▼■◆■❙❚➱❘■❖ ❉❆ ❊❉❯❈❆➬➹❖ ❊ ❉❖ ❉❊❙P❖❘❚❖ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦
❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ▼✐♥❛s
Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧ ✲ PP●❊▼
❯▼ ❆▲●❖❘■❚▼❖ ❍❊❯❘❮❙❚■❈❖ ❍❮❇❘■❉❖ P❆❘❆
▼■◆■▼■❩❆❘ ❖❙ ❈❯❙❚❖❙ ❈❖▼ ❆ ❆◆❚❊❈■P❆➬➹❖ ❊ ❖
❆❚❘❆❙❖ ❉❆ P❘❖❉❯➬➹❖ ❊▼ ❆▼❇■❊◆❚❊❙ ❈❖▼
❏❆◆❊▲❆❙ ❉❊ ❊◆❚❘❊●❆ ❊ ❚❊▼P❖❙ ❉❊ P❘❊P❆❘❆➬➹❖
❉❊P❊◆❉❊◆❚❊❙ ❉❆ ❙❊◗❯✃◆❈■❆
❆✉t♦r✿ P✉❝❛ ❍✉❛❝❤✐ ❱❛③ P❡♥♥❛
❖r✐❡♥t❛❞♦r✿ ▼❛r❝♦♥❡ ❏❛♠✐❧s♦♥ ❋r❡✐t❛s ❙♦✉③❛
❚r❛❜❛❧❤♦ ❞❡ ❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞♦ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧ ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ▼✐♥❛s ❞❛ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦✱ ❝♦♠♦ ♣❛rt❡ ✐♥t❡❣r❛♥t❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧✳
➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ▲❛✈r❛ ❞❡ ▼✐✲ ♥❛s✳
✳
P✹✶✷❛ P❡♥♥❛✱ P✉❝❛ ❍✉❛❝❤✐ ❱❛③✳
❯♠ ❛❧❣♦r✐t♠♦ ❤❡✉ríst✐❝♦ ❤í❜r✐❞♦ ♣❛r❛ ♠✐♥✐♠✐③❛r ♦s ❝✉st♦s ❝♦♠ ❛ ❛♥t❡❝✐♣❛çã♦ ❡ ♦ ❛tr❛s♦ ❞❛ ♣r♦❞✉çã♦ ❡♠ ❛♠❜✐❡♥t❡s ❝♦♠ ❥❛♥❡❧❛s ❞❡ ❡♥tr❡❣❛ ❡ t❡♠♣♦s ❞❡ ♣r❡♣❛r❛çã♦ ❞❡♣❡♥❞❡♥t❡s ❞❛ s❡q✉❡♥❝✐❛ ❬♠❛♥✉s❝r✐t♦❪ ✴ P✉❝❛ ❍✉❛❝❤✐ ❱❛③ P❡♥♥❛✳ ✲ ✷✵✵✾✳
①✐✐✱ ✽✷ ❢✳✿ ✐❧✳❀ ❣r❛❢s✳ ❀ t❛❜s✳
❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ▼❛r❝♦♥❡ ❏❛♠✐❧s♦♥ ❋r❡✐t❛s ❙♦✉③❛✳
❉✐ss❡rt❛çã♦ ✭▼❡str❛❞♦✮ ✲ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦✳ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s✳ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡♥❤❛r✐❛ ❞❡ ▼✐♥❛s✳ Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠
❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧✳
➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ▲❛✈r❛ ❞❡ ▼✐♥❛s✳
✶✳ ❊♥❣❡♥❤❛r✐❛ ✲ ❚❡s❡s✳ ✷✳ ▲❛✈r❛ ❞❡ ♠✐♥❛s ✲ ❚❡s❡s✳ ✸✳ ❍❡✉ríst✐❝❛ ✲ ❚❡s❡s✳ ■✳ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦✳ ❊s❝♦❧❛ ❞❡ ▼✐♥❛s✳ ■■✳ ❚ít✉❧♦✳
❈❉❯✿ ✻✺✽✳✺✶✷
❯▼ ❆▲●❖❘■❚▼❖ ❍❊❯❘❮❙❚■❈❖ ❍❮❇❘■❉❖ P❆❘❆
▼■◆■▼■❩❆❘ ❖❙ ❈❯❙❚❖❙ ❈❖▼ ❆ ❆◆❚❊❈■P❆➬➹❖ ❊ ❖
❆❚❘❆❙❖ ❉❆ P❘❖❉❯➬➹❖ ❊▼ ❆▼❇■❊◆❚❊❙ ❈❖▼
❏❆◆❊▲❆❙ ❉❊ ❊◆❚❘❊●❆ ❊ ❚❊▼P❖❙ ❉❊ P❘❊P❆❘❆➬➹❖
❉❊P❊◆❉❊◆❚❊❙ ❉❆ ❙❊◗❯✃◆❈■❆
P✉❝❛ ❍✉❛❝❤✐ ❱❛③ P❡♥♥❛
❊st❛ ❞✐ss❡rt❛çã♦ ❢♦✐ ❛♣r❡s❡♥t❛❞❛ ❡♠ s❡ssã♦ ♣ú❜❧✐❝❛ ❡ ❛♣r♦✈❛❞❛ ❡♠ ✵✸ ❞❡ ♠❛rç♦ ❞❡ ✷✵✵✾✱ ♣❡❧❛ ❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛ ❝♦♠♣♦st❛ ♣❡❧♦s s❡❣✉✐♥t❡s ♠❡♠❜r♦s✿
Pr♦❢✳ ❉r✳ ▼❛r❝♦♥❡ ❏❛♠✐❧s♦♥ ❋r❡✐t❛s ❙♦✉③❛ ✭❖r✐❡♥t❛❞♦r ✲ ❉❊❈❖▼✴❯❋❖P✮
Pr♦❢✳ ❉r✳ ❈❛r❧✐❧❡ ❈❛♠♣♦s ▲❛✈♦r ✭❉▼❆✴❯◆■❈❆▼P✮
Pr♦❢✳ ❉r✳ ❋r❡❞❡r✐❝♦ ●❛❞❡❧❤❛ ●✉✐♠❛rã❡s ✭❉❊❈❖▼✴❯❋❖P✮
❆❣r❛❞❡❝✐♠❡♥t♦s
✏❆ ♥❛t✉r❡③❛ é ❡①❛t❛♠❡♥t❡ s✐♠♣❧❡s✱ s❡ ❝♦♥s❡❣✉✐r♠♦s ❡♥❝❛rá✲❧❛ ❞❡ ♠♦❞♦ ❛♣r♦♣r✐❛❞♦✳ ❊ss❛ ❝r❡♥ç❛ t❡♠✲♠❡ ❛✉①✐❧✐❛❞♦✱ ❞✉r❛♥t❡ t♦❞❛ ❛ ♠✐♥❤❛ ✈✐❞❛✱ ❛ ♥ã♦ ♣❡r❞❡r ❛s ❡s♣❡r❛♥ç❛s✱ q✉❛♥❞♦ s✉r❣❡♠ ❣r❛♥❞❡s ❞✐✜❝✉❧❞❛❞❡s ❞❡ ✐♥✈❡st✐❣❛çã♦✳✑ ❬❆❧❜❡rt ❊✐♥st❡✐♥❪
●♦st❛r✐❛ ❞❡ ❡①♣r❡ss❛r ♠❡✉s ❛❣r❛❞❡❝✐♠❡♥t♦s ❛ t♦❞♦s✱ q✉❡ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛✱ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✱ ❡♠ ❡s♣❡❝✐❛❧✿
❆ ❉❡✉s ♣❡❧♦ ❞♦♠ ❞❛ ✈✐❞❛✳
❆♦s ♠❡✉s ♣❛✐s ❚❛tt✉ P❡♥♥❛ ❡ ◆❡✐❞❡ ❱❛③ q✉❡ ♠❡ ❡♥s✐♥❛r❛♠ q✉❡ ♦ ✈❡r❞❛❞❡✐r♦ ❛❧✐❝❡r❝❡ ❞❡ ♥♦ss❛s ✈✐❞❛s é ❛ ❢❛♠í❧✐❛✳
➚s ♠✐♥❤❛s ✐r♠ãs ❯✐❛r❛✱ ❱✐♦❧❡t❛ ❈❛♠é❧✐❛✱ ❛♦s ✐r♠ã♦s ❚❛✐❛♥❞✐r ❡ ❘❛✐r✉ ❡ ❛♦s ♠❡✉s t✐♦s✱ t✐❛s✱ ♣r✐♠♦s ❡ ♣r✐♠❛s✱ q✉❡ ❥✉♥t♦s✱ ♠❡ ❢❛③❡♠ ❡♥t❡♥❞❡r ❡ ❛❝r❡❞✐t❛r ♥♦s ❡♥s✐♥❛♠❡♥t♦s ❞❡ ♠❡✉s ♣❛✐s✳
➚ ❚❡♠✐s✱ ♠❡✉ ❛♠♦r✱ q✉❡ ❝♦♠ s❡✉ ❛♣♦✐♦ ❡ ❝❛r✐♥❤♦ t❡♠ ❞❡✐①❛❞♦ ♥♦ss❛s ✈✐❞❛s ♠❛✐s ❢❡❧✐③❡s✳
❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r Pr♦❢✳ ▼❛r❝♦♥❡ ♣❡❧❛ ❛♠✐③❛❞❡ ❡ ❡♥s✐♥❛♠❡♥t♦s✱ q✉❡ ♣♦r s✉❛ ❞❡❞✐❝❛çã♦ ❛ ❞♦❝ê♥❝✐❛ ❡ ❛ ♣❡sq✉✐s❛ t❡r ❞❡s♣❡rt❛❞♦ ❡♠ ♠✐♠ ❡ss❡ ❣♦st♦✳
❆♦s ❛♠✐❣♦s ❞♦ ♠❡str❛❞♦✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦ ❋r❡❞✱ ♣♦r ❝❛♠✐♥❤❛r♠♦s ❥✉♥t♦s✳
❆♦s ♣r♦❢❡ss♦r❡s ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧ ❞❛ ❯❋❖P ♣❡❧♦s ❡♥s✐♥❛♠❡♥t♦s✳
❆♦ Pr♦❣r❛♠❛ ❞❡ Pós✲❣r❛❞✉❛çã♦ ❡♠ ❊♥❣❡♥❤❛r✐❛ ▼✐♥❡r❛❧ ❞❛ ❯❋❖P ♣❡❧❛ ♦♣♦r✲ t✉♥✐❞❛❞❡✳
➚ r❡♣ú❜❧✐❝❛ ◗✉❛rt♦ ❈r❡s❝❡♥t❡ ♣❡❧❛ ❛♠✐③❛❞❡✳
❘❡s✉♠♦
❊st❡ tr❛❜❛❧❤♦ ❞❡ ❞✐ss❡rt❛çã♦ t❡♠ s❡✉ ❢♦❝♦ ♥♦ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❡♠ ✉♠❛ ♠áq✉✐♥❛ ❝♦♠ ♣❡♥❛❧✐❞❛❞❡s ♣♦r ❛♥t❡❝✐♣❛çã♦ ❡ ❛tr❛s♦ ❞❛ ♣r♦❞✉çã♦✳ ❙ã♦ ❝♦♥s✐❞❡r❛✲ ❞♦s t❡♠♣♦s ❞❡ ♣r❡♣❛r❛çã♦ ❞❛ ♠áq✉✐♥❛ ❞❡♣❡♥❞❡♥t❡s ❞❛ s❡q✉ê♥❝✐❛ ❞❡ ♣r♦❞✉çã♦✱ ❜❡♠ ❝♦♠♦ ❛ ❡①✐stê♥❝✐❛ ❞❡ ❥❛♥❡❧❛s ❞❡ ❡♥tr❡❣❛ ❞✐st✐♥t❛s✳ P❛r❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❞❡s❡♥✈♦❧✈❡✉✲s❡ ✉♠ ❛❧❣♦r✐t♠♦ ❤❡✉ríst✐❝♦ ❞❡ três ❢❛s❡s✳ ❆ ♣r✐♠❡✐r❛ ❢❛s❡ ❜❛s❡❛❞❛ ❡♠ ●❘❆❙P ❡ ❉❡s❝✐❞❛ ❡♠ ❱✐③✐♥❤❛♥ç❛ ❱❛r✐á✈❡❧ ♣❛r❛ ❛ ❣❡r❛çã♦ ❞❛ s♦❧✉çã♦ ✐♥✐❝✐❛❧✱ ❛ s❡❣✉♥❞❛ ❢❛s❡ ❜❛s❡❛❞❛ ❡♠ ❇✉s❝❛ ❚❛❜✉ ♣❛r❛ r❡✜♥❛♠❡♥t♦ ❞❛ s♦❧✉çã♦✱ ❡ ♣♦r ✜♠✱ ❛ ❘❡❝♦♥❡①ã♦ ♣♦r ❈❛♠✐♥❤♦s ❝♦♠♦ ❡str❛té❣✐❛ ❞❡ ♣ós✲♦t✐♠✐③❛çã♦✱ ♥❛ t❡r❝❡✐r❛ ❢❛s❡✳ P❛r❛ ❝❛❞❛ s❡q✉ê♥❝✐❛ ❣❡r❛❞❛ ♣❡❧❛ ❤❡✉ríst✐❝❛ é ✉t✐❧✐③❛❞♦ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ t❡♠♣♦ ♣♦❧✐♥♦♠✐❛❧ ♣❛r❛ ❞❡t❡r♠✐♥❛r ❛ ❞❛t❛ ót✐♠❛ ❞❡ ✐♥í❝✐♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❝❛❞❛ t❛r❡❢❛✳ ❖s r❡✲ s✉❧t❛❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ♠♦str❛r❛♠ q✉❡ ❤♦✉✈❡ ♠❡❧❤♦r✐❛ ❡♠ r❡❧❛çã♦ ❛ ✉♠ ❛❧❣♦r✐t♠♦ ❞❛ ❧✐t❡r❛t✉r❛✱ t❛♥t♦ ❝♦♠ r❡❧❛çã♦ à q✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦ ✜♥❛❧ q✉❛♥t♦ ❡♠ r❡❧❛çã♦ ❛♦ ❞❡s✈✐♦ ♠é❞✐♦✳
