Abordagens de solução para o problema de alocação de aulas a salas

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Abordagens de solução para o problema de

alo

cação de aulas a salas

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SERVIÇO DE PÓS-GRADUAÇÃO DO ICMC-USP

Data de Depósito: 05/07/2016

Assinatura:_______________________

Rafael Bernardo Zanetti Cirino

Abordagens de solução para o problema de alocação de

aulas a salas

Dissertação apresentada ao Instituto de Ciências Matemáticas e de Computação - ICMC-USP, como parte dos requisitos para obtenção do título de Mestre em Ciências - Ciências de Computação e Matemática Computacional. VERSÃO REVISADA

Área de Concentração: Ciências de Computação e Matemática Computacional

Orientadora: Profa. Dra. Maristela Oliveira dos Santos

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Ficha catalográfica elaborada pela Biblioteca Prof. Achille Bassi e Seção Técnica de Informática, ICMC/USP,

com os dados fornecidos pelo(a) autor(a)

C578a

Cirino, Rafael Bernardo Zanetti

Abordagens de solução para o problema de alocação de aulas a salas / Rafael Bernardo Zanetti Cirino; orientadora Maristela Oliveira dos Santos. -- São Carlos, 2016.

95 p.

Dissertação (Mestrado - Programa de Pós-Graduação em Ciências de Computação e Matemática

Computacional) -- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 2016.

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Rafael Bernardo Zanetti Cirino

Solution approaches for the classroom assignment problem

Master dissertation submitted to the Instituto de Ciências Matemáticas e de Computação - ICMC-USP, in partial fulfillment of the requirements for the degree of the Master Program in Computer Science and Computational Mathematics. FINAL VERSION

Concentration Area: Computer Science and Computational Mathematics

Advisor: Profa. Dra. Maristela Oliveira dos Santos

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❆●❘❆❉❊❈■▼❊◆❚❖❙

➚ ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛✱ Pr♦❢❛✳ ❉r❛✳ ▼❛r✐st❡❧❛ ❖❧✐✈❡✐r❛ ❞♦s ❙❛♥t♦s✱ ♣♦r s❡✉s s❡✉s ❡❧♦❣✐♦s ❡ ❝rít✐❝❛s✱ ❜❡♠ ❝♦♠♦ ♣♦r s✉❛ ❝❛❧♠❛ ❡ ♣❛❝✐ê♥❝✐❛ ❡♠ t♦❞❛s ❛s ❡t❛♣❛s ❞♦ tr❛❜❛❧❤♦✳

❆♦ Pr♦❢✳ ❉r✳ ❆❧②ss♦♥ ▼❛❝❤❛❞♦ ❈♦st❛✱ ♣♦r s✉❛s ❧✐çõ❡s q✉❡ t❛♥❣❡♠ ❛❧é♠ ❞❛ ❛❝❛❞ê♠✐❛✳

❆♦ Pr♦❢✳ ❉r✳ ❆❧❡①❛♥❞r❡ ❈❧❛ú❞✐♦ ❇♦t❛③③♦ ❉❡❧❜❡♠✱ q✉❡ ❝♦♥tr✐❜✉✐✉ ❛t✐✈❛♠❡♥t❡ ❝♦♠ ✐❞❡✐❛s ❡ ❝♦♥❝❡✐t♦s✱ t❛♥t♦ ✐♥♦✈❛❞♦r❡s q✉❛♥t♦ ❞❡s❛✜❛♥t❡s✳

❆♦s ❝♦❧❡❣❛s ▼s✳ ▼✐❝❤❡❧ ❇❡ss❛♥✐ ❡ ▼s✳ ▼❛r❝♦s P❛✉❧♦ ●♦♥ç❛❧✈❡s P❡❞r♦s♦✱ ♣❡❧❛s ❧♦♥❣❛s ❤♦r❛s ❞❡ ❞✐s❝✉ssã♦ ❡ ♠♦t✐✈❛çã♦✳

❆♦s ❝♦❧❡❣❛s ❞♦ ▲❖t ✭▲❛❜♦r❛tór✐♦ ❞❡ ❖t✐♠✐③❛çã♦✮ ❞♦ ■❈▼❈✱ s❡♠♣r❡ ❛❜❡rt♦s ❛♦ ❛✉①í❧✐♦ ❡ ❞❡❜❛t❡s✳

➚ ❈❆P❊❙✱ ♣❡❧♦ ❛✉①í❧✐♦ ✜♥❛♥❝❡✐r♦ ♥❡❝❡ssár✐♦ ♣❛r❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳

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✧✭✳✳✳✮ ♠❛s ❞✐❛♥t❡ ❞♦s ❝❛s♦s ❡①tr❡♠❛♠❡♥t❡ s✐♠♣❧❡s✱ ❛ss✐♠ ❝♦♠♦ ❞✐❛♥t❡ ❞♦s ♣❛rt✐❝✉❧❛r♠❡♥t❡ ❞✐❢í❝❡✐s✱

