‬ﺩﺭ ﺿﻤﻦ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﺗﻌﺪﺍﺩ ﺯﻳﺎﺩ ‪ AS‬ﻫﺎ ﻧﻴﺎﺯ ﺑﻪ ﺍﻟﮕﻮﺭﻳﺘﻢ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺩﺭ ﺍﻳﻦ‬
‫ﺟﺎ ﻣﻄﺮﺡ ﺍﺳﺖ‪.‬‬
‫ﻫﺮ ﮔﺮﻩ ‪ k‬ﺑﺮﺍي ﮔﺬﺭﺩﻫﻲ ﻳﮏ ﺑﺴﺘﻪ ﺑﻪ ﻫﻤﺴﺎﻳﻪ ﺧﻮﺩ ﻫﺰﻳﻨﻪ‬
‫ﺭﺍ ﻣﺘﺤﻤﻞ ﻣﻲ ﺷﻮﺩ‪.‬‬
‫ﺗﻌﺪﺍﺩ ﺑﺴﺘﻪ ﻫﺎﻳﻲ ﺍﺳﺖ ﮐﻪ ﺍﺯ‬
‫ﻣﺒﺪﺍ ‪ i‬ﺑﻪ ﻣﻘﺼﺪ ‪ j‬ﺍﺭﺳﺎﻝ ﻣﻲ ﺷﻮﺩ‪ .‬ﻓﺮﺽ ﻣﻲ ﺷﻮﺩ ﺳﻴﺎﺳﺖ ‪ AS‬ﻫﺎ ﺩﺭ ﺍﻧﺘﺨﺎﺏ ﻣﺴﻴﺮ‪ ،‬ﻣﺴﻴﺮ ﺑﺎ ﮐﻤﺘﺮﻳﻦ ﻫﺰﻳﻨﻪ ﺍﺳﺖ‪ .‬ﻣﺴﻴﺮ ﺍﻧﺘﺨﺎﺑﻲ‬
‫ﺭﺍ ‪ LCP‬ﻣﻲ ﻧﺎﻣﻴﻢ‪c; i, j .‬‬
‫ﻳﮏ ﺗﺎﺑﻊ ﺍﺳﺖ ﮐﻪ ﺩﻭ ﻣﻘﺪﺍﺭ ‪ 0‬ﻭ ‪ 1‬ﻣﻲ ﮔﻴﺮﺩ‪ .‬ﻣﻘﺪﺍﺭ ‪ ،0‬ﻳﻌﻨﻲ ﮔﺮﻩ ‪ k‬ﺭﻭي ﮐﻮﺗﺎﻫﺘﺮﻳﻦ ﻣﺴﻴﺮ ﻣﻴﺎﻥ ﺩﻭ‬
‫ﮔﺮﻩ ‪ i‬ﻭ ‪ j‬ﻗﺮﺍﺭ ﻧﺪﺍﺭﺩ ﻭ ‪ c‬ﺑﺮﺩﺍﺭ ﻫﺰﻳﻨﻪ ﻫﺎي ﺍﻋﻼﻣﻲ ﺍﺯ ﺳﻮي ﻫﻤﻪ ﮔﺮﻩ ﻫﺎ ﺍﺳﺖ ﻭ ﻣﻘﺪﺍﺭ ‪ ۱‬ﺑﻪ ﻗﺮﺍﺭ ﺩﺍﺷﺘﻦ ‪ k‬ﺭﻭي ﻣﺴﻴﺮ ﺑﻬﻴﻨﻪ ﺑﻴﻦ ‪ i‬ﻭ ‪j‬‬
‫ﺩﻻﻟﺖ ﺩﺍﺭﺩ‪.‬‬
‫ﺩﺭ ]‪ [5‬ﺍﺑﺘﺪﺍ ﻣﮑﺎﻧﻴﺰﻡ ﻭي ﺳﻲ ﺟﻲ ﺑﺮﺍي ﻳﮏ ﺣﺎﻟﺖ ﮐﻠﻲ ﮐﻪ ﻣﺴﻴﺮﻫﺎي ﻣﻴﺎﻥ ﻫﻤﻪ ﺯﻭﺝ ﮔﺮﻩ ﻫﺎﻳﻲ ﮐﻪ ﺩﺭﺧﻮﺍﺳﺖ ﻣﺴﻴﺮ‬