P❛❧❛✈r❛s✲❈❤❛✈❡s✿ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ❡♠ ✉♠❛ ♠áq✉✐♥❛❀ ●❘❆❙P❀ ❇✉s❝❛ ❚❛✲ ❜✉❀ ❉❡s❝✐❞❛ ❡♠ ❱✐③✐♥❤❛♥ç❛ ❱❛r✐á✈❡❧❀ ❘❡❝♦♥❡①ã♦ ♣♦r ❈❛♠✐♥❤♦s✳
❆❜str❛❝t
❚❤✐s ✇♦r❦ ❞❡❛❧s ✇✐t❤ t❤❡ s✐♥❣❧❡ ♠❛❝❤✐♥❡ s❝❤❡❞✉❧✐♥❣ ♣r♦❜❧❡♠ ✇✐t❤ ❡❛r❧✐♥❡ss ❛♥❞ t❛r✲ ❞✐♥❡ss ♣❡♥❛❧t✐❡s✳ ❙❡q✉❡♥❝❡ ❞❡♣❡♥❞❡♥t s❡t✉♣ t✐♠❡s ❛♥❞ ❞✐st✐♥❝t ❞✉❡ ✇✐♥❞♦✇s ❛r❡ ❝♦♥✲ s✐❞❡r❡❞✳ ❚♦ s♦❧✈❡ t❤✐s ♣r♦❜❧❡♠✱ ❛ t❤r❡❡✲♣❤❛s❡ ❤❡✉r✐st✐❝ ❛♣♣r♦❛❝❤ ✇❛s ❞❡✈❡❧♦♣❡❞✳ ❚❤❡ ✜rst ♣❤❛s❡ ✐s ❜❛s❡❞ ♦♥ ●❘❆❙P ❛♥❞ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❉❡s❝❡♥t t♦ ❣❡♥❡r❛t❡ ❛♥ ✐♥✐t✐❛❧ s♦❧✉t✐♦♥❀ t❤❡ s❡❝♦♥❞ ♣❤❛s❡ ✐s ❜❛s❡❞ ♦♥ ❛ ❚❛❜✉ ❙❡❛r❝❤ ❢♦r s♦❧✉t✐♦♥ r❡✜♥✐♥❣✱ ❛♥❞ ✜♥❛❧❧② P❛t❤ ❘❡❧✐♥❦✐♥❣ ✐s ✉s❡❞ ❛s ❛ ♠❡❝❤❛♥✐s♠ ♦❢ ♣♦st✲♦♣t✐♠✐③❛t✐♦♥ ❛s ❛ t❤✐r❞ ♣❤❛✲ s❡✳ ❋♦r ❡❛❝❤ ❥♦❜ s❡q✉❡♥❝❡ ❣❡♥❡r❛t❡❞ ❜② t❤❡ ❤❡✉r✐st✐❝✱ ❛♥ ♦♣t✐♠❛❧ t✐♠✐♥❣ ❛❧❣♦r✐t❤♠ ✐s ✉s❡❞ t♦ ❞❡t❡r♠✐♥❡ t❤❡ ❝♦♠♣❧❡t✐♦♥ t✐♠❡ ❢♦r ❡❛❝❤ ❥♦❜ ✐♥ t❤❡ ❥♦❜ s❡q✉❡♥❝❡✳ ❈♦♠♣✉t❛t✐♦✲ ♥❛❧ ❡①♣❡r✐♠❡♥ts ❝❛rr✐❡❞ ♦✉t s❤♦✇ t❤❛t ♣r❡✈✐♦✉s ❛❧❣♦r✐t❤♠s ❢♦✉♥❞ ✐♥ r❡❧❛t❡❞ ❧✐t❡r❛t✉r❡ ❤❛✈❡ ❜❡❡♥ ✐♠♣r♦✈❡❞✱ r❡❣❛r❞✐♥❣ t❤❡ q✉❛❧✐t② ♦❢ t❤❡ ✜♥❛❧ s♦❧✉t✐♦♥ ❛♥❞ t❤❡ ❛✈❡r❛❣❡ ❣❛♣✳
❑❡②✇♦r❞s✿ ❙✐♥❣❧❡ ▼❛❝❤✐♥❡ ❙❝❤❡❞✉❧✐♥❣❀ ●❘❆❙P❀ ❚❛❜✉ ❙❡❛r❝❤❀ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❉❡s❝❡♥t❀ P❛t❤ ❘❡❧✐♥❦✐♥❣✳
❙✉♠ár✐♦
✶ Pr❡❧✐♠✐♥❛r❡s ✶
✶✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶
✶✳✷ ❏✉st✐✜❝❛t✐✈❛ ❡ ❘❡❧❡✈â♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✶✳✸ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✶✳✸✳✶ ❖❜❥❡t✐✈♦ ●❡r❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✶✳✸✳✷ ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷ ❖ Pr♦❜❧❡♠❛ ❞❡ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ✾
✷✳✶ ❚✐♣♦s ❞❡ Pr♦❜❧❡♠❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✷ ❖ Pr♦❜❧❡♠❛ ❞❡ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ♥❛ ▼✐♥❡r❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵
✷✳✸ Pr♦❜❧❡♠❛ ❆❜♦r❞❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼
✸ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✶✾
✸✳✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✹ ▼❡t♦❞♦❧♦❣✐❛ ✷✻
✹✳✶ ▼♦❞❡❧♦ ▼❛t❡♠át✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✹✳✷ Pr♦❝❡❞✐♠❡♥t♦ ❞❡ ❉❡t❡r♠✐♥❛çã♦ ❞❛s ❉❛t❛s Ót✐♠❛s ❞❡ ■♥í❝✐♦ ❞❡ Pr♦✲ ❝❡ss❛♠❡♥t♦ ❞❛s ❚❛r❡❢❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶
✹✳✸ ▼♦❞❡❧♦ ❍❡✉ríst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✹✳✸✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ ❙♦❧✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✹✳✸✳✷ ❱✐③✐♥❤❛♥ç❛ ❞❡ ✉♠❛ ❙♦❧✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✹✳✸✳✸ ❋✉♥çã♦ ❞❡ ❆✈❛❧✐❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✹✳✸✳✹ ●❡r❛çã♦ ❞❛ s♦❧✉çã♦ ✐♥✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✹✳✸✳✺ ❇✉s❝❛ ❚❛❜✉ ❛♣❧✐❝❛❞❛ ❛♦ P❙❯▼❆❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸
✹✳✸✳✻ ❘❡❝♦♥❡①ã♦ ♣♦r ❈❛♠✐♥❤♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻
✹✳✸✳✼ ❆❧❣♦r✐t♠♦ ●❚❙P❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✺ ❘❡s✉❧t❛❞♦s ❈♦♠♣✉t❛❝✐♦♥❛✐s ✺✷
✺✳✶ Pr♦❜❧❡♠❛s✲t❡st❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷
✺✳✷ ❘❡s✉❧t❛❞♦s ❞♦ P▲■▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✺✳✸ ❈❛❧✐❜r❛çã♦ ❡ P❛râ♠❡tr♦s ❞♦ ▼ét♦❞♦ ❍❡✉ríst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✺✳✹ ❘❡s✉❧t❛❞♦s ❞♦ ❆❧❣♦r✐t♠♦ ❍❡✉ríst✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✻ ❈♦♥❝❧✉sõ❡s ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✻✺
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✻✻
■ ❘❡s✉❧t❛❞♦s ❉❡t❛❧❤❛❞♦s ✼✶
■✳✶ ❊①❡❝✉çã♦ ❞♦ ●❚❙P❘ ■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
■✳✷ ❊①❡❝✉çã♦ ❞♦ ●❚❙P❘ ■■ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻
■■ P✉❜❧✐❝❛çõ❡s ✽✶
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❧♦❝❛çã♦ ❞❡ ❝❛♠✐♥❤õ❡s ✶✷
✷✳✷ ❙♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❛❧♦❝❛çã♦ ❞❡ ❝❛♠✐♥❤õ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸
✷✳✸ ❚❡♠♣♦ ❞❡ ♦♣❡r❛çã♦ ❞♦s ❝❛♠✐♥❤õ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✷✳✹ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛ ❙♦❧✉çã♦ ❞❛ ❋r❡♥t❡ ▼✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✷✳✺ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛ ❙♦❧✉çã♦ ❞❛ ❋r❡♥t❡ ❊✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻
✷✳✻ ❊①❡♠♣❧✐✜❝❛çã♦ ❞♦s ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✺✳✶ ❘❡s✉❧t❛❞♦s ❞♦ P▲■▼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸
✺✳✷ P❛râ♠❡tr♦s ❞♦ ❆❧❣♦r✐t♠♦ ●❚❙P❘ ✲ ❙♦❧✉çã♦ ❈♦♠♣❧❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
✺✳✸ ❈♦♠♣❛r❛çã♦ ❞❡ r❡s✉❧t❛❞♦s ❞❡ ❝❛❞❛ ❢❛s❡ ❞♦ ❛❧❣♦r✐t♠♦ ●❚❙P❘× ●♦✲
♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ × ❈P▲❊❳ ✭P❛râ♠❡tr♦s Pr✐♥❝✐♣❛✐s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶
✺✳✹ ❈♦♠♣❛r❛çã♦ ❞❡ r❡s✉❧t❛❞♦s ❞❡ ❝❛❞❛ ❢❛s❡ ❞♦ ❛❧❣♦r✐t♠♦ ●❚❙P❘× ●♦✲
♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ × ❈P▲❊❳ ✭P❛râ♠❡tr♦s ❙❡❝✉♥❞ár✐♦s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷
✺✳✺ ❈♦♠♣❛r❛çã♦ ❞♦s t❡♠♣♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ●❚❙P❘ ■ × ●❚❙P❘ ■■ ×
●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ ❝♦rr✐❣✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹
■✳✶ ❘❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦s ●❚❙P❘ ■ × ●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ ✭✽ ❛ ✶✵
t❛r❡❢❛s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷
■✳✷ ❘❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦s ●❚❙P❘ ■ × ●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ ✭✶✶ ❛ ✶✺
t❛r❡❢❛s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸
■✳✸ ❘❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦s ●❚❙P❘ ■ × ●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ ✭✷✵ ❛ ✸✵
t❛r❡❢❛s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹
■✳✹ ❘❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦ ●❚❙P❘ ■ × ●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ ✭✹✵ ❛ ✼✺
t❛r❡❢❛s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
■✳✺ ❘❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦s ●❚❙P❘ ■■× ●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ ✭✽ ❛ ✶✵
t❛r❡❢❛s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼
■✳✻ ❘❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦s ●❚❙P❘ ■■×●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ ✭✶✶ ❛ ✶✺
t❛r❡❢❛s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽
■✳✼ ❘❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦s ●❚❙P❘ ■■×●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ ✭✷✵ ❛ ✸✵
t❛r❡❢❛s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾
■✳✽ ❘❡s✉❧t❛❞♦s ❞❡t❛❧❤❛❞♦ ●❚❙P❘ ■■ × ●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮ ✭✹✵ ❛ ✼✺
t❛r❡❢❛s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❊①❡♠♣❧♦ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ s❡♠ t❡♠♣♦ ♦❝✐♦s♦ ❡♥tr❡ t❛r❡❢❛s ✳ ✳ ✳ ✳ ✳ ✹
✶✳✷ ❊①❡♠♣❧♦ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❝♦♠ t❡♠♣♦ ♦❝✐♦s♦ ❡♥tr❡ t❛r❡❢❛s ✳ ✳ ✳ ✳ ✳ ✹
✷✳✶ Pr♦❜❧❡♠❛ ❊st✉❞❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✹✳✶ ▼❡t♦❞♦❧♦❣✐❛ ❤❡✉ríst✐❝❛ ❞❡ s♦❧✉çã♦ ♣❛r❛ ♦ P❙❯▼❆❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
✹✳✷ Pr♦❣r❛♠❛çã♦ ❞❛s t❛r❡❢❛s ❞❡ ✉♠ ❜❧♦❝♦ ♥❛ s❡q✉ê♥❝✐❛✿ 1o P❛ss♦ ✳ ✳ ✳ ✳ ✳ ✸✸
✹✳✸ Pr♦❣r❛♠❛çã♦ ❞❛s t❛r❡❢❛s ❞❡ ✉♠ ❜❧♦❝♦ ♥❛ s❡q✉ê♥❝✐❛✿ 2o P❛ss♦ ✳ ✳ ✳ ✳ ✳ ✸✹
✹✳✹ Pr♦❣r❛♠❛çã♦ ❞❛s t❛r❡❢❛s ❞❡ ✉♠ ❜❧♦❝♦ ♥❛ s❡q✉ê♥❝✐❛✿ 3o P❛ss♦ ✳ ✳ ✳ ✳ ✳ ✸✺
✹✳✺ Pr♦❣r❛♠❛çã♦ ❞❛s t❛r❡❢❛s ❞❡ ✉♠ ❜❧♦❝♦ ♥❛ s❡q✉ê♥❝✐❛✿ 4o P❛ss♦ ✳ ✳ ✳ ✳ ✳ ✸✻
✹✳✻ Pr♦❝❡❞✐♠❡♥t♦ P❉❉❖■P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼
✹✳✼ ▼♦✈✐♠❡♥t♦ ❞❡ tr♦❝❛ ✲NT ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽
✹✳✽ ▼♦✈✐♠❡♥t♦ ❞❡ r❡❛❧♦❝❛çã♦ ✲NR ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✹✳✾ ▼♦✈✐♠❡♥t♦ ❞❡ r❡❛❧♦❝❛çã♦ ❞❡ ✉♠ ❜❧♦❝♦ ✲NOr ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾
✹✳✶✵ Pr♦❝❡❞✐♠❡♥t♦ ●❘❆❙P✲❱◆❉ ❛♣❧✐❝❛❞♦ ❛♦ P❙❯▼❆❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
✹✳✶✶ Pr♦❝❡❞✐♠❡♥t♦ ❈♦♥str♦✐❴❙♦❧✉❝❛♦❴●❘❆❙P ❛♣❧✐❝❛❞♦ ❛♦ P❙❯▼❆❆ ✳ ✳ ✳ ✹✶
✹✳✶✷ Pr♦❝❡❞✐♠❡♥t♦ ❱◆❉1 ❛♣❧✐❝❛❞♦ ❛♦ P❙❯▼❆❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷
✹✳✶✸ Pr♦❝❡❞✐♠❡♥t♦ ❇✉s❝❛ ❚❛❜✉ ❛♣❧✐❝❛❞♦ ❛♦ P❙❯▼❆❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺
✹✳✶✹ Pr♦❝❡❞✐♠❡♥t♦ P❘ ❛♣❧✐❝❛❞♦ ❛♦ P❙❯▼❆❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵
✹✳✶✺ ❆❧❣♦r✐t♠♦ ●❚❙P❘ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶
✺✳✶ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦GRASP max ❡♠ ❢✉♥çã♦ ❞❡F o ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹
✺✳✷ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦GRASP max ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ✳ ✳ ✳ ✳ ✳ ✺✺
✺✳✸ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦M RDmax ❡♠ ❢✉♥çã♦ ❞❡ F o ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✺✳✹ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦M RDmax ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✺✳✺ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦T Smax ❡♠ ❢✉♥çã♦ ❞❡ F o ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
✺✳✻ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦T Smax ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✺✳✼ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦|T| ❡♠ ❢✉♥çã♦ ❞❡F o ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✺✳✽ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦|T| ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
