rsts rt - - PowerPoint PPT Presentation

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r st s r t r t s

rsts rt - - PowerPoint PPT Presentation

Aug 07, 2023 214 likes •321 views

rsts rt rts rs r r rt rts

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❉▼✽✻✺ ✖ ❍❡✉r✐st✐❝s ❛♥❞ ❆♣♣r♦①✐♠❛t✐♦♥ ❆❧❣♦r✐t❤♠s

❚❡❛❝❤❡rs✿ ▼❛r❝♦ ❈❤✐❛r❛♥❞✐♥✐ ✫ ▲❡♥❡ ❋❛✈r❤♦❧❞t ❈r❡❞✐ts✿ ✶✵ ❊❈❚❙ Pr❡r❡q✉✐s✐t❡s✿ Pr♦❣r❛♠♠✐♥❣ ✭❉▼✺✵✷✱ ❉▼✺✵✸✱ ❉▼✺✺✵✮ ❆❧❣♦r✐t❤♠s ❛♥❞ ❉❛t❛str✉❝t✉r❡s ✭❉▼✺✵✼✮ ❈♦♠♣❧❡①✐t② ❛♥❞ ❈♦♠♣✉t❛❜✐❧✐t② ✭❉▼✺✵✽✱ ❉▼✺✺✸✮ ▲✐♥❡❛r ❛♥❞ ■♥t❡❣❡r Pr♦❣r❛♠♠✐♥❣ ✭❉▼✺✺✾✱ ❉▼✺✹✺✱ ❉▼✺✺✹✱ ❉▼✽✼✶✮ ▲❛♥❣✉❛❣❡✿ ❊♥❣❧✐s❤ ❛♥❞✴♦r ❉❛♥✐s❤ ❈❧❛ss❡s✿ ■♥tr♦✿ ✷h × ✷✵❀ tr❛✐♥✐♥❣✿ ✷h × ✶✺ ▼❛t❡r✐❛❧✿ ❙❧✐❞❡s ✰ t❡①t❜♦♦❦ ✰ ❛rt✐❝❧❡s ✰ st❛rt✐♥❣ ❝♦❞❡ ❆ss❡ss♠❡♥t✿ Pr❛❝t✐❝❛❧ ♣r♦❥❡❝ts ✰ ♦r❛❧ ❡①❛♠

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❆♣♣r♦①✐♠❛t✐♦♥ ❆❧❣♦r✐t❤♠s

❆ ✷✲❛♣♣r♦①✐♠❛t✐♦♥ ❛❧❣♦r✐t❤♠ ❢♦r ▼❡tr✐❝ ❚❙P✿ ❉♦✉❜❧❡✲❚r❡❡

❉♦✉❜❧❡ tr❡❡ ❛❧❣♦r✐t❤♠✿

✶✳ T ← ▼❙❚ ✷✳ ❉♦✉❜❧❡ ❛❧❧ ❡❞❣❡s ✐♥ T ✸✳ Etour ← ❊✉❧❡r t♦✉r ✹✳ ❚♦✉r ← ✈❡rt✐❝❡s ✐♥ ♦r❞❡r ♦❢ ❛♣♣❡❛r❛♥❝❡ ✐♥ Etour

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❆♣♣r♦①✐♠❛t✐♦♥ ❆❧❣♦r✐t❤♠s

❆ ✷✲❛♣♣r♦①✐♠❛t✐♦♥ ❛❧❣♦r✐t❤♠ ❢♦r ▼❡tr✐❝ ❚❙P✿ ❉♦✉❜❧❡✲❚r❡❡

▼❙❚ c(▼❙❚) ≤ c(❖P❚) : ❚♦✉r c(❚♦✉r) ≤ ✷ · c(MST) ❖P❚ → ❙❚

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❉♦✉❜❧❡ tr❡❡ ❛❧❣♦r✐t❤♠✿

✶✳ T ← ▼❙❚ ✷✳ ❉♦✉❜❧❡ ❛❧❧ ❡❞❣❡s ✐♥ T ✸✳ Etour ← ❊✉❧❡r t♦✉r ✹✳ ❚♦✉r ← ✈❡rt✐❝❡s ✐♥ ♦r❞❡r ♦❢ ❛♣♣❡❛r❛♥❝❡ ✐♥ Etour

❈❤r✐st♦✜❞❡✬s ❛❧❣♦r✐t❤♠✿

✶✳ T ← MST ✷✳ ❆❞❞ ♠✐♥✐♠✉♠ ♣❡r❢❡❝t ♠❛t❝❤✐♥❣ ♦❢ ♦❞❞ ❞❡❣r❡❡ ✈❡rt✐❝❡s ✐♥ T ✸✳ Etour ← ❊✉❧❡r t♦✉r ✹✳ ❚♦✉r ← ✈❡rt✐❝❡s ✐♥ ♦r❞❡r ♦❢ ❛♣♣❡❛r❛♥❝❡ ✐♥ Etour