‫ﮐﺮﺩﻩ ﺍﻧﺪ‪ ،‬ﮔﺴﺘﺮﺵ ﺩﺍﺩﻩ ﺷﺪﻩ ﻭ ﺑﻌﺪ ﺑﺮ ﺍﺳﺎﺱ ﻋﻤﻠﮑﺮﺩ ﭘﺮﻭﺗﮑﻞ ﻣﻌﺮﻭﻑ ‪ ،BGP١٤‬ﻳﮏ ﻣﮑﺎﻧﻴﺰﻡ ﻣﺤﺎﺳﺒﻪ ﭘﺮﺩﺍﺧﺘﻲ ﻫﺎ ﺑﻪ ﺻﻮﺭﺕ ﺗﻮﺯﻳﻊ‬
‫ﺷﺪﻩ ﺍﺭﺍﺋﻪ ﻣﻲ ﺩﻫﺪ‪ .‬ﺩﺭ ﺍﺩﺍﻣﻪ ﺑﻪ ﻫﺮ ﮐﺪﺍﻡ ﺍﺯ ﺍﻳﻦ ﻣﻮﺍﺭﺩ ﻣﻲ ﭘﺮﺩﺍﺯﻳﻢ‪.‬‬
‫ﻣﮑﺎﻧﻴﺰﻡ ﻭي ﺳﻲ ﺟﻲ ﺭﺍ ﺑﺮﺍي ﺍﻳﻦ ﻣﺴﺌﻠﻪ ﺑﻪ ﺍﻳﻦ ﺻﻮﺭﺕ ﻣﻲ ﺗﻮﺍﻥ ﺍﺳﺘﻔﺎﺩﻩ ﻧﻤﻮﺩ ﮐﻪ ﺍﺑﺘﺪﺍ ﻓﺮﺽ ﻣﻲ ﺷﻮﺩ ﺍﮔﺮ ﺑﺎﺯﻳﮑﻨﺎﻥ‬
‫ﺻﺎﺩﻗﺎﻧﻪ ﻣﻘﺎﺩﻳﺮ ﺧﻮﺩ ﺭﺍ ﺍﺯ ﻃﺮﻳﻖ ﺑﺮﺩﺍﺭ ‪ c‬ﺍﻋﻼﻡ ﮐﻨﻨﺪ‪ ،‬ﻣﮑﺎﻧﻴﺰﻡ ﺑﺎﻳﺪ ﺑﻪ ﮐﻤﻴﻨﻪ ﮐﺮﺩﻥ ﺗﺎﺑﻊ )‪ V(c‬ﮐﻪ ﺑﺼﻮﺭﺕ ﺯﻳﺮ ﺗﻌﺮﻳﻒ ﻣﻲ ﺷﻮﺩ‬
‫ﺑﭙﺮﺩﺍﺯﺩ‪:‬‬
‫)‪( ۳‬‬
‫‪; ,‬‬
‫∑‬
‫‪∑,‬‬
‫∑‬
‫ﮐﻤﻴﻨﻪ ﮐﺮﺩﻥ ‪ V‬ﻣﻌﺎﺩﻝ ﮐﻤﻴﻨﻪ ﮐﺮﺩﻥ ﻣﺴﻴﺮ ﻣﻴﺎﻥ ﻫﺮ ‪ i‬ﻭ ‪ j‬ﺍﺳﺖ‪ .‬ﻣﺤﺎﺳﺒﻪ ﺍﻳﻦ ﻣﻘﺪﺍﺭ ﮐﻤﻴﻨﻪ ﺗﻮﺳﻂ ﻳﮑﻲ ﺍﺯ ﭘﺮﻭﺗﮑﻞ ﻫﺎي ﻣﺴﻴﺮﻳﺎﺑﻲ‬
‫ﻣﻲ ﺗﻮﺍﻧﺪ ﺍﻧﺠﺎﻡ ﺷﻮﺩ ﮐﻪ ﺩﺭ ﺍﻳﻦ ﺟﺎ ﺍﺯ ‪ BGP‬ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﺷﻮﺩ‪ .‬ﺩﺭ ﻭﺍﻗﻊ ﺍﮔﺮ ﺑﺎﺯﻳﮑﻨﺎﻥ ﻣﻘﺎﺩﻳﺮ ﺧﻮﺩ ﺭﺍ ﺻﺎﺩﻗﺎﻧﻪ ﺍﻋﻼﻡ ﮐﻨﻨﺪ‪ ،‬ﺑﺎ ﺍﺳﺘﻔﺎﺩﻩ‬