✺✳✾ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦|GE| ❡♠ ❢✉♥çã♦ ❞❡ F o ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺✳✶✵ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦|GE| ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺✳✶✶ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦divElite ❡♠ ❢✉♥çã♦ ❞❡ F o ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽
✺✳✶✷ ❈❛❧✐❜r❛çã♦ ❞♦ ♣❛râ♠❡tr♦divElite ❡♠ ❢✉♥çã♦ ❞♦ t❡♠♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾
▲✐st❛ ❞❡ ❙✐❣❧❛s
❆❈❖ ❆♥t ❈♦❧♦♥② ❖♣t✐♠✐③❛t✐♦♥
❆● ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s
❇❚ ❇✉s❝❛ ❚❛❜✉
❋■❋❖ ❋✐rst ■♥ ❋✐rst ❖✉t
●❊ ●r✉♣♦ ❊❧✐t❡
●❘❆❙P ●r❡❡❞② ❘❛♥❞♦♠✐③❡❞ ❆❞❛♣t✐✈❡ ❙❡❛r❝❤ Pr♦❝❡❞✉r❡s
■▲❙ ■t❡r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤
▲❈ ▲✐st❛ ❞❡ ❈❛♥❞✐❞❛t♦s
▲❘❈ ▲✐st❛ ❘❡str✐t❛ ❞❡ ❈❛♥❞✐❞❛t♦s
P❈❱ Pr♦❜❧❡♠❛ ❞♦ ❈❛✐①❡✐r♦ ❱✐❛❥❛♥t❡
P❉❉❖■P Pr♦❝❡❞✐♠❡♥t♦ ❞❡ ❉❡t❡r♠✐♥❛çã♦ ❞❛s ❉❛t❛s Ót✐♠❛s ❞❡ ■♥í❝✐♦ ❞❡ Pr♦❝❡ss❛♠❡♥t♦ ❞❛s t❛r❡❢❛s
P▲■▼ Pr♦❣r❛♠❛çã♦ ▲✐♥❡❛r ■♥t❡✐r❛ ▼✐st❛
P❖ P❡sq✉✐s❛ ❖♣❡r❛❝✐♦♥❛❧
P❘ P❛t❤ ❘❡❧✐♥❦✐♥❣
P❙❯▼ Pr♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❡♠ ✉♠❛ ♠áq✉✐♥❛
P❙❯▼❆❆ Pr♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❡♠ ✉♠❛ ♠áq✉✐♥❛ ❝♦♠ ♠✐♥✐♠✐③❛çã♦ ❞❛s ♣❡♥❛❧✐❞❛❞❡s ♣♦r ❛♥t❡❝✐♣❛çã♦ ❡ ❛tr❛s♦
❙❆ ❙✐♠✉❧❛t❡❞ ❆♥♥❡❛❧✐♥❣
❱◆❉ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❉❡s❝❡♥t
❱◆❙ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❙❡❛r❝❤
❈❛♣ít✉❧♦ ✶
Pr❡❧✐♠✐♥❛r❡s
✶✳✶ ■♥tr♦❞✉çã♦
❆ P❡sq✉✐s❛ ❖♣❡r❛❝✐♦♥❛❧ ✭P❖✮ é ❛ ár❡❛ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦ q✉❡ ✉s❛ ♦ ♠ét♦❞♦ ❝✐❡♥tí✜❝♦ ♣❛r❛ ❛ t♦♠❛❞❛ ❞❡ ❞❡❝✐sõ❡s✱ ♣r♦❝✉r❛♥❞♦ ❞❡t❡r♠✐♥❛r ❝♦♠♦ ♠❡❧❤♦r ♣r♦❥❡t❛r ❡ ♦♣❡r❛r ✉♠ s✐st❡♠❛✱ ✉s✉❛❧♠❡♥t❡ s♦❜ ❝♦♥❞✐çõ❡s q✉❡ r❡q✉❡r❡♠ ❛ ❛❧♦❝❛çã♦ ❞❡ r❡❝✉rs♦s ❡s❝❛ss♦s ✭❆r❡♥❛❧❡s ❡t ❛❧✳✱ ✷✵✵✼✮✳
❆s ❛♣❧✐❝❛çõ❡s ❡♠ P❖ sã♦ ❞✐✈❡rs❛s✳ ❉❡♥tr♦ ❞♦ ❝♦♥❥✉♥t♦ ❞❡ ♣r♦❜❧❡♠❛s ❡s✲ t✉❞❛❞♦s ❡♥❝♦♥tr❛✲s❡✱ ❝♦♠ ❣r❛♥❞❡ ❞❡st❛q✉❡✱ ❛t✉❛❧♠❡♥t❡✱ ❛ ❝❧❛ss❡ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ♣r♦❣r❛♠❛çã♦ ❞❡ t❛r❡❢❛s ✭❥♦❜ s❝❤❡❞✉❧✐♥❣✮✳
❈♦♠ r❡❧❛çã♦ às ❡♥tr❡❣❛s✱ sã♦ ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ três t✐♣♦s ❞❡ ♣r♦❜❧❡✲ ♠❛s✿
✶✳ ♦s ❝♦♠ ❞❛t❛s ❞❡ ❡♥tr❡❣❛ ❝♦♠✉♥s ✭❝♦♠♠♦♥ ❞✉❡ ❞❛t❡✮❀
✷✳ ♦s ❝♦♠ ❞❛t❛s ❞❡ ❡♥tr❡❣❛ ❞✐st✐♥t❛s ✭❞✐st✐♥❝t ❞✉❡ ❞❛t❡s✮ ❡
✸✳ ♦s q✉❡ tê♠ ❥❛♥❡❧❛s ❞❡ ❡♥tr❡❣❛ ❞✐st✐♥t❛s ✭❞✐st✐♥❝t ❞✉❡ ✇✐♥❞♦✇s✮✳
◆♦ ♣r✐♠❡✐r♦ t✐♣♦✱ ❡①✐st❡ ✉♠❛ ú♥✐❝❛ ❞❛t❛ ♣❛r❛ ❡♥tr❡❣❛r t♦❞❛s ❛s t❛r❡❢❛s✱ ❡♥q✉❛♥t♦ ♥♦ s❡❣✉♥❞♦ ❡①✐st❡ ✉♠❛ ❞❛t❛ ❞❡ ❡♥tr❡❣❛ ❡s♣❡❝í✜❝❛ ❛ss♦❝✐❛❞❛ ❛ ❝❛❞❛ t❛r❡❢❛✳ ◆♦ t❡r❝❡✐r♦ t✐♣♦✱ ❤á ✉♠ ♣❡rí♦❞♦ ♣❛r❛ ❛ ❝♦♥❝❧✉sã♦ ❞❡ ❝❛❞❛ t❛r❡❢❛✳ ❙❡❣✉♥❞♦ ❲❛♥ ❡ ❨❡♥ ✭✷✵✵✷✮✱ ❡st❛ ú❧t✐♠❛ s✐t✉❛çã♦ ❛♣❛r❡❝❡ ❡♠ s✐t✉❛çõ❡s ❞❡ ✐♥❝❡rt❡③❛s ♦✉ t♦❧❡râ♥❝✐❛s ❝♦♠ r❡❧❛çã♦ às ❞❛t❛s ❞❡ ❡♥tr❡❣❛ ❡ ♥ã♦ ❤á ❝✉st♦s s❡ ❛s t❛r❡❢❛s ❢♦r❡♠ ❝♦♥❝❧✉í❞❛s ❞❡♥tr♦ ❞❛ ❥❛♥❡❧❛ ❞❡ ❡♥tr❡❣❛✳
P❛r❛ ♣r♦❜❧❡♠❛s ❞❡ ♣r♦❞✉çã♦ ❡♥✈♦❧✈❡♥❞♦ ♣❡♥❛❧✐③❛çõ❡s ♣❡❧❛ ❛♥t❡❝✐♣❛çã♦ ❡ ♣❡❧♦ ❛tr❛s♦ ❝♦♠ ❞❛t❛s ❝♦♠✉♥s ❞❡ ❡♥tr❡❣❛✱ ❤á ♠✉✐t❛s ♣r♦♣r✐❡❞❛❞❡s q✉❡ ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞❛s ♥♦s ❛❧❣♦r✐t♠♦s ❞❡ s♦❧✉çã♦ ❡ q✉❡ ♣❡r♠✐t❡♠ ✉♠❛ r❡❞✉çã♦ ❛❝❡♥t✉❛❞❛ ❞♦ ❡s❢♦rç♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♥❛ ❡①♣❧♦r❛çã♦ ❞♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛✳ P♦r ❡①❡♠♣❧♦✱ ❞❡ ❛❝♦r✲ ❞♦ ❝♦♠ ❇❛❦❡r ❡ ❙❝✉❞❞❡r ✭✶✾✾✵✮✱ s❡ Ci r❡♣r❡s❡♥t❛ ❛ ❞❛t❛ ❞❡ ❝♦♥❝❧✉sã♦ ❞❛ t❛r❡❢❛
i ❡ f(Ci) ♦ ✈❛❧♦r ❞❛ ❢✉♥çã♦ ❝✉st♦ r❡❧❛t✐✈♦ à t❛r❡❢❛ i✱ ❡♥tã♦ ♥❛ s❡q✉ê♥❝✐❛ ót✐♠❛✱ ♦s ♣♦♥t♦s (si, f(Ci)) ❢♦r♠❛♠ ✉♠ V ✭❞✐③✲s❡ q✉❡ ❛ s❡q✉ê♥❝✐❛ é V − s❤❛♣❡❞✮✳ ❊♠ ♦✉tr❛s ♣❛❧❛✈r❛s✱ ♥❛ s❡q✉ê♥❝✐❛ ót✐♠❛✱ ❛s t❛r❡❢❛s ❛♥t❡❝✐♣❛❞❛s ❞❡✈❡♠ s❡r ♦r❞❡♥❛❞❛s ❞❡ ❢♦r♠❛ ♥ã♦✲❝r❡s❝❡♥t❡ ♣❡❧❛ r❡❧❛çã♦ ❡♥tr❡ ♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❛ ♣❡♥❛❧✐③❛✲ çã♦ ♣❡❧❛ ❛♥t❡❝✐♣❛çã♦✱ ❡♥q✉❛♥t♦ ❛s t❛r❡❢❛s ❛tr❛s❛❞❛s ❞❡✈❡♠ s❡r ♦r❞❡♥❛❞❛s ❞❡ ❢♦r♠❛ ♥ã♦✲❞❡❝r❡s❝❡♥t❡ ♣❡❧❛ r❡❧❛çã♦ ❡♥tr❡ ♦ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ❛ ♣❡♥❛❧✐③❛çã♦ ♣❡❧♦ ❛tr❛s♦✳ ❖✉tr❛ ♣r♦♣r✐❡❞❛❞❡ ✐♥t❡r❡ss❛♥t❡ é q✉❡ ♥❛ s❡q✉ê♥❝✐❛ ót✐♠❛ ♥ã♦ ❤á t❡♠♣♦s ♦❝✐♦s♦s ❡♥tr❡ ❛s t❛r❡❢❛s✳
P❛r❛ ♦ ❝❛s♦ ❡♠ q✉❡ ❛s ❞❛t❛s ❞❡ ❡♥tr❡❣❛ sã♦ ❞✐st✐♥t❛s✱ ❛ss✐♠ ❝♦♠♦ ♣❛r❛ ♦ ❝❛s♦ ❡♠ ❤á ❥❛♥❡❧❛s ❞❡ ❡♥tr❡❣❛ ❞✐st✐♥t❛s✱ t❛✐s ♣r♦♣r✐❡❞❛❞❡s ♥ã♦ sã♦ ♥❡❝❡ss❛r✐❛♠❡♥t❡ ✈á❧✐❞❛s✱ t♦r♥❛♥❞♦ ♠❛✐s ❝♦♠♣❧❡①❛ ❛ ❡①♣❧♦r❛çã♦ ❞♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛✳ P❛r❛ ❡ss❡s t✐♣♦s ❞❡ ♣r♦❜❧❡♠❛s é ♥❡❝❡ssár✐♦ s❛❜❡r s❡ é ♣❡r♠✐t✐❞❛ ❛ ♦❝✐♦s✐❞❛❞❡ ❞❛s ♠áq✉✐♥❛s ♦✉ ♥ã♦✳
❙❡❣✉♥❞♦ ❋r❛♥ç❛ ❋✐❧❤♦ ✭✷✵✵✼✮✱ ❡①✐st❡♠ s✐t✉❛çõ❡s ❡♠ q✉❡ ❛ ♦❝✐♦s✐❞❛❞❡ ♥ã♦ é ♣❡r♠✐t✐❞❛ ♣♦r ❣❡r❛r ❝✉st♦s ♠❛✐♦r❡s q✉❡ ❛q✉❡❧❡s ❞❡❝♦rr❡♥t❡s ❞❛ ❝♦♥❝❧✉sã♦ ❛♥t❡❝✐♣❛❞❛ ❞❛s t❛r❡❢❛s✳ ❊♥tr❡t❛♥t♦✱ ❤á s✐t✉❛çõ❡s ❡♠ q✉❡ ✈❛❧❡ ❛ ♣❡♥❛ ♠❛♥t❡r ✉♠❛ ♠áq✉✐♥❛ ♦❝✐♦s❛✱ ♠❡s♠♦ q✉❡ ❤❛❥❛ ✉♠❛ t❛r❡❢❛ ❡♠ ❝♦♥❞✐çõ❡s ❞❡ t❡r s❡✉ ♣r♦❝❡ss❛♠❡♥t♦ ✐♥✐❝✐❛❞♦✳ P❛r❛ ✐❧✉str❛r ❡st❛ s✐t✉❛çã♦✱ s❡❥❛♠ ❞✉❛s t❛r❡❢❛si❡j✱ q✉❡ ❞❡✈❡♠ s❡r ❝♦♥s❡❝✉t✐✈❛s ❡♠ ✉♠❛ s❡q✉ê♥❝✐❛