✜❝❛✈❛♠ ❝♦♠ ❢r❡q✉ê♥❝✐❛ ♣❡r♣❧❡①♦s ✭✳✳✳✮✧

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❘❊❙❯▼❖

❊st❛ ❉✐ss❡rt❛çã♦ ❛❜♦r❞❛ ♦ Pr♦❜❧❡♠❛ ❞❡ ❆❧♦❝❛çã♦ ❞❡ ❆✉❧❛s ❛ ❙❛❧❛s ✭P❆❆❙✮✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ Pr♦❜❧❡♠❛ ❞❡ ❆❧♦❝❛çã♦ ❞❡ ❙❛❧❛s ✭P❆❙✮✳ ❆s ✐♥st✐t✉✐çõ❡s ❞❡ ❡♥s✐♥♦ s✉♣❡r✐♦r✱ ♥♦ ❝♦♠❡ç♦ ❞❡ s❡✉s ❝❛❧❡♥❞ár✐♦s ❧❡t✐✈♦s✱ r❡s♦❧✈❡♠ ✉♠ P❆❆❙ ❛♦ ❞❡t❡r♠✐♥❛r ♦s ❡s♣❛ç♦s ❛ s❡✲ r❡♠ ✉t✐❧✐③❛❞♦s ♣❛r❛ ❛s ❛t✐✈✐❞❛❞❡s ❞✐❞át✐❝❛s✳ P♦ré♠✱ ❡♠ ♠✉✐t❛s ❞❡st❛s ✐♥st✐t✉✐çõ❡s ♦ P❆❆❙ é ❛✐♥❞❛ r❡s♦❧✈✐❞♦ ♠❛♥✉❛❧♠❡♥t❡✱ ❣❡r❛♥❞♦ ❛❧t❛s ❝❛r❣❛s ❞❡ tr❛❜❛❧❤♦ ♣❛r❛ ♦s r❡s♣♦♥sá✈❡✐s✳ ◆❡st❡ tr❛❜❛❧❤♦✱ ♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ▼❛t❡♠át✐❝❛s ❡ ❞❡ ❈♦♠♣✉t❛çã♦ ✭■❈▼❈✮ ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦ ✭❯❙P✮ ❢♦✐ t♦♠❛❞♦ ❝♦♠♦ ❝❛s♦ ❞❡ ❡st✉❞♦ ♣❛r❛ ♦ P❆❆❙✳ ❯♠ ♠♦❞❡❧♦ ❞❡ ♣r♦❣r❛♠❛çã♦ ♠❛t❡♠át✐❝❛ ✐♥t❡✐r♦ é ♣r♦♣♦st♦ ❡ ❛❜♦r❞❛❞♦ ♣♦r té❝♥✐❝❛s ❞❡ r❡s♦❧✉çã♦ ❡①❛t❛✱ ♠❡t❛❤❡✉ríst✐❝❛s ♠♦♥♦✲♦❜❥❡t✐✈♦ ❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠✉❧t✐✲♦❜❥❡t✐✈♦✳ ❯♠❛ ❡str✉t✉r❛ ❞❡ ✈✐③✐✲ ♥❤❛♥ç❛ ♣r♦♣♦st❛ ♦❜t❡✈❡ r❡s✉❧t❛❞♦s ❝♦♠♣❛rá✈❡✐s à ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❡①❛t❛✱ ♣❛r❛ ✉♠ t❡♠♣♦ ✜①♦ ❞❡ ❡①❡❝✉çã♦✳ ❉❡♠♦♥str❛✲s❡ q✉❡✱ ❛ ❛❜♦r❞❛❣❡♠ ♠✉❧t✐✲♦❜❥❡t✐✈♦ é ✉♠❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❝♦♥t♦r♥❛r ❛❧❣✉♠❛s ❞✐✜❝✉❧❞❛❞❡s ❝❧áss✐❝❛s ❞♦ ♣r♦❜❧❡♠❛✱ ❝♦♠♦ ✐♥❝❡rt❡③❛s s♦❜r❡ ❛ ❡s❝♦❧❤❛ ❞♦s ♣❡s♦s ❞❛s ♠étr✐❝❛s✳ ❖s ♠ét♦❞♦s ❞❡ s♦❧✉çã♦ ♣r♦♣♦st♦s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❢♦r♥❡❝❡♠✱ ❛♦s r❡s♣♦♥sá✈❡✐s✱ ❜♦♥s ✐♥str✉♠❡♥t♦s ❞❡ ❛✉①í❧✐♦ à t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ♣❛r❛ ♦ P❆❆❙✳