‫ﺍﺯ ‪ ،BGP‬ﺣﺘﻤﺎ ﻣﺴﻴﺮ ﻫﺎي ‪ LCP‬ﭘﻴﺪﺍ ﺧﻮﺍﻫﻨﺪ ﺷﺪ ﻭ ﺗﺎﺑﻊ ﺭﻓﺎﻩ ﺍﺟﺘﻤﺎﻋﻲ ﺑﻪ ﺑﻴﺸﻴﻨﻪ ﻣﻘﺪﺍﺭ ﺧﻮﺩ ﻣﻲ ﺭﺳﺪ‪ .‬ﭘﺲ ﺗﻨﻬﺎ ﮐﺎﺭي ﮐﻪ ﻣﻲ‬
‫‪dominant strategy ١٢‬‬
‫‪autonomous system ١٣‬‬
‫‪ ١٤‬ﮐﻠﻤﻪ ﺍﺧﺘﺼﺎﺭي ﺑﺮﺍي ‪Border Gateway Protocol‬‬
‫ﻣﺎﻧﺪ ﺍﻳﻦ ﺍﺳﺖ ﮐﻪ ﺑﺎ ﻳﮏ ﻣﮑﺎﻧﻴﺰﻡ ﺑﺮﺍي ﻣﺤﺎﺳﺒﻪ ﭘﺮﺩﺍﺧﺘﻲ ﻫﺎ ﺑﺎﺯﻳﮑﻨﺎﻥ ﺭﺍ ﻭﺍﺩﺍﺭ ﺑﻪ ﺭﺍﺳﺘﮕﻮﻳﻲ ﮐﺮﺩ ﮐﻪ ﺩﺭ ﺍﺩﺍﻣﻪ ﺑﻪ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ‬
‫ﻣﺤﺎﺳﺒﻪ ﭘﺮﺩﺍﺧﺘﻲ ﻫﺎ ﻣﻲ ﭘﺮﺩﺍﺯﻳﻢ‪.‬‬
‫ﺑﺮﺍي ﻣﺤﺎﺳﺒﻪ ﭘﺮﺩﺍﺧﺘﻲ ﻣﻲ ﺗﻮﺍﻥ ﻣﮑﺎﻧﻴﺰﻡ ﻭي ﺳﻲ ﺟﻲ ﺭﺍ ﺑﻪ ﺍﻳﻦ ﺻﻮﺭﺕ ﮔﺴﺘﺮﺵ ﺩﺍﺩ‪.‬‬
‫‪p‬‬
‫)‪( ۴‬‬
‫)‪( ۵‬‬
‫‪NT‬‬
‫‪c; i, j c‬‬
‫‪∑,‬‬
‫‪NI‬‬
‫∑‬
‫‪c| ∞; i, j c‬‬
‫‪NI‬‬
‫∑‬
‫‪c I c; i, j‬‬
‫‪p‬‬
‫ﺩﺭ ﻓﺮﻣﻮﻝ ﺷﻤﺎﺭﻩ ‪ c| ∞ ،۵‬ﻳﻌﻨﻲ ﻫﺰﻳﻨﻪ ﺑﺎﺯﻳﮑﻦ ‪ k‬ﺑﻲ ﻧﻬﺎﻳﺖ ﺍﺳﺖ ﻭ ﺩﺭ ﻭﺍﻗﻊ ﺑﻪ ﻣﻌﻨﻲ ﺣﺬﻑ ‪ k‬ﺍﺯ ﺑﺎﺯي ﺍﺳﺖ‪ p .‬ﻫﺰﻳﻨﻪ ﺍﺭﺳﺎﻝ ﻳﮏ‬