❞❡ ♣r♦❞✉çã♦ ❡♥✈♦❧✈❡♥❞♦ ✉♠❛ ♠áq✉✐♥❛✱ às q✉❛✐s ❡stã♦ ❛ss♦❝✐❛❞♦s ♦s ❝✉st♦s ✉♥✐tár✐♦s ♣♦r ❛tr❛s♦ ❞❡ ✶✵✵ ❡ ✷✵✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❝✉st♦s ✉♥✐tár✐♦s ♣♦r ❛♥t❡❝✐♣❛çã♦ ❞❡ ✷✷ ❡ ✷✱ ❡ q✉❡ t❡♥❤❛♠ ❝♦♠♦ ❞❛t❛s ❞❡ ❡♥tr❡❣❛ ♦s ✐♥st❛♥t❡s Ti = 50 ❡Tj = 55✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ❡ ✶✺ ❡ ✷✺ ✉♥✐❞❛❞❡s ❞❡ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❙✉♣♦♥❤❛ q✉❡ ❛ ♠áq✉✐♥❛ ❥á ❡st❡❥❛ ❞✐s♣♦♥í✈❡❧ ❞❡s❞❡ ♦ ✐♥st❛♥t❡ ✷✵✳ ❙❡ ❛ t❛r❡❢❛ i ❝♦♠❡ç❛r ♥♦ ✐♥st❛♥t❡
✷✵✱ s❡rá ❝♦♥❝❧✉í❞❛ ♥♦ ✐♥st❛♥t❡ ✸✺ ❡✱ ♣♦rt❛♥t♦✱ ❤❛✈❡rá ✉♠❛ ♣❡♥❛❧✐③❛çã♦ ✐❣✉❛❧ ❛ ✸✸✵
(= 15 × 22) ♣❡❧❛ ❛♥t❡❝✐♣❛çã♦✳ ◆❡ss❡ ❝❛s♦✱ ❛ t❛r❡❢❛ j ♣♦❞❡rá ❝♦♠❡ç❛r s♦♠❡♥t❡
♥♦ ✐♥st❛♥t❡ ✸✺✳ ❈♦♥s✐❞❡r❛♥❞♦ s❡✉ t❡♠♣♦ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✱ ❡❧❛ s❡rá ❝♦♥❝❧✉í❞❛ ♥♦ ✐♥st❛♥t❡ ✻✵✱ ♣♦rt❛♥t♦ ✺ ✉♥✐❞❛❞❡s ❞❡ t❡♠♣♦ ❛tr❛s❛❞❛ ❡♠ r❡❧❛çã♦ à ❞❛t❛ ❞❡ ❡♥tr❡❣❛✱ r❡s✉❧t❛♥❞♦ ❡♠ ✉♠ ❝✉st♦ ♣♦r ❛tr❛s♦ ✐❣✉❛❧ ❛ ✶✵✵ (= 5 ×20)✱ ❡ ✉♠ ❝✉st♦ t♦t❛❧ ❞❡
✹✸✵ (= 330 + 100)✱ ❝♦♥❢♦r♠❡ ♣♦❞❡ s❡r ✈✐st♦ ♥❛ ✜❣✉r❛ ✶✳✶✳ ❈♦♥s✐❞❡r❡✱ ❛❣♦r❛✱ q✉❡
♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛ t❛r❡❢❛ i s❡❥❛ ✐♥✐❝✐❛❞♦ ♥♦ ✐♥st❛♥t❡ ✸✺✱ ♠❡s♠♦ s❛❜❡♥❞♦ q✉❡ ❛
♠áq✉✐♥❛ ❡stá ❞✐s♣♦♥í✈❡❧ ❞❡s❞❡ ♦ ✐♥st❛♥t❡ ✷✵✳ ◆❡st❡ ❝❛s♦✱ ❛ t❛r❡❢❛ i s❡r✐❛ ❝♦♥❝❧✉í❞❛
♥♦ ✐♥st❛♥t❡ ✺✵✱ s❡♠ ♠✉❧t❛ ♥❡♠ ♣♦r ❛♥t❡❝✐♣❛çã♦ ♥❡♠ ♣♦r ❛tr❛s♦✳ ❆ t❛r❡❢❛j✱ ❡♥tã♦✱ ❥á
♣♦❞❡r✐❛ ❝♦♠❡ç❛r✱ t❡r♠✐♥❛♥❞♦ ♥♦ ✐♥st❛♥t❡ ✼✺✱ ❝♦♠ ✷✵ ✉♥✐❞❛❞❡s ❞❡ t❡♠♣♦ ❞❡ ❛tr❛s♦✱ r❡s✉❧t❛♥❞♦ ❡♠ ✉♠❛ ♠✉❧t❛ ♣♦r ❛tr❛s♦ ❞❡ ✹✵✵ (= 20×20)✱ ♠♦str❛❞♦ ♥❛ ✜❣✉r❛ ✶✳✷✳
❖ ❝✉st♦ t♦t❛❧ ♥❡st❛ ú❧t✐♠❛ s✐t✉❛çã♦ s❡r✐❛ ❞❡ ✹✵✵ ✉♥✐❞❛❞❡s✱ ♠❡♥♦r q✉❡ ❛q✉❡❧❡ ♥♦ q✉❛❧ ❛ t❛r❡❢❛ i ❝♦♠❡ç❛✈❛ ❞❡s❞❡ ♦ ✐♥st❛♥t❡ ❞❡ ❧✐❜❡r❛çã♦ ❞❛ ♠áq✉✐♥❛✳ ❆ss✐♠✱ ♥ã♦
❤❛✈❡♥❞♦ r❡str✐çõ❡s à ♦❝✐♦s✐❞❛❞❡ ❞❛s ♠áq✉✐♥❛s✱ ❞❡t❡r♠✐♥❛r ❛ ♠❡❧❤♦r ❞❛t❛ ♣❛r❛ ✐♥✐❝✐❛r ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❝❛❞❛ t❛r❡❢❛ ♦✉✱ ❡q✉✐✈❛❧❡♥t❡♠❡♥t❡✱ ✐♥s❡r✐r t❡♠♣♦s ♦❝✐♦s♦s ❡♥tr❡ t❛r❡❢❛s✱ ♣♦❞❡rá ♣r♦❞✉③✐r s♦❧✉çõ❡s ❞❡ ♠❡♥♦r❡s ❝✉st♦s✳
❈♦♠ r❡❧❛çã♦ à ✐♥✢✉ê♥❝✐❛ ❞♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❛s t❛r❡❢❛s ♥❛ s❡q✉ê♥❝✐❛ ❞❡ ♣r♦❞✉çã♦✱ ❝❤❛♠❛❞♦ ❞❡ t❡♠♣♦ ❞❡ s❡t✉♣✱ ♦❜s❡r✈❛✲s❡ q✉❡ ❛ ♠❛✐♦r✐❛ ❞♦s tr❛❜❛❧❤♦s ❝✐❡♥tí✜❝♦s ❝♦♥s✐❞❡r❛ q✉❡ t❛✐s t❡♠♣♦s sã♦ ♥❡❣❧✐❣❡♥❝✐á✈❡✐s ♦✉✱ ❡♥tã♦✱ ♣♦❞❡♠ s❡r ❛❞✐❝✐✲ ♦♥❛❞♦s ❛♦s t❡♠♣♦s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞❛s t❛r❡❢❛s✳ ■st♦ é✱ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ♦s t❡♠♣♦s ❞❡ s❡t✉♣ sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s ❞❛ s❡q✉ê♥❝✐❛ ❞❡ t❛r❡❢❛s✳ ❈♦♥t✉❞♦✱ ♠✉✐t♦s ❡st✉❞♦s✱ ❝♦♠♦
❚❛r❡❢❛i−1 ❚❛r❡❢❛i ❚❛r❡❢❛j
Ti Tj
Recurso
M
´
aq
uina
T empo
❋✐❣✉r❛ ✶✳✶✿ ❊①❡♠♣❧♦ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ s❡♠ t❡♠♣♦ ♦❝✐♦s♦ ❡♥tr❡ t❛r❡❢❛s
❚❛r❡❢❛i−1 ❚❛r❡❢❛i ❚❛r❡❢❛j
❚❡♠♣♦ ♦❝✐♦s♦
Ti Tj
Recurso
M
´
aq
uina
T empo
❋✐❣✉r❛ ✶✳✷✿ ❊①❡♠♣❧♦ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❝♦♠ t❡♠♣♦ ♦❝✐♦s♦ ❡♥tr❡ t❛r❡❢❛s
♦s ❞❡ P❛♥✇❛❧❦❛r ❡t ❛❧✳ ✭✶✾✼✸✮✱ ❛♣✉❞ ●✉♣t❛ ❡ ❙♠✐t❤ ✭✷✵✵✻✮✱ ✐♥❞✐❝❛♠ q✉❡ t❡♠♣♦s ❞❡ s❡t✉♣ s✐❣♥✐✜❝❛t✐✈♦s ❛♣❛r❡❝❡r❡♠ ❝♦♠ ❢r❡q✉ê♥❝✐❛ ❡♠ ♠✉✐t❛s s✐t✉❛çõ❡s ♣rát✐❝❛s s❡♠✲ ♣r❡ q✉❡ ❤á ❛❧t❡r❛çã♦ ❞❛ t❛r❡❢❛ ❛ s❡r ♣r♦❝❡ss❛❞❛ ♥❛ ♠áq✉✐♥❛✳ ❙❡❣✉♥❞♦ ♦s ❛✉t♦r❡s✱ ❝♦♠ ❜❛s❡ ❡♠ ✐♥❢♦r♠❛çõ❡s ♣r❡st❛❞❛s ♣♦r ❣❡r❡♥t❡s ❞❡ ♣r♦❞✉çã♦✱ ❝❡r❝❛ ❞❡ ✼✵✪ ❞♦s ❡♥tr❡✈✐st❛❞♦s ❛✜r♠❛r❛♠ q✉❡ ❡♠ ♣❡❧♦ ♠❡♥♦s ✷✺✪ ❞❛s ♦♣❡r❛çõ❡s✱ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛✲ r❛çã♦ ❡r❛ ❞❡♣❡♥❞❡♥t❡ ❞❛ s❡q✉ê♥❝✐❛ ❞❡ ♣r♦❞✉çã♦✳ ❉❡ ❛❝♦r❞♦ ❝♦♠ ❑✐♠ ❡ ❇♦❜r♦✇s❦✐ ✭✶✾✾✹✮✱ ♣❛r❛ ♠♦❞❡❧❛r ♠❡❧❤♦r ❝❛s♦s ♣rát✐❝♦s✱ ❡ss❡s t❡♠♣♦s ❞❡✈❡♠ s❡r ❝♦♥s✐❞❡r❛❞♦s ❡①♣❧✐❝✐t❛♠❡♥t❡ s❡♠♣r❡ q✉❡ ❡❧❡s ❢♦r❡♠ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♠❛✐♦r❡s q✉❡ ♦s t❡♠♣♦s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✳ ❯♠❛ r❡✈✐sã♦ ❞❡ tr❛❜❛❧❤♦s s♦❜r❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ ❝♦♠ t❡♠♣♦s ❞❡ ♣r❡♣❛r❛çã♦ ♣♦❞❡ s❡r ❡♥❝♦♥tr❛❞❛ ❡♠ ❆❧❧❛❤✈❡r❞✐ ❡t ❛❧✳ ✭✶✾✾✾✮✳
❆✐♥❞❛ s❡❣✉♥❞♦ ❆❧❧❛❤✈❡r❞✐ ❡t ❛❧✳ ✭✶✾✾✾✮✱ ♦s ♣r♦❜❧❡♠❛s ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❡♥✈♦❧✈❡♥❞♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ♣♦❞❡♠ s❡r ❝❧❛ss✐✜❝❛❞♦s ❡♠ ❞♦✐s t✐♣♦s ❞❡ ♣r♦❜❧❡♠❛s✿
✶✳ ❝♦♠ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❛ s❡q✉ê♥❝✐❛ ✭s❡q✉❡♥❝❡✲✐♥❞❡♣❡♥❞❡♥t✮❀
✷✳ ❝♦♠ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❡♣❡♥❞❡♥t❡ ❞❛ s❡q✉ê♥❝✐❛ ✭s❡q✉❡♥❝❡✲❞❡♣❡♥❞❡♥t✮✳
◆♦ ♣r✐♠❡✐r♦ t✐♣♦ ❞❡ ♣r♦❜❧❡♠❛ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❡♣❡♥❞❡ s♦♠❡♥t❡ ❞❛ t❛r❡❢❛ ❛ s❡r ♣r♦❝❡ss❛❞❛✱ ❥á ♥♦ s❡❣✉♥❞♦✱ ♦ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❡♣❡♥❞❡ ❞❛ t❛r❡❢❛ ❛ s❡r ♣r♦❝❡ss❛❞❛ ❡ ❞❛ t❛r❡❢❛ q✉❡ ❛ ✐♠❡❞✐❛t❛♠❡♥t❡ ♣r❡❝❡❞❡✳ ◆❡st❡ ❝❛s♦✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❆❧❧❛❤✈❡r❞✐ ❡t ❛❧✳ ✭✶✾✾✾✮✱ ❛❧❣✉♥s ❛✉t♦r❡s r❡s♦❧✈❡r❛♠ ❡st❡ ♣r♦❜❧❡♠❛ ❛tr❛✈és ❞♦ Pr♦❜❧❡♠❛ ❞♦ ❈❛✐①❡✐r♦ ❱✐❛❥❛♥t❡ ✲ P❈❱ ✭tr❛✈❡❧✐♥❣ s❛❧❡s♠❛♥ ♣r♦❜❧❡♠ ✲ ❚❙P✮✱ ❡♠ q✉❡ ♦s t❡♠♣♦s ❞❡ ♣r❡♣❛r❛çã♦ sã♦ tr❛t❛❞♦s ❝♦♠♦ ❞✐stâ♥❝✐❛s ❡♥tr❡ ❛s ❝✐❞❛❞❡s✳