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❆♣♣r♦①✐♠❛t✐♦♥ ❆❧❣♦r✐t❤♠s

❆ ✸/✷✲❛♣♣r♦①✐♠❛t✐♦♥ ❛❧❣♦r✐t❤♠ ❢♦r ▼❡tr✐❝ ❚❙P✿ ❈❤r✐st♦✜❞❡s

c(M) ≤ ✶ ✷❖P❚ : c(M) ≤ ✶ ✷c(❚♦✉r) ≤ c(❚♦✉r) ≤ c(❖P❚)

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❆♣♣r♦①✐♠❛t✐♦♥ ❆❧❣♦r✐t❤♠s

▲♦✇❡r ❜♦✉♥❞s

❚❤❡♦r❡♠

❋♦r α < ✶✽✺

✶✽✹✱ t❤❡r❡ ✐s ♥♦ α✲❛♣♣r♦①✐♠❛t✐♦♥ ❛❧❣♦r✐t❤♠ ❢♦r ▼❡tr✐❝ ❚❙P✳

❚❤❡♦r❡♠

❚❤❡r❡ ✐s ♥♦ ❛♣♣r♦①✐♠❛t✐♦♥ ❛❧❣♦r✐t❤♠ ❢♦r ❣❡♥❡r❛❧ ❚❙P✳

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▲♦❝❛❧ ❙❡❛r❝❤

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▼❡t❛❤❡✉r✐st✐❝s

❚r②✐♥❣ ❞✐✛❡r❡♥t ❝❤❛♥❣❡s ✴ ❛❝❝❡♣t✐♥❣ ✇♦rs❡♥✐♥❣ ❝❤❛♥❣❡s✿

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❈♦♥t❡♥ts

❆♣♣r♦① ❆❧❣♦r✐t❤♠s ▲♦❝❛❧ ❙❡❛r❝❤ ✰ ▼❡t❛❤❡✉r✐st✐❝s ❙❡t ❈♦✈❡r

❙❛t✐s✜❛❜✐❧✐t②
❚r❛✈❡❧✐♥❣ ❙❛❧❡s♠❛♥
❙❝❤❡❞✉❧✐♥❣
❑♥❛♣s❛❝❦
❇✐♥ ♣❛❝❦✐♥❣

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❉▼✽✻✺ ✖ ❍❡✉r✐st✐❝s ❛♥❞ ❆♣♣r♦①✐♠❛t✐♦♥ ❆❧❣♦r✐t❤♠s

❚❡❛❝❤❡rs✿ ▼❛r❝♦ ❈❤✐❛r❛♥❞✐♥✐ ✫ ▲❡♥❡ ❋❛✈r❤♦❧❞t ❈r❡❞✐ts✿ ✶✵ ❊❈❚❙ Pr❡r❡q✉✐s✐t❡s✿ Pr♦❣r❛♠♠✐♥❣ ✭❉▼✺✵✷✱ ❉▼✺✵✸✱ ❉▼✺✺✵✮ ❆❧❣♦r✐t❤♠s ❛♥❞ ❉❛t❛str✉❝t✉r❡s ✭❉▼✺✵✼✮ ❈♦♠♣❧❡①✐t② ❛♥❞ ❈♦♠♣✉t❛❜✐❧✐t② ✭❉▼✺✵✽✱ ❉▼✺✺✸✮ ▲✐♥❡❛r ❛♥❞ ■♥t❡❣❡r Pr♦❣r❛♠♠✐♥❣ ✭❉▼✺✺✾✱ ❉▼✺✹✺✱ ❉▼✺✺✹✱ ❉▼✽✼✶✮ ▲❛♥❣✉❛❣❡✿ ❊♥❣❧✐s❤ ❛♥❞✴♦r ❉❛♥✐s❤ ❈❧❛ss❡s✿ ■♥tr♦✿ ✷h × ✷✵❀ tr❛✐♥✐♥❣✿ ✷h × ✶✺ ▼❛t❡r✐❛❧✿ ❙❧✐❞❡s ✰ t❡①t❜♦♦❦ ✰ ❛rt✐❝❧❡s ✰ st❛rt✐♥❣ ❝♦❞❡ ❆ss❡ss♠❡♥t✿ Pr❛❝t✐❝❛❧ ♣r♦❥❡❝ts ✰ ♦r❛❧ ❡①❛♠