‫ﺑﺴﺘﻪ ﺑﺎ ﻣﺒﺪﺍ ‪ i‬ﻭ ﻣﻘﺼﺪ ‪ j‬ﺗﻮﺳﻂ ‪ k‬ﺍﺳﺖ‪.‬‬
‫ﺣﺎﻝ ﺑﺮﺍي ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﮐﺮﺩﻥ ﻣﺤﺎﺳﺒﻪ ﭘﺮﺩﺍﺧﺘﻲ ﻫﺎ ﺍﺯ ﺳﺎﺧﺘﺎﺭ ‪ BGP‬ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ ﺷﻮﺩ‪ BGP .‬ﻳﮏ ﭘﺮﻭﺗﮑﻞ ﻣﺴﻴﺮ‪-‬‬
‫ﺑﺮﺩﺍﺭي‪ ١٥‬ﺍﺳﺖ ﮐﻪ ﻫﺮ ﮔﺮﻩ ‪ i‬ﺑﺮﺍي ﻫﺮ ﮔﺮﻩ ﻣﻘﺼﺪ ‪ j‬ﻳﮏ ﻣﺴﻴﺮ ﺑﺎ ﮐﻤﺘﺮﻳﻦ ﻫﺰﻳﻨﻪ ﺭﺍ ﺩﺭ ﻳﮏ ﺟﺪﻭﻝ ﻣﺴﻴﺮﻳﺎﺑﻲ ﻧﮕﻪ ﻣﻲ ﺩﺍﺭﺩ‪ .‬ﺑﺎ ﺗﻐﻴﻴﺮ‬
‫ﺍﻳﻦ ﺟﺪﻭﻝ‪ ،‬ﺑﻪ ﻫﻤﺴﺎﻳﮕﺎﻥ ﺧﻮﺩ ﺍﻃﻼﻉ ﻣﻲ ﺩﻫﺪ ﺗﺎ ﺁﻧﻬﺎ ﻧﻴﺰ ﺟﺪﺍﻭﻝ ﺧﻮﺩ ﺭﺍ ﺩﺭ ﺻﻮﺭﺕ ﻟﺰﻭﻡ ﺑﻪ ﺭﻭﺯ ﮐﻨﻨﺪ‪ .‬ﺗﻐﻴﻴﺮ ﻳﺎ ﺗﻮﺳﻂ ﺍﻋﻼﻡ ﺧﻮﺩ‬
‫ﮔﺮﻩ ﻣﻘﺼﺪ ﺩﺭ ﻫﻤﺴﺎﻳﮕﺎﻥ ﺁﻥ ﺍﻧﺠﺎﻡ ﻣﻲ ﮔﻴﺮﺩ ﻭ ﻳﺎ ﻭﻗﺘﻲ ﮔﺮﻩ ﺍي ﺍﺯ ﻫﻤﺴﺎﻳﻪ ﺍي ﭘﻴﺎﻣﻲ ﺩﺭﻳﺎﻓﺖ ﮐﺮﺩ ﮐﻪ ﺑﺎﻋﺚ ﺗﻐﻴﻴﺮ ﺷﺪ‪ ،‬ﺍﻳﻦ ﺗﻐﻴﻴﺮ ﺭﺍ‬
‫ﺑﻪ ﻫﻤﺴﺎﻳﮕﺎﻥ ﺩﻳﮕﺮ ﺧﻮﺩ ﺍﻃﻼﻉ ﻣﻲ ﺩﻫﺪ ﺗﺎ ﺁﻧﻬﺎ ﻧﻴﺰ ﺗﻐﻴﻴﺮ ﺩﺭ ﺟﺪﺍﻭﻝ ﺧﻮﺩ ﺭﺍ ﺍﻧﺠﺎﻡ ﺩﻫﻨﺪ‪.‬‬
‫ﺷﮑﻞ ‪ .۱‬ﺩﺭﺧﺖ ﻣﺴﻴﺮﺩﻫﻲ ﺑﺮﺍي ﮔﺮﻩ ‪[5]..Z‬‬