❉❡♥tr❡ ♦s ♣r♦❜❧❡♠❛s ❞❡ ♣r♦❞✉çã♦✱ ♦ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❡♠ ✉♠❛ ♠áq✉✐♥❛ ❝♦♠ ♠✐♥✐♠✐③❛çã♦ ❞❛s ♣❡♥❛❧✐❞❛❞❡s ♣♦r ❛♥t❡❝✐♣❛çã♦ ❡ ❛tr❛s♦ ❞❛ ♣r♦❞✉çã♦ ✭❙✐♥❣❧❡ ▼❛✲ ❝❤✐♥❡ ❙❝❤❡❞✉❧✐♥❣ ❢♦r ▼✐♥✐♠✐③✐♥❣ ❊❛r❧✐♥❡ss ❛♥❞ ❚❛r❞✐♥❡ss P❡♥❛❧t✐❡s✮✱ r❡♣r❡s❡♥t❛❞♦ s✐♠♣❧❡s♠❡♥t❡ ♣♦r P❙❯▼❆❆✱ é ✉♠ ❞♦s ♠❛✐s s✐♠♣❧❡s✳
❆❧é♠ ❞❛ ✐♠♣♦rtâ♥❝✐❛ ♣rát✐❝❛ ❞❡ss❡ ♣r♦❜❧❡♠❛✱ ❝♦♠ ✐♥ú♠❡r❛s ❛♣❧✐❝❛çõ❡s ✐♥✲ ❞✉str✐❛✐s ✭❆❧❧❛❤✈❡r❞✐ ❡t ❛❧✳✱ ✶✾✾✾✮✱ tr❛t❛✲s❡ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞✐❢í❝✐❧ ❞❡ s❡r r❡s♦❧✈✐❞♦ ♥❛ ♦t✐♠❛❧✐❞❛❞❡ ❡♠ t❡♠♣♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ❛❝❡✐tá✈❡✐s✱ ♣♦r ♣❡rt❡♥❝❡r à ❝❧❛ss❡ ◆P✲❞✐❢í❝✐❧ ✭❉✉ ❡ ▲❡✉♥❣✱ ✶✾✾✵❀ ▲✐❛✇✱ ✶✾✾✾❀ ❇✐s❦✉♣ ❡ ❋❡❧❞♠❛♥♥✱ ✷✵✵✶❀ ❲❛♥ ❡ ❨❡♥✱ ✷✵✵✷✮✳ ❊ss❛ ❝♦♥❥✉♥çã♦ ❞❡ ❛♣❧✐❝❛❜✐❧✐❞❛❞❡ ❡ ❞✐✜❝✉❧❞❛❞❡ ❞❡ r❡s♦❧✉çã♦ ♥❛ ♦t✐♠❛❧✐❞❛❞❡ t❡♠ ♠♦t✐✈❛❞♦ ♦s ♣❡sq✉✐s❛❞♦r❡s ❛ ❞❡s❡♥✈♦❧✈❡r❡♠ ❛❧❣♦r✐t♠♦s ❡✜❝✐❡♥t❡s ♣❛r❛ r❡s♦❧✈ê✲❧♦✳
◆❡st❡ tr❛❜❛❧❤♦✱ tr❛t❛✲s❡ ♦ P❙❯▼❆❆ ❝♦♠ ❥❛♥❡❧❛s ❞❡ ❡♥tr❡❣❛ ❞✐st✐♥t❛s ❡ t❡♠✲ ♣♦s ❞❡ ♣r❡♣❛r❛çã♦ ❞❛ ♠áq✉✐♥❛ ❞❡♣❡♥❞❡♥t❡s ❞❛ s❡q✉ê♥❝✐❛ ❞❛ ♣r♦❞✉çã♦✳ ❙✉r♣r❡❡♥✲ ❞❡♥t❡♠❡♥t❡✱ ❡ss❛ ✈❛r✐❛♥t❡ ❞♦ P❙❯▼❆❆ ❛✐♥❞❛ ♥ã♦ t❡♠ ♠❡r❡❝✐❞♦ ❛ ❞❡✈✐❞❛ ❛t❡♥çã♦✳ ❖ ú♥✐❝♦ tr❛❜❛❧❤♦ ❡♥❝♦♥tr❛❞♦ ♥❛ ❧✐t❡r❛t✉r❛✱ ❝♦♠ ❡ss❛s ❝❛r❛❝t❡ríst✐❝❛s✱ é ♦ ❞❡ ●♦♠❡s ❏r✳ ❡t ❛❧✳ ✭✷✵✵✼✮✳
P❛r❛ r❡s♦❧✈ê✲❧♦✱ ♣r♦♣õ❡✲s❡ ✉♠ ❛❧❣♦r✐t♠♦ ❞❡ ✸ ❢❛s❡s✱ ❝♦♠❜✐♥❛♥❞♦ ♦s ♣r♦❝❡✲ ❞✐♠❡♥t♦s ●❘❆❙P ✭❋❡♦ ❡ ❘❡s❡♥❞❡✱ ✶✾✾✺✮✱ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❉❡s❝❡♥t ✲ ❱◆❉ ✭▼❧❛❞❡♥♦✈✐➣ ❡ ❍❛♥s❡♥✱ ✶✾✾✼✮✱ ❇✉s❝❛ ❚❛❜✉ ✭●❧♦✈❡r✱ ✶✾✽✻✮ ❡ ❘❡❝♦♥❡①ã♦ ♣♦r ❈❛♠✐✲ ♥❤♦s ✭P❛t❤ ❘❡❧✐♥❦✐♥❣✮ ✭●❧♦✈❡r✱ ✶✾✾✻✮✳ ◆❛ ♣r✐♠❡✐r❛ ❢❛s❡ é ✉t✐❧✐③❛❞♦ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ❜❛s❡❛❞♦ ❡♠ ●❘❆❙P ♣❛r❛ ❣❡r❛r ✉♠❛ s♦❧✉çã♦ ✐♥✐❝✐❛❧✳ ◆❡st❛ ❢❛s❡✱ ❝❛❞❛ s♦❧✉çã♦ ❝♦♥s✲ tr✉í❞❛ é r❡✜♥❛❞❛ ♣♦r ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ❜❛s❡❛❞♦ ❡♠ ❉❡s❝✐❞❛ ❡♠ ❱✐③✐♥❤❛♥ç❛ ❱❛r✐á✈❡❧ ✭❱◆❉✮✱ q✉❡ ✉t✐❧✐③❛ ♠♦✈✐♠❡♥t♦s ❞❡ r❡❛❧♦❝❛çã♦ ❡ tr♦❝❛ ❞❡ t❛r❡❢❛s ♣❛r❛ ❡①♣❧♦r❛r ♦ ❡s✲ ♣❛ç♦ ❞❡ s♦❧✉çõ❡s✳ ◆❛ s❡❣✉♥❞❛ ❢❛s❡✱ ❛ s♦❧✉çã♦ ♣r♦✈❡♥✐❡♥t❡ ❞♦ ●❘❆❙P é r❡✜♥❛❞❛ ♣♦r ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ❇✉s❝❛ ❚❛❜✉✳ ❉✉r❛♥t❡ ❡ss❛ ❢❛s❡ é ❢♦r♠❛❞❛ ✉♠❛ ❧✐st❛ ❞❡ s♦❧✉çõ❡s
❡❧✐t❡ ✭❣r✉♣♦ ❡❧✐t❡✮✱ ❝♦♥t❡♥❞♦ s♦❧✉çõ❡s ❞❡ ❛❧t❛ q✉❛❧✐❞❛❞❡ ❡ ❞✐❢❡r❡♥❝✐❛❞❛s ❡♥tr❡ s✐✳ ❈♦✲ ♠♦ ♣ós✲♦t✐♠✐③❛çã♦✱ ♥❛ t❡r❝❡✐r❛ ❡ ú❧t✐♠❛ ❢❛s❡✱ é ❛♣❧✐❝❛❞❛ ❛ ❘❡❝♦♥❡①ã♦ ♣♦r ❈❛♠✐♥❤♦s ❛ ♣❛r❡s ❞❡ s♦❧✉çõ❡s ❞♦ ❣r✉♣♦ ❡❧✐t❡✳
✶✳✷ ❏✉st✐✜❝❛t✐✈❛ ❡ ❘❡❧❡✈â♥❝✐❛
❖ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ ❡stá ❡♥tr❡ ♦s ♠❛✐s ❡st✉❞❛❞♦s ❞❡st❛ ❞é❝❛❞❛✳ ❙❡❣✉♥❞♦ ❆❧❧❛❤✈❡r❞✐ ❡t ❛❧✳ ✭✷✵✵✽✮ ❡♠ s❡✉ tr❛❜❛❧❤♦ ❞❡ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ s♦❜r❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❝♦♠ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦✱ ❡♥tr❡ ♦s ❛♥♦s ❞❡ ✶✾✾✾ ❡ ✷✵✵✺✱ ❢♦r❛♠ ♣✉❜❧✐❝❛❞♦s ❡♠ ♣❡r✐ó❞✐❝♦s ♠❛✐s ❞❡ ✸✵✵ tr❛❜❛❧❤♦s s♦❜r❡ ♦ ❛ss✉♥t♦✱ ✉♠❛ ♠é❞✐❛ s✉♣❡r✐♦r ❛ ✹✵ tr❛❜❛❧❤♦s ♣♦r ❛♥♦✳ ❊st❡ ♥ú♠❡r♦ é ♠✉✐t♦ s✉♣❡r✐♦r ❛♦s ✶✾✵ tr❛❜❛❧❤♦s ❡♥❝♦♥tr❛❞♦s ❡♥tr❡ ❛s ❞é❝❛❞❛s ❞❡ ✻✵ ❡ ✾✵✳
❆♣❡s❛r ❞♦ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ tr❛❜❛❧❤♦s ♣✉❜❧✐❝❛❞♦s s♦❜r❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦✱ ♥❛ r❡✈✐sã♦ ❞❡ ❆❧❧❛❤✈❡r❞✐ ❡t ❛❧✳ ✭✷✵✵✽✮ ♥ã♦ ❢♦r❛♠ ❡♥❝♦♥tr❛❞♦s tr❛✲ ❜❛❧❤♦s s♦❜r❡ ♦ P❙❯▼❆❆ ❝♦♠ ❥❛♥❡❧❛s ❞❡ ❡♥tr❡❣❛ ❞✐st✐♥t❛s ❡ t❡♠♣♦s ❞❡ ♣r❡♣❛r❛çã♦ ❞❛ ♠áq✉✐♥❛ ❞❡♣❡♥❞❡♥t❡s ❞❛ s❡q✉ê♥❝✐❛ ❞❛ ♣r♦❞✉çã♦✱ ❢♦❝♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❉❡ ❛❝♦r❞♦ ❛✐♥❞❛ ❝♦♠ ❆❧❧❛❤✈❡r❞✐ ❡t ❛❧✳ ✭✷✵✵✽✮✱ ❛ ♠❡t❛❤❡✉ríst✐❝❛ ❇✉s❝❛ ❚❛❜✉ é ✉♠❛ ❞❛s ♠❛✐s ✉t✐❧✐③❛❞❛s ♣❛r❛ r❡s♦❧✈❡r ❡st❛ ❝❧❛ss❡ ❞❡ ♣r♦❜❧❡♠❛s✳ ❈♦♠♦ ❡st❛ té❝♥✐❝❛ r❡q✉❡r ✉♠❛ s♦❧✉çã♦ ✐♥✐❝✐❛❧ ❞❡ q✉❛❧✐❞❛❞❡✱ ♥❛❞❛ ♠❛✐s ♥❛t✉r❛❧ q✉❡ ✉t✐❧✐③❛r ❛ ♠❡t❛❤❡✉✲ ríst✐❝❛ ●❘❆❙P ♣❛r❛ ❣❡rá✲❧❛✳ P♦r s✉❛ ✈❡③✱ s♦♠❡♥t❡ ❛ ❢❛s❡ ❞❡ ❝♦♥str✉çã♦ ●❘❆❙P ♥ã♦ ❣✉✐❛ ❛ ót✐♠♦s ❧♦❝❛✐s ❝♦♠ r❡❧❛çã♦ às ❡str✉t✉r❛s ❞❡ ✈✐③✐♥❤❛♥ç❛s ❛❞♦t❛❞❛s✳ ❆ss✐♠✱ ❛♣❧✐❝❛✲s❡ t❛♠❜é♠ ✉♠ ♠ét♦❞♦ ❞❡ ❜✉s❝❛ ❧♦❝❛❧ ♣❛r❛ ♠❡❧❤♦r❛r ❛s s♦❧✉çõ❡s ❝♦♥str✉í✲ ❞❛s✳ ❆ ♠❡t❛❤❡✉ríst✐❝❛ ❱◆❉ ❢♦✐ ✉s❛❞❛ ♣❛r❛ ❡ss❡ ✜♠✱ ♣♦✐s r❡q✉❡r ♣♦✉❝♦s ♣❛râ♠❡tr♦s ✭❜❛s✐❝❛♠❡♥t❡ ❛ ❞❡✜♥✐çã♦ ❞❛s ✈✐③✐♥❤❛♥ç❛s ❡ ❛ ♦r❞❡♠ ❞❡ ❡①♣❧♦r❛çã♦ ❞❡st❛s✮✱ ♣r♦❞✉③ s♦❧✉çõ❡s ❞❡ ❜♦❛ q✉❛❧✐❞❛❞❡ ✭▼❧❛❞❡♥♦✈✐➣ ❡ ❍❛♥s❡♥✱ ✶✾✾✼✮ ❡ é ❞❡ ❢á❝✐❧ ✐♠♣❧❡♠❡♥t❛✲ çã♦✳ ❆ ❛♣❧✐❝❛çã♦ ❞❡ ❘❡❝♦♥❡①ã♦ ♣♦r ❈❛♠✐♥❤♦s ❞❡✈❡✉✲s❡ ❛♦ s✉❝❡ss♦ ❞❡st❛ té❝♥✐❝❛ ♥❛ s♦❧✉çã♦ ❞❡ ✈ár✐♦s ♦✉tr♦s ♣r♦❜❧❡♠❛s ❝♦♠❜✐♥❛tór✐♦s ✭●❧♦✈❡r ❡ ❑♦❝❤❡♥❜❡r❣❡r✱ ✷✵✵✸✮✳
❊st❡ tr❛❜❛❧❤♦ ❛♣r❡s❡♥t❛ r❡❧❡✈â♥❝✐❛ ♣♦r tr❛t❛r ✉♠ s✉❜♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛✲ ♠❡♥t♦ ❛✐♥❞❛ ♣♦✉❝♦ ❡st✉❞❛❞♦ ❡ ❝♦♥tr✐❜✉✐r ❝♦♠ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠❛ ❢❡rr❛♠❡♥t❛ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ❛ ♦t✐♠✐③❛çã♦ ❞❡ ♣r♦❝❡ss♦s ♣r♦❞✉t✐✈♦s ♥❛s ✐♥❞ústr✐❛s tê①t✐❧✱ ♣❡✲
tr♦q✉í♠✐❝❛✱ s✐❞❡rúr❣✐❝❛ ❡ ♠✐♥❡r❛çã♦✱ ❞❡♥tr❡ ♦✉tr❛s✳
✶✳✸ ❖❜❥❡t✐✈♦s
✶✳✸✳✶ ❖❜❥❡t✐✈♦ ●❡r❛❧
❊st❡ tr❛❜❛❧❤♦ ♣♦ss✉✐ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❣❡r❛❧ ❞❡s❡♥✈♦❧✈❡r ✉♠ ❛❧❣♦r✐t♠♦ ❡✜❝✐❡♥t❡ ❞❡ ♦t✐✲ ♠✐③❛çã♦✱ ❜❛s❡❛❞♦ ❡♠ té❝♥✐❝❛s ♠❡t❛❤❡✉ríst✐❝❛s✱ ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐✲ ❛♠❡♥t♦ ❡♠ ✉♠❛ ♠áq✉✐♥❛ ❝♦♠ ♠✐♥✐♠✐③❛çã♦ ❞❛s ♣❡♥❛❧✐❞❛❞❡s ♣♦r ❛♥t❡❝✐♣❛çã♦ ❡ ❛tr❛s♦ ❞❛ ♣r♦❞✉çã♦✱ ❝♦♠ t❡♠♣♦ ❞❡ ♣r❡♣❛r❛çã♦ ❞❡♣❡♥❞❡♥t❡ ❞❛ s❡q✉ê♥❝✐❛ ❞❡ ♣r♦❞✉çã♦✳