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❆❇❙❚❘❆❈❚

❚❤✐s ❉✐ss❡rt❛t✐♦♥ ❛❞❞r❡ss❡s t❤❡ ❈❧❛ssr♦♦♠ ❆ss✐❣♥♠❡♥t Pr♦❜❧❡♠ ✭❈❆P✮✳ ❆❧❧ ❍✐❣❤❡r ❊❞✉❝❛t✐♦♥ ■♥st✐t✉t❡s✱ ❛t t❤❡ s❝❤♦♦❧②❡❛r✬s ❜❡❣✐♥✱ ❢❛❝❡s ❛ ❈❆P t♦ ❞❡✜♥❡ ✇❤❡r❡ t❤❡ ❝❧❛ss❡s ✇✐❧❧ ❜❡ t❛✉❣❤t✳ ❍♦✇❡✈❡r✱ ♠❛♥② ♦❢ t❤♦s❡ st✐❧❧ s♦❧✈❡s t❤✐s ♣r♦❜❧❡♠ ♠❛♥✉❛❧❧②✱ ❞❡♠❛♥❞✐♥❣ ❤✐❣❤ ❡✛♦rts ❢r♦♠ t❤❡ r❡s♣♦♥s✐❜❧❡ st❛✛✳ ■♥ t❤✐s st✉❞②✱ t❤❡ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦✬s ✭❯❙P✮ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ▼❛t❡♠át✐❝❛s ❡ ❞❡ ❈♦♠♣✉t❛çã♦ ✭■❈▼❈✮ ✇❛s t❛❝❦❧❡❞ ❛s st✉❞② ❝❛s❡ ❢♦r t❤❡ ❈❆P✳ ❆♥ ■♥t❡❣❡r Pr♦❣r❛♠♠✐♥❣ ▼♦❞❡❧ ✐s ♣r♦♣♦s❡❞ ❛♥❞ t❛❝❦❧❡❞ ❜② ❡①❛❝t ♠❡t❤♦❞s✱ ♠❡t❛✲❤❡✉r✐st✐❝s ❛♥❞ ❛ ♠✉❧t✐✲♦❜❥❡❝t✐✈❡ ❛♣♣r♦❛❝❤✳ ❆ ♥♦✈❡❧ ♥❡✐❣❤❜♦r❤♦♦❞ ♦♣❡r❛t♦r ✐s ♣r♦♣♦✲ s❡❞ ❢♦r t❤❡ ❧♦❝❛❧ s❡❛r❝❤ ❛♥❞ ♦❜t❛✐♥s ❣♦♦❞ r❡s✉❧ts✱ ❡✈❡♥ ❝♦♠♣❛r❛❜❧❡ t♦ t❤❡ ❡①❛❝t ♠❡t❤♦❞✳ ❚❤❡ ♠✉❧t✐✲♦❜❥❡❝t✐✈❡ ❛♣♣r♦❛❝❤ ✐s s❤♦✇♥ t♦ ♦✈❡r❝♦♠❡ s♦♠❡ ♦❢ t❤❡ ❝❧❛ss✐❝❛❧ ❛❞✈❡rs✐t② ♦❢ t❤❡ ♠♦♥♦✲♦❜❥❡❝t✐✈❡ ❛♣♣r♦❛❝❤✱ ❡✳❣✳✱ ❝❤♦♦s✐♥❣ ✇❡✐❣❤ts t♦ q✉❛❧✐t② ♠❡tr✐❝✳ ❚❤♦s❡ ❈❆P✬s ♣r♦♣♦s❡❞ s♦❧✉t✐♦♥ ♠❡t❤♦❞s✱ ❣✐✈❡s t❤❡ r❡s♣♦♥s✐❜❧❡ st❛✛ ❛ ❣♦♦❞ ❞❡❝✐s✐♦♥ ♠❛❦✐♥❣ s✉♣♣♦rt✳

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❙❯▼➪❘■❖

✶ ■♥tr♦❞✉çã♦ ♣✳ ✶

✷ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ♣✳ ✺

✸ ❈❛s♦s ❞❡ ❊st✉❞♦ ♣✳ ✾

✸✳✶ ▼♦❞❡❧❛❣❡♠ ❝♦♠ ❞✉❛s ♠étr✐❝❛s ❞❡ q✉❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✵

✸✳✷ ▼♦❞❡❧❛❣❡♠ ❝♦♠ ❝✐♥❝♦ ♠étr✐❝❛s ❞❡ q✉❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✸

✹ ❆❜♦r❞❛❣❡♠ ▼♦♥♦✲♦❜❥❡t✐✈♦ ♣✳ ✶✼

✹✳✶ ❍❡✉ríst✐❝❛ ❈♦♥str✉t✐✈❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽

✹✳✷ ❇✉s❝❛ ▲♦❝❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶

✹✳✸ ❇✉s❝❛ ❚❛❜✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✼

✹✳✹ ●❘❆❙P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✾

✹✳✺ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✷

✹✳✻ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❈♦♠♣❛❝t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✾

✺ ❆❜♦r❞❛❣❡♠ ▼✉❧t✐✲♦❜❥❡t✐✈♦ ♣✳ ✹✺

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✻ ❚❡st❡s