‫ﺑﺮﺍي ﻣﺤﺎﺳﺒﻪ ﭘﺮﺩﺍﺧﺘﻲ ﻫﺎ ﺑﻪ ﺻﻮﺭﺕ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﺮ ﺍﺳﺎﺱ ﺭﻓﺘﺎﺭ ‪ BGP‬ﻋﻤﻞ ﻣﻲ ﺷﻮﺩ‪ .‬ﺑﺎ ﻓﺮﺽ ﺍﻳﻨﮑﻪ )‪ P(c;i,j‬ﻧﺸﺎﻥ‬
‫ﺩﻫﻨﺪﻩ ‪ LCP‬ﺍﺯ ‪ i‬ﺑﻪ ‪ j‬ﺍﺳﺖ‪ ،‬ﻭ )‪ c(i,j‬ﻫﺰﻳﻨﻪ ﺍﻳﻦ ﻣﺴﻴﺮ ﺍﺳﺖ‪ ،‬ﻭ‬
‫‪; ,‬‬
‫ﻣﺴﻴﺮ ﺑﺎ ﮐﻤﺘﺮﻳﻦ ﻫﺰﻳﻨﻪ ﺑﺪﻭﻥ ﺩﺭ ﻧﻈﺮ ﮔﺮﻓﺘﻦ ‪ k‬ﺍﺳﺖ‪،‬‬
‫‪ p‬ﺑﻪ ﺍﻳﻦ ﺻﻮﺭﺕ ﻣﺤﺎﺳﺒﻪ ﻣﻲ ﺷﻮﺩ‪:‬‬
‫) ‪(۶‬‬
‫‪Path‐vector ١٥‬‬
‫‪c i, j‬‬
‫‪c; i, j‬‬
‫‪Cost P‬‬
‫‪p‬‬
‫ﺑﺮﺍي ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﮐﺮﺩﻥ ﻣﺤﺎﺳﺒﺎﺕ‪ ،‬ﺟﻬﺖ ﻣﺤﺎﺳﺒﻪ ‪ p‬ﺍﺯ ﺍﻃﻼﻋﺎﺕ ﻫﻤﺴﺎﻳﮕﺎﻥ ﮔﺮﻩ ﺩﺭ ﻣﻮﺭﺩ ﻫﺰﻳﻨﻪ ﻫﺎ ﻭ ﭘﺮﺩﺍﺧﺘﻲ ﻫﺎ ﺍﺳﺘﻔﺎﺩﻩ ﻣﻲ‬
‫ﺷﻮﺩ ﻭ ﺍﻳﻦ ﺭﻭﻳﻪ ﺍﺩﺍﻣﻪ ﻣﻲ ﻳﺎﺑﺪ ﺗﺎ ﺩﺭ ﻧﻬﺎﻳﺖ ﻫﺰﻳﻨﻪ ﻫﺎ ﺑﻪ ﻣﻘﺎﺩﻳﺮ ﭘﺎﻳﺪﺍﺭ ﺑﺮﺳﻨﺪ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﺑﺎﻳﺪ ﺭﺍﺑﻄﻪ ﺍي ﻣﻴﺎﻥ ﻣﻘﺪﺍﺭ ‪ p‬ﺩﺭ ‪ i‬ﻭ‬
‫ﮔﺮﻩ ﻫﻤﺴﺎﻳﻪ ‪ i‬ﺑﻪ ﺩﺳﺖ ﺁﻭﺭﺩ‪ .‬ﺑﺮﺍي ﺍﻳﻦ ﮐﺎﺭ ﻳﮏ ﺩﺭﺧﺖ ﺍﺯ ﺭﻭي ﮔﺮﺍﻑ ﺑﺮﺍي ﻫﺮ ﮔﺮﻩ ﻣﻘﺼﺪ ‪ j‬ﺳﺎﺧﺘﻪ ﻣﻲ ﺷﻮﺩ‪ .‬ﺍﻳﻦ ﺩﺭﺧﺖ ﮐﻪ ﺭﻳﺸﻪ‬