✶✳✸✳✷ ❖❜❥❡t✐✈♦s ❊s♣❡❝í✜❝♦s
❖s ♦❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ❛ s❡r❡♠ ❛t✐♥❣✐❞♦s sã♦ ♦s s❡❣✉✐♥t❡s✿
✶✳ ❋❛③❡r ✉♠❛ r❡✈✐sã♦ ❞❡ ❧✐t❡r❛t✉r❛ s♦❜r❡ ❛s ♠❡t♦❞♦❧♦❣✐❛s ✉t✐❧✐③❛❞❛s ♣❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❡♠ ✉♠❛ ♠áq✉✐♥❛❀
✷✳ ❋❛③❡r ✉♠❛ r❡✈✐sã♦ ❞❡ ❧✐t❡r❛t✉r❛ s♦❜r❡ ❛s té❝♥✐❝❛s ♠❡t❛❤❡✉ríst✐❝❛s ●❘❆❙P✱ ❱❛r✐❛❜❧❡ ◆❡✐❣❤❜♦r❤♦♦❞ ❉❡s❝❡♥t ✲ ❱◆❉✱ ❇✉s❝❛ ❚❛❜✉ ❡ ❘❡❝♦♥❡①ã♦ ♣♦r ❈❛♠✐♥❤♦s ✭P❛t❤ ❘❡❧✐♥❦✐♥❣✮❀
✸✳ ❉❡s❡♥✈♦❧✈❡r ✉♠❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❡ ♦t✐♠✐③❛çã♦ ❤í❜r✐❞❛✱ ❜❛s❡❛❞❛ ❡♠ ♠❡t❛❤❡✉rís✲ t✐❝❛s✱ ♣❛r❛ r❡s♦❧✈❡r ❡✜❝✐❡♥t❡♠❡♥t❡ ♦ ♣r♦❜❧❡♠❛❀
✹✳ ❈♦♥tr✐❜✉✐r ❝♦♠ ❛ ❢♦r♠❛çã♦ ❞❡ r❡❝✉rs♦s ❤✉♠❛♥♦s ❡s♣❡❝✐❛❧✐③❛❞♦s ♥❡ss❛ ár❡❛ ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦❀
✺✳ P♦ss✐❜✐❧✐t❛r ♠❛✐♦r ❡✜❝✐ê♥❝✐❛ ♥♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞♦ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦✳
✶✳✹ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦
❖ r❡st❛♥t❡ ❞❡st❡ tr❛❜❛❧❤♦ ❡stá ❡str✉t✉r❛❞♦ ❝♦♠♦ s❡❣✉❡✳
◆♦ ❝❛♣ít✉❧♦ ✷✱ ❛s ❝❛r❛❝t❡ríst✐❝❛s ❞♦ ♣r♦❜❧❡♠❛ ❡st✉❞❛❞♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ❡♠ ❞❡t❛❧❤❡s✱ ❜❡♠ ❝♦♠♦ ✉♠❛ ♣♦ssí✈❡❧ ❛♣❧✐❝❛çã♦ ♥❛ ár❡❛ ❞❡ ▼✐♥❡r❛çã♦✳
❯♠❛ r❡✈✐sã♦ ❞♦s tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s ❡ ❞❛s té❝♥✐❝❛s ❤❡✉ríst✐❝❛s ✉t✐❧✐③❛❞❛s sã♦ ❛♣r❡s❡♥t❛❞❛s ♥♦ ❝❛♣ít✉❧♦ ✸✳
◆♦ ❝❛♣ít✉❧♦ ✹ é ❞❡s❝r✐t♦ ♦ ❛❧❣♦r✐t♠♦ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❛r❛ r❡s♦❧✉çã♦ ❞♦ P❙❯▼❆❆✳
◆♦ ❝❛♣ít✉❧♦ ✺ sã♦ ❛♣r❡s❡♥t❛❞♦s ❡ ❞✐s❝✉t✐❞♦s ♦s r❡s✉❧t❛❞♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳
P♦r ✜♠✱ ♦ ❝❛♣ít✉❧♦ ✻ ❝♦♥❝❧✉✐ ♦ tr❛❜❛❧❤♦ ❡ ❛♣♦♥t❛ ♣❡rs♣❡❝t✐✈❛s ❢✉t✉r❛s ♣❛r❛ ♠❡❧❤♦r❛♠❡♥t♦ ❞♦ ❛❧❣♦r✐t♠♦ ♣r♦♣♦st♦✳
❈❛♣ít✉❧♦ ✷
❖ Pr♦❜❧❡♠❛ ❞❡ ❙❡q✉❡♥❝✐❛♠❡♥t♦
◆❡st❡ ❝❛♣ít✉❧♦ é ❛♣r❡s❡♥t❛❞♦ ♦s ♣r✐♥❝✐♣❛✐s t✐♣♦s ❞❡ ♣r♦❜❧❡♠❛s ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦ ❡✱ ❡♠ ❞❡t❛❧❤❡s✱ ♦ ♣r♦❜❧❡♠❛ ❡st✉❞❛❞♦ ♥❡st❡ tr❛❜❛❧❤♦✳
✷✳✶ ❚✐♣♦s ❞❡ Pr♦❜❧❡♠❛s
◆❛ r❡✈✐sã♦ ❞❡ ❆❧❧❛❤✈❡r❞✐ ❡t ❛❧✳ ✭✷✵✵✽✮✱ ♦s ❛✉t♦r❡s ❛♣r❡s❡♥t❛♠ ♦s ♣r✐♥❝✐♣❛✐s t✐♣♦s ❞❡ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦✱ sã♦ ❡❧❡s✿
✶✳ ❯♠❛ ♠áq✉✐♥❛ ✭s✐♥❣❧❡✲♠❛❝❤✐♥❡✮✿ ◆❡st❡ t✐♣♦ ❞❡ ♣r♦❜❧❡♠❛✱ ❢♦❝♦ ❞❡st❡ tr❛✲ ❜❛❧❤♦✱ t♦❞❛s ❛s t❛r❡❢❛s sã♦ ♣r♦❝❡ss❛❞❛s ❡♠ ✉♠❛ ú♥✐❝❛ ♠áq✉✐♥❛❀
✷✳ ▼áq✉✐♥❛s ♣❛r❛❧❡❧❛s ✭♣❛r❛❧❧❡❧ ♠❛❝❤✐♥❡s✮✿ ❊①✐st❡♠ m ♠áq✉✐♥❛s ❡♠ ♣❛✲
r❛❧❡❧♦✱ q✉❡ ♣♦❞❡♠ s❡r ✐❞ê♥t✐❝❛s ♦✉ ♥ã♦✳ ❈❛❞❛ t❛r❡❢❛ ♣♦❞❡ s❡r ♣r♦❝❡ss❛❞❛ ❡♠ q✉❛❧q✉❡r ✉♠❛ ❞❛s ♠áq✉✐♥❛s❀
✸✳ ❋❧♦✇ s❤♦♣✿ ❊♠ ✉♠ ❛♠❜✐❡♥t❡ ✢♦✇ s❤♦♣ ❝♦♠ m ♠áq✉✐♥❛s ❤ám ❡stá❣✐♦s ❡♠
sér✐❡✱ ❝♦♠ ✉♠❛ ♦✉ ♠❛✐s ♠áq✉✐♥❛s ❡♠ ❝❛❞❛ ❡stá❣✐♦✳ ❈❛❞❛ t❛r❡❢❛ t❡♠ q✉❡ s❡r ♣r♦❝❡ss❛❞❛ ❡♠ ❝❛❞❛ ✉♠ ❞♦s m ❡stá❣✐♦s ♥❛ ♠❡s♠❛ ♦r❞❡♠✳ ❖ t❡♠♣♦ ❞❡
♣r♦❝❡ss❛♠❡♥t♦ ♣❛r❛ ❝❛❞❛ t❛r❡❢❛ ❡♠ ❞✐❢❡r❡♥t❡s ❡stá❣✐♦s ♣♦❞❡♠ s❡r ❞✐❢❡r❡♥t❡s✳ ❖s ♣r♦❜❧❡♠❛s ✢♦✇ s❤♦♣ ♣♦❞❡♠ s❡r ❝❧❛ss✐✜❝❛❞♦s ❝♦♠♦✿
✭❛✮ r❡❣✉❧❛r ✢♦✇ s❤♦♣✿ ❊①✐st❡ ✉♠❛ ♠áq✉✐♥❛ ❡♠ ❝❛❞❛ ❡stá❣✐♦❀
✭❜✮ ♥♦✲✇❛✐t ✢♦✇ s❤♦♣✿ ❯♠❛ ♦♣❡r❛çã♦ s✉❝❡ss♦r❛ ✐♥✐❝✐❛ ✐♠❡❞✐❛t❛♠❡♥t❡ ❛♣ós s✉❛ ❛♥t❡❝❡ss♦r❛ t❡r♠✐♥❛r❀
✭❝✮ ✢❡①✐❜❧❡ ✭❤②❜r✐❞✮ ✢♦✇ s❤♦♣✿ ♠❛✐s ❞❡ ✉♠❛ ♠áq✉✐♥❛ ❡①✐st❡ ❡♠ ♣❡❧♦ ♠❡♥♦s ✉♠ ❡stá❣✐♦❀
✭❞✮ ❛ss❡♠❜❧② ✢♦✇ s❤♦♣✿ ❊♠ ✉♠ ❛♠❜✐❡♥t❡ ❛ss❡♠❜❧② ✢♦✇ s❤♦♣ ❞❡ ❞♦✐s ❡stá✲ ❣✐♦s✱ ❝❛❞❛ t❛r❡❢❛ ♣❛ss❛ ♣♦rm−1 ♦♣❡r❛çõ❡s ❡s♣❡❝í✜❝❛s ❡♠ ✉♠❛ ♠áq✉✐♥❛
♣r❡❞❡t❡r♠✐♥❛❞❛ ♥♦ ♣r✐♠❡✐r♦ ❡stá❣✐♦✱ s❡❣✉✐❞❛ ❞❡ ✉♠❛ ♦♣❡r❛çã♦ ❞❡ ♠♦♥t❛✲ ❣❡♠ ✭❛ss❡♠❜❧② ♦♣❡r❛t✐♦♥✮ ♥❛ ♠áq✉✐♥❛ ❞♦ s❡❣✉♥❞♦ ❡stá❣✐♦❀
✹✳ ❏♦❜ s❤♦♣✿ ❈♦♥s✐st❡ ❡♠m ♠áq✉✐♥❛s ❞✐❢❡r❡♥t❡s ❡ ❝❛❞❛ t❛r❡❢❛ ♣♦ss✉✐ ✉♠❛ ❞❛❞❛
♦r❞❡♠ ❞❡ ❡①❡❝✉çã♦✱ ♥❛ q✉❛❧ ❛❧❣✉♠❛s ♠áq✉✐♥❛s ♣♦❞❡♠ ♥ã♦ s❡r ✉s❛❞❛s ❡ ♦✉tr❛s ♣♦❞❡♠ s❡r r❡♣❡t✐❞❛s❀
✺✳ ❖♣❡♥ s❤♦♣✿ ❊st❡ ❛♠❜✐❡♥t❡ é s❡♠❡❧❤❛♥t❡ ❛♦ ❛♥t❡r✐♦r✱ ♣♦ré♠ ❝❛❞❛ t❛r❡❢❛ ❞❡✈❡ s❡r ♣r♦❝❡ss❛❞❛ ✉♠❛ ú♥✐❝❛ ✈❡③ ❡♠ ❝❛❞❛ ✉♠❛ ❞❛s m ♠áq✉✐♥❛s✱ ♣❛ss❛♥❞♦ ♣♦r
❡❧❛s ❡♠ q✉❛❧q✉❡r ♦r❞❡♠✳
✷✳✷ ❖ Pr♦❜❧❡♠❛ ❞❡ ❙❡q✉❡♥❝✐❛♠❡♥t♦ ♥❛ ▼✐♥❡r❛çã♦
❆ ♠✐♥❡r❛çã♦ r❡❛❧✐③❛ s✉❛s ❛t✐✈✐❞❛❞❡s ❡♠ ♠✐♥❛s s✉❜t❡rrâ♥❡❛s ♦✉ ❛ ❝é✉ ❛❜❡rt♦✳ ❊♠ ✉♠❛ ♠✐♥❛ ❛ ❝é✉ ❛❜❡rt♦✱ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛ ❝♦♥s✐st❡ ♥♦ ♣❧❛♥❡✲ ❥❛♠❡♥t♦ ❞❡ ❝✉rt♦ ♣r❛③♦✱ ♦♥❞❡ ♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ é ❛ ❞❡t❡r♠✐♥❛çã♦ ❞♦ r✐t♠♦ ❞❡ ❧❛✈r❛ ❛ s❡r ✐♠♣❧❡♠❡♥t❛❞♦ ❡♠ ❝❛❞❛ ❢r❡♥t❡✱ ❢♦r♥❡❝❡♥❞♦ à ✉s✐♥❛ ❞❡ ❜❡♥❡✜❝✐❛♠❡♥t♦ ✉♠❛ ❛❧✐♠❡♥t❛çã♦ ❛❞❡q✉❛❞❛✳
❱ár✐♦s tr❛❜❛❧❤♦s tr❛t❛♠ ❡ss❡ ♣r♦❜❧❡♠❛ ❡♠ s✉❛s ✈ár✐❛s ❡t❛♣❛s✱ ❡♥tr❡ ❡❧❛s ♦ ♣r♦❜❧❡♠❛ ❞❡ ♠✐st✉r❛ ❞❡ ♠✐♥ér✐♦s✱ ❛❧♦❝❛çã♦ ❞❡ ❡q✉✐♣❛♠❡♥t♦s ❞❡ ❝❛r❣❛ ❡ tr❛♥s♣♦rt❡ ❡ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❞❡s♣❛❝❤♦✱ ❞❡ ❢♦r♠❛ ✐♥❞❡♣❡♥❞❡♥t❡ ♦✉ ✐♥t❡❣r❛❞❛✳
❙❡❣✉♥❞♦ ●❡rs❤♦♥ ✭✶✾✽✷✮✱ ❛♣✉❞ ❈♦st❛ ✭✷✵✵✺✮✱ ♦t✐♠✐③❛r ♦ ♣r♦❜❧❡♠❛ ❞❡ ♣❧❛✲ ♥❡❥❛♠❡♥t♦ ❞❡ ❧❛✈r❛ ❡♠ ♣❛rt❡s ✐♥❞❡♣❡♥❞❡♥t❡s ♣♦❞❡ ❣❡r❛r ❝♦♥✢✐t♦s q✉❡ ✐♥✈✐❛❜✐❧✐③❛♠ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❛s s♦❧✉çõ❡s ♦❜t✐❞❛s ❡♠ ❝❛❞❛ ♣❛rt❡✳
❈♦st❛ ✭✷✵✵✺✮ ❡st✉❞♦✉ três ♣r♦❜❧❡♠❛s ❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛✱
❛ ♠✐st✉r❛ ❞❡ ♠✐♥ér✐♦s✱ ♠✐st✉r❛ ❞❡ ♠✐♥ér✐♦s ❝♦♠ ❛❧♦❝❛çã♦ ❞✐♥â♠✐❝❛ ❞❡ ❝❛♠✐♥❤õ❡s ❡ ♠✐st✉r❛ ❞❡ ♠✐♥ér✐♦s ❝♦♠ ❛❧♦❝❛çã♦ ❡stát✐❝❛ ❞❡ ❝❛♠✐♥❤õ❡s✳ ❖s ♣r♦❜❧❡♠❛s ❢♦r❛♠ r❡s♦❧✈✐❞♦s ❛tr❛✈és ❞❡ ❞✉❛s ♠❡t♦❞♦❧♦❣✐❛s✱ ✉♠❛ ❜❛s❡❛❞❛ ❡♠ ♣r♦❣r❛♠❛çã♦ ♠❛t❡♠át✐❝❛ ❡ ♦✉tr❛ ✉t✐❧✐③❛♥❞♦ té❝♥✐❝❛s ❤❡✉ríst✐❝❛s✳
❘♦❞r✐❣✉❡s ✭✷✵✵✻✮ ❢❡③ ✉♠❛ ❛♥á❧✐s❡ ❝♦♠♣❛r❛t✐✈❛ ❞❛s ♠❡t♦❞♦❧♦❣✐❛s ❞❡ ❞❡s♣❛✲ ❝❤♦ ❞❡ ❝❛♠✐♥❤õ❡s ❡♠ ♠✐♥❛s ❛ ❝é✉ ❛❜❡rt♦✳ P❛r❛ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❢♦✐ ✉t✐❧✐③❛❞♦ ♣r♦❣r❛♠❛çã♦ ❧✐♥❡❛r✱ ♣r♦❣r❛♠❛çã♦ ❞✐♥â♠✐❝❛ ❡ ✉♠❛ ❤❡✉ríst✐❝❛ ❜❛s❡❛❞❛ ❡♠ ❆❧❣♦r✐t♠♦s ●❡♥ét✐❝♦s ✭❆●✮✳
❆r❛ú❥♦ ✭✷✵✵✽✮ tr❛t♦✉ ♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛ ❝♦♠ ❛❧♦❝❛çã♦ ❞✐♥â♠✐❝❛ ❞❡ ❝❛♠✐♥❤õ❡s✳ ❖ ♣r♦❜❧❡♠❛ ❛❜♦r❞❛❞♦ ❝♦♥s✐st✐❛ ❡♠ ❞❡t❡r♠✐♥❛r ♦ ♥ú♠❡r♦ ❞❡ ✈✐❛❣❡♥s q✉❡ ❝❛❞❛ ❝❛♠✐♥❤ã♦ ❞❡✈✐❛ ❢❛③❡r ❛ ❝❛❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛✱ ❜❡♠ ❝♦♠♦ ❞❡❝✐❞✐r ❡♠ q✉❛✐s ❢r❡♥t❡s ❞❡ ❧❛✈r❛ ❛❧♦❝❛r ❛s ❝❛rr❡❣❛❞❡✐r❛s✱ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ ❛t❡♥❞❡r às ♠❡t❛s ❞❡ ♣r♦❞✉çã♦ ❡ q✉❛❧✐❞❛❞❡ r❡q✉❡r✐❞❛s ♣❛r❛ ♦ ♠✐♥ér✐♦ ❛ s❡r ♣r♦❞✉③✐❞♦✱ ❢❛③❡♥❞♦ ♦ ♠❡❧❤♦r ❛♣r♦✈❡✐t❛♠❡♥t♦ ❞❛ ❢r♦t❛ ❞❡ ✈❡í❝✉❧♦s ❞✐s♣♦♥í✈❡❧✳ ◆❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❢♦✐ ❡♠♣r❡❣❛❞♦ ✉♠ ♣r♦❝❡❞✐♠❡♥t♦ ❤❡✉ríst✐❝♦ ❜❛s❡❛❞♦ ♥❛ ♠❡t❛❤❡✉ríst✐❝❛ ■t❡r❛t❡❞ ▲♦❝❛❧ ❙❡❛r❝❤✱ ❡ ✉♠ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ❢♦✐ ❢♦r♠✉❧❛❞♦ ♣❛r❛ ✈❛❧✐❞❛r ♦ ♠ét♦❞♦ ❤❡✉ríst✐❝♦ ♣r♦♣♦st♦✳
❆ ♣r❡s❡♥t❡ ♣❡sq✉✐s❛ t❡♠ s❡✉ ❢♦❝♦ ♥♦ s❡q✉❡♥❝✐❛♠❡♥t♦ ❞❛ ♣r♦❞✉çã♦✱ q✉❡ é ✉♠❛ ❡t❛♣❛ ❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛ q✉❡ s✉r❣❡ ❛♣ós ❛ ❛❧♦❝❛çã♦ ❞♦s ❡q✉✐♣❛♠❡♥t♦s ❞❡ ❝❛r❣❛ ✭❝❛rr❡❣❛❞❡✐r❛s✮ ❡ tr❛♥s♣♦rt❡ ✭❝❛♠✐♥❤õ❡s✮ às ❢r❡♥t❡s✳
❈♦st❛ ✭✷✵✵✺✮ ❞❡s❝r❡✈❡ q✉❡ ♦ ♣r♦❜❧❡♠❛ ❞❛ ♠✐st✉r❛ ❞❡ ♠✐♥ér✐♦s ❝♦♠ ❛❧♦❝❛çã♦ ❞❡ ❝❛♠✐♥❤õ❡s ♦❜❥❡t✐✈❛ ❞❡t❡r♠✐♥❛r ♦ r✐t♠♦ ❞❡ ❧❛✈r❛ ❞❡ ❝❛❞❛ ❢r❡♥t❡ ❞❡ ❛❝♦r❞♦ ❝♦♠ s✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ♣r♦❞✉çã♦✳ ❆ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ♣r♦❞✉çã♦ ❞❡ ❝❛❞❛ ❢r❡♥t❡ é ❞❡t❡r♠✐✲ ♥❛❞❛ ♣❡❧♦s ❡q✉✐♣❛♠❡♥t♦s ❞❡ ❝❛r❣❛ ♥❡❧❛ ❛❧♦❝❛❞❛ ❡ ♣❡❧♦s ❝❛♠✐♥❤õ❡s q✉❡ r❡❛❧✐③❛♠ ♦ tr❛♥s♣♦rt❡ ❞♦ ♠❛t❡r✐❛❧ ❛té ♦ ♣♦♥t♦ ❞❡ ❜❛s❝✉❧❛♠❡♥t♦✳ ◆❡st❡ ♣r♦❜❧❡♠❛ ❤á ♦♣❡r❛çã♦ ❞❡ ❧❛✈r❛ ❞❡ ♠✐♥ér✐♦ ❡ ❡stér✐❧✱ ❛ ♠✐♥❛ ❝♦♥t❛ ❝♦♠ ✉♠❛ ❢r♦t❛ ❧✐♠✐t❛❞❛ ❞❡ ❡q✉✐♣❛♠❡♥t♦s ❞❡ ❝❛r❣❛✱ ♦s q✉❛✐s ❞❡✈❡♠ s❡r ❛❧♦❝❛❞♦s às ❢r❡♥t❡s ❞❡ ❧❛✈r❛ ❡ ♦♣❡r❛r ❡♠ ✉♠❛ ❢❛✐①❛ ❞❡ ♣r♦❞✉t✐✈✐❞❛❞❡ q✉❡ t♦r♥❡ ✈✐á✈❡❧ s✉❛ ✉t✐❧✐③❛çã♦✳ ❖ tr❛♥s♣♦rt❡ ❞♦ ♠❛t❡r✐❛❧ r❡t✐r❛❞♦ ❞❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛ é r❡❛❧✐③❛❞♦ ♣♦r ✉♠❛ ❢r♦t❛ ❞❡ ❝❛♠✐♥❤õ❡s ❝♦♠ ❝❛♣❛❝✐❞❛❞❡ ❞❡ ❝❛r❣❛ ❞✐❢❡r❡♥t❡s✳
❊ss❡s ❝❛♠✐♥❤õ❡s sã♦ ❛❧♦❝❛❞♦s às ❢r❡♥t❡s ❞❡ ❧❛✈r❛✱ t❡♥t❛♥❞♦✲s❡ ❡✈✐t❛r ❛ ❢♦r✲ ♠❛çã♦ ❞❡ ✜❧❛s✱ ♦✉ s❡❥❛✱ ♦ ❝❛♠✐♥❤ã♦ é ❛❧♦❝❛❞♦ ❛ ✉♠ ♣♦♥t♦ ❞❡ ❝❛r❣❛ ♦✉ ❜❛s❝✉❧❛♠❡♥t♦ q✉❡ ♣r♦♣♦r❝✐♦♥❡ ♦ ♠❡♥♦r t❡♠♣♦ ❞❡ ✜❧❛ ♣♦ssí✈❡❧✳ ❊♥tr❡t❛♥t♦✱ ✉♠ ❝❛♠✐♥❤ã♦ s♦♠❡♥t❡ ♣♦❞❡ s❡r ❞✐r❡❝✐♦♥❛❞♦ à ✉♠❛ ❢r❡♥t❡ q✉❡ ♣♦ss✉❛ ✉♠ ❡q✉✐♣❛♠❡♥t♦ ❞❡ ❝❛r❣❛ ❝♦♠♣❛tí✈❡❧✳
P❛r❛ ❡①❡♠♣❧✐✜❝á✲❧♦✱ s❡❥❛ ❛ ❚❛❜❡❧❛ ✷✳✶✱ ❛ q✉❛❧ ❛♣r❡s❡♥t❛ ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡✲ ♠❛ ❞❡ ❛❧♦❝❛çã♦ ❞✐♥â♠✐❝❛ ❞❡ ❝❛♠✐♥❤õ❡s ❞❡ ❆r❛ú❥♦ ✭✷✵✵✽✮✳ ◆❡st❛ t❛❜❡❧❛✱ ❛ ♣r✐♠❡✐r❛ ❝♦❧✉♥❛ ✐♥❞✐❝❛ ❛s ❢r❡♥t❡s ❞❡ ❧❛✈r❛❀ ❛ s❡❣✉♥❞❛✱ ❛s ❝❛rr❡❣❛❞❡✐r❛s ❡ ♦ st❛t✉s ❞❛ ❛❧♦❝❛çã♦ ✭✶ s❡ ❡❧❛ ❡stá ❡♠ ♦♣❡r❛çã♦ ❡ ✵✱ ❝❛s♦ ❡stá ✐♥❛t✐✈❛✮ ❡ ❛s ❞❡♠❛✐s ❝♦❧✉♥❛s✱ ♦s ❝❛♠✐♥❤õ❡s✳ ❈❛❞❛ ❝é❧✉❧❛ ❞❡st❛ t❛❜❡❧❛ ✐♥❞✐❝❛ ♦ ♥ú♠❡r♦ ❞❡ ✈✐❛❣❡♥s q✉❡ ❝❛❞❛ ❝❛♠✐♥❤ã♦ ❢❛③ à ❢r❡♥✲ t❡ ❞❡ ❧❛✈r❛✳ ❯♠ ♥ú♠❡r♦ ♥❡❣❛t✐✈♦ ✐♥❞✐❝❛ ✐♥❝♦♠♣❛t✐❜✐❧✐❞❛❞❡ ❡♥tr❡ ♦ ❝❛♠✐♥❤ã♦ ❡ ❛ ❝❛rr❡❣❛❞❡✐r❛ ❛❧♦❝❛❞❛ à ❢r❡♥t❡✳ P♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ❛ ❝❛rr❡❣❛❞❡✐r❛ ✺ ❡stá ❛❧♦❝❛❞❛ ❡ ❡♠ ♦♣❡r❛çã♦ ♥❛ ❢r❡♥t❡ ❞❡ ❧❛✈r❛ F1✳ ◆❛ ❢r❡♥t❡ F2 ❛ ❝❛rr❡❣❛❞❡✐r❛ ✸ ❡stá ❛❧♦❝❛❞❛✱
♣♦ré♠ ♥ã♦ ❡stá ❡♠ ♦♣❡r❛çã♦✳ ❏á ♥❛ F3 ♥ã♦ ❤á ♥❡♥❤✉♠❛ ❝❛rr❡❣❛❞❡✐r❛ ❛❧♦❝❛❞❛✳ ❊♠
r❡❧❛çã♦ ❛♦s ❝❛♠✐♥❤õ❡s✱ ❛ t❛❜❡❧❛ ✐♥❞✐❝❛ q✉❡ ♦ Cam1 ❡❢❡t✉❛ ✺ ✈✐❛❣❡♥s à ❢r❡♥t❡ F1✱
♥ã♦ é ❝♦♠♣❛tí✈❡❧ ❝♦♠ ❛ ❝❛rr❡❣❛❞❡✐r❛ ❞❛ ❢r❡♥t❡F2✱ ♥ã♦ ❢❛③ ✈✐❛❣❡♥s ❛ ❢r❡♥t❡F3✱ ❢❛③ ✼
✈✐❛❣❡♥s ❛ ❢r❡♥t❡ F4✱ ❡ ❛ss✐♠ ♣♦r ❞✐❛♥t❡✳
❚❛❜❡❧❛ ✷✳✶✿ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❧♦❝❛çã♦ ❞❡ ❝❛♠✐♥❤õ❡s ❋r❡♥t❡s ❈❛r❣❛ Cam1 Cam2 · · · Cam|V|
F1 ✭✺✱ ✶✮ ✺ ✵ · · · ✷
F2 ✭✸✱ ✵✮ ✲✶ ✲✶ · · · ✵
F3 ✭✲✶✱ ✵✮ ✵ ✵ · · · ✲✶
F4 ✭✻✱ ✶✮ ✼ ✲✶ · · · ✵
✳✳✳ ✳✳✳ ✳✳✳ ✳✳✳ ✳✳✳ ✳✳✳
F|F| ✭✷✱ ✶✮ ✹ ✵ · · · ✶
P❛r❛ ♠♦str❛r ❝♦♠♦ ♦ ♣r♦❜❧❡♠❛ ❞❡ s❡q✉❡♥❝✐❛♠❡♥t♦ ❛♣❛r❡❝❡ ♥♦ ♣❧❛♥❡❥❛♠❡♥t♦ ♦♣❡r❛❝✐♦♥❛❧ ❞❡ ❧❛✈r❛✱ s✉♣♦♥❤❛♠♦s ❛ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❧♦❝❛çã♦ ❞❡ ❝❛♠✐♥❤õ❡s✱ ❞❛❞❛ ♥❛ ❚❛❜❡❧❛ ✷✳✷✳ ◆❡st❛ t❛❜❡❧❛ sã♦ ❞❡s❝r✐t♦s ♦ ♥ú♠❡r♦ ❞❡ ✈✐❛❣❡♥s ❛❧♦❝❛❞❛s ♣❛r❛ ❝❛❞❛ ❝❛♠✐♥❤ã♦✱ C0 àC27✱ às ❢r❡♥t❡s ❞❡ ❧❛✈r❛✱ s❡♥❞♦ ❛s ❧✐♥❤❛s M1 ❛ M12✱ ❢r❡♥t❡s ❞❡
♠✐♥ér✐♦ ❡ E1 à E5 ❢r❡♥t❡s ❞❡ ❡stér✐❧✳
❚❛❜❡❧❛ ✷✳✷✿ ❙♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❛❧♦❝❛çã♦ ❞❡ ❝❛♠✐♥❤õ❡s
❋r✳ C01 C02 C03 C04 C05 C06 C07 C08 C09 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27
M1
M2 ✸ ✺ ✺
M3 ✸ ✺ ✹
M4 ✷ ✷ ✺ ✹ ✹
M5 M6 M7
M8 ✶ ✺ ✺ ✹ ✸
M9 ✺ ✶ ✺ ✶
M10 M11
M12 ✷ ✺ ✺ ✶
E1 ✸ ✸ ✺ ✷ ✶ ✶ ✶ ✷
E2 E3
E4 ✹ ✺ ✹ ✺
E5