‫ﺁﻥ ‪ j‬ﺍﺳﺖ ﺑﺎ )‪ T(j‬ﻧﺸﺎﻥ ﺩﺍﺩﻩ ﻣﻲ ﺷﻮﺩ ﮐﻪ ﺩﺭ ﺁﻥ ﻫﺮ ﻣﺴﻴﺮ ﺍﺯ ﻫﺮ ﮔﺮﻩ ﺑﻪ ﮔﺮﻩ ‪ j‬ﻫﻤﺎﻥ ﻣﺴﻴﺮ ﺑﻬﻴﻨﻪ ﺍﺳﺖ‪ .‬ﻣﺜﺎﻟﻲ ﺍﺯ ﺍﻳﻦ ﺩﺭﺧﺖ ﺑﺮﺍي‬
‫ﻣﻘﺼﺪ ‪ Z‬ﺩﺭ ﺷﮑﻞ ‪ ۱‬ﺩﻳﺪﻩ ﻣﻲ ﺷﻮﺩ‪ .‬ﺩﺭ ﺩﺭﺧﺖ )‪ D ،T(Z‬ﭘﺪﺭ ‪ B‬ﻭ ‪ B‬ﻓﺮﺯﻧﺪ ‪ D‬ﺍﺳﺖ‪ .‬ﭼﻬﺎﺭ ﺣﺎﻟﺖ ﺩﺭ ﺩﺭﺧﺖ ﺩﺭ ﻣﻮﺭﺩ ﺭﺍﺑﻄﻪ ‪ i‬ﺑﺎ‬
‫ﻫﻤﺴﺎﻳﻪ ﺍﺵ ﮐﻪ ﺁﻥ ﺭﺍ ‪ a‬ﻣﻲ ﻧﺎﻣﻴﻢ ﻭﺟﻮﺩ ﺩﺍﺭﺩ‪.‬‬
‫ﺣﺎﻟﺖ ‪ a :۱‬ﭘﺪﺭ ‪ i‬ﺩﺭ )‪ T(j‬ﺑﺎﺷﺪ‬
‫ﺑﺎ ﻓﺮﺽ ﺍﻳﻨﮑﻪ ‪ a‬ﻏﻴﺮ ﺍﺯ ‪ k‬ﺍﺳﺖ‪ ،‬ﻣﻲ ﺗﻮﺍﻥ ﻫﺮ ﻣﺴﻴﺮ ﺑﺪﻭﻥ ‪ k‬ﺍﺯ ‪ a‬ﺑﻪ ‪ j‬ﺭﺍ ﺑﻪ ﻣﺴﻴﺮ ﺑﺪﻭﻥ ‪ k‬ﺍﺯ ‪ i‬ﺑﻪ ‪ j‬ﮔﺴﺘﺮﺵ ﺩﺍﺩ‪ ،‬ﺩﺭ ﻧﺘﻴﺠﻪ ﻧﺎﻣﺴﺎﻭي‬
‫ﺯﻳﺮ ﺭﺍ ﺧﻮﺍﻫﻴﻢ ﺩﺍﺷﺖ‪:‬‬
‫)‪( ۷‬‬
‫‪p‬‬
‫‪p‬‬
‫ﺣﺎﻟﺖ ‪ a :۲‬ﻓﺮﺯﻧﺪ ‪ i‬ﺩﺭ )‪ T(j‬ﺍﺳﺖ‬
‫ﺩﺭ ﺍﻳﻦ ﺟﺎ ‪ k‬ﺑﺎﻳﺪ ﺭﻭي ‪ LCP‬ﺍﺯ ‪ a‬ﺑﻪ ‪ j‬ﺑﺎﺷﺪ‪ .‬ﺑﻪ ﻋﻼﻭﻩ ﺑﺎ ﺩﺍﺩﻥ ﻫﺮ ﻣﺴﻴﺮ ﺑﺪﻭﻥ ‪ k‬ﺍﺯ ‪ a‬ﺑﻪ ‪ ،j‬ﻣﻲ ﺗﻮﺍﻥ ﺍﺗﺼﺎﻝ ‪ ia‬ﺭﺍ ﺑﺮﺍي ﺑﺪﺳﺖ ﺁﻭﺭﺩﻥ‬
‫ﻣﺴﻴﺮ ﺑﺪﻭﻥ ‪ k‬ﺍﺯ ‪ i‬ﺑﻪ ‪ j‬ﺍﺿﺎﻓﻪ ﻳﺎ ﮐﻢ ﮐﺮﺩ‪ ،‬ﺩﺭ ﻧﺘﻴﺠﻪ‪:‬‬
‫)‪( ۸‬‬
‫‪c‬‬
‫‪c‬‬
‫‪p‬‬
‫‪p‬‬
‫ﺣﺎﻟﺖ ‪ a :۳‬ﺩﺭ )‪ T(j‬ﺑﻪ ‪ i‬ﻣﺘﺼﻞ ﻧﻴﺴﺖ‪ ،‬ﻭ ‪ k‬ﺭﻭي )‪ P(c;a,j‬ﺍﺳﺖ‪ .‬ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﺩﺍﺭﻳﻢ‪:‬‬
‫)‪( ۹‬‬
‫‪c i, j‬‬
‫‪c a, j‬‬
‫‪c‬‬
‫‪p‬‬
‫‪p‬‬
‫ﺣﺎﻟﺖ ‪ a :۴‬ﺩﺭ )‪ T(j‬ﺑﻪ ‪ i‬ﻣﺘﺼﻞ ﻧﻴﺴﺖ ﻭ ‪ k‬ﺭﻭي )‪ P(c;a,j‬ﻧﻤﻲ ﺑﺎﺷﺪ‪.‬‬
‫)‪(۱۰‬‬
‫‪c i, j‬‬
‫ﺩﺭ ][ ﺛﺎﺑﺖ ﺷﺪﻩ ﮐﻪ ﺍﮔﺮ ‪ ib‬ﺍﻭﻟﻴﻦ ﺍﺗﺼﺎﻝ ﺩﺭ ‪c; i, j‬‬
‫‪c a, j‬‬
‫‪c‬‬
‫‪c‬‬
‫‪p‬‬
‫ﺑﺎﺷﺪ‪ ،‬ﺩﺭ ﺍﻳﻦ ﺻﻮﺭﺕ ﻧﺎﻣﺴﺎﻭي ﻫﺎي ﺫﮐﺮ ﺷﺪﻩ ﺑﻪ ﻣﺴﺎﻭي ﺗﺒﺪﻳﻞ ﺧﻮﺍﻫﻨﺪ‬
‫ﺷﺪ‪ .‬ﺑﻪ ﺍﻳﻦ ﺗﺮﺗﻴﺐ ﺑﺮﺍي ﻣﺤﺎﺳﺒﻪ ‪ p‬ﮐﺎﻓﻲ ﺍﺳﺖ ﮔﺮﻩ ‪ i‬ﺑﻴﻦ ﻣﻘﺎﺩﻳﺮ ﺳﻤﺖ ﭼﭗ ﻧﺎﻣﺴﺎﻭي ﻫﺎ ﺩﺭ ﻫﻤﺴﺎﻳﮕﺎﻥ ﮐﻤﺘﺮﻳﻦ ﻣﻘﺪﺍﺭ ﺭﺍ ﺑﻪ‬
‫ﻋﻨﻮﺍﻥ ‪ p‬ﺍﻧﺘﺨﺎﺏ ﮐﻨﺪ‪ .‬ﺩﺭ ﻧﺘﻴﺠﻪ ﻣﻲ ﺗﻮﺍﻥ ﻳﮏ ﺍﻟﮕﻮﺭﻳﺘﻢ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺑﺮﺍي ﻣﺤﺎﺳﺒﻪ ‪ p‬ﺩﺍﺷﺖ‪.‬‬
‫‪ ۵‬ﻧﺘﻴﺠﻪ ﮔﻴﺮي‬
‫ﺩﺭ ﺍﻳﻦ ﺗﺤﻘﻴﻖ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﻣﻮﺭﺩ ﻣﻄﺎﻟﻌﻪ ﻗﺮﺍﺭ ﮔﺮﻓﺖ ﻭ ﻣﺴﺎﺋﻞ ﺟﺪﻳﺪي ﮐﻪ ﺍﻳﻦ ﺷﺎﺧﻪ ﻧﺴﺒﺖ ﺑﻪ ﻃﺮﺍﺣﻲ ﻣﮑﺎﻧﻴﺰﻡ‬
‫ﻣﺮﮐﺰي ﺩﺍﺭﻧﺪ ﺑﺮﺭﺳﻲ ﺷﺪ ﻭ ﺫﮐﺮ ﺷﺪ ﮐﻪ ﺩﻭ ﻣﺴﺌﻠﻪ ﭘﻴﭽﻴﺪﮔﻲ ﺷﺒﮑﻪ ﺍي ﻭ ﺩﺳﺘﮑﺎﺭي ﻣﺤﺎﺳﺒﺎﺗﻲ ﺍﺯ ﻣﺴﺎﺋﻞ ﻣﻮﺭﺩ ﺗﻮﺟﻪ ﻫﺴﺘﻨﺪ ﮐﻪ‬
‫ﺗﺤﻘﻴﻘﺎﺗﻲ ﮐﻪ ﺗﺎﮐﻨﻮﻥ ﺭﻭي ﺁﻧﻬﺎ ﺍﻧﺠﺎﻡ ﮔﺮﻓﺘﻪ ﻫﻨﻮﺯ ﭘﺨﺘﻪ ﻧﺸﺪﻩ ﻭ ﺑﻪ ﺻﻮﺭﺕ ﻳﮏ ﻧﻈﺮﻳﻪ ﺟﺪﺍﮔﺎﻧﻪ ﺩﺭ ﻧﻴﺎﻣﺪﻩ ﺍﺳﺖ ﻭ ﻧﻴﺎﺯ ﺑﻪ ﺗﺤﻘﻴﻘﺎﺕ‬
‫ﺑﻴﺸﺘﺮ ﺩﺭ ﺍﻳﻦ ﺯﻣﻴﻨﻪ ﺍﺣﺴﺎﺱ ﻣﻲ ﺷﻮﺩ‪ .‬ﺩﻭ ﻧﻤﻮﻧﻪ ﻣﺴﺌﻠﻪ ﮐﻪ ﻫﺮ ﮐﺪﺍﻡ ﺑﻪ ﻳﮑﻲ ﺍﺯ ﻣﺸﮑﻼﺕ ﺫﮐﺮ ﺷﺪﻩ ﺗﻮﺟﻪ ﺩﺍﺷﺘﻨﺪ ﺑﻴﺎﻥ ﺷﺪﻧﺪ‪ .‬ﺍﻟﺒﺘﻪ‬
‫ﻣﮑﺎﻧﻴﺰﻡ ﻫﺎي ﺗﻮﺯﻳﻊ ﺷﺪﻩ ﺭﻭي ﻣﺴﺎﺋﻠﻲ ﭼﻮﻥ ‪ ،Web caching‬ﺷﺒﮑﻪ ﻫﺎي ﺍﺷﺘﺮﺍﮎ ﻓﺎﻳﻞ ﻧﻈﻴﺮ ﺑﻪ ﻧﻈﻴﺮ‪ ،‬ﻣﺴﺌﻠﻪ ﺯﻣﺎﻧﺒﻨﺪي ﮐﺎﺭﻫﺎ‪،‬‬
‫ﺗﺴﻬﻴﻢ ﻫﺰﻳﻨﻪ ﺑﺮﺍي ﺍﺭﺳﺎﻝ ﺑﺴﺘﻪ ﻫﺎي ﻫﻤﻪ ﭘﺨﺸﻲ ﻧﻴﺰ ﺑﺮﺭﺳﻲ ﺷﺪﻩ ﺍﻧﺪ‪.‬‬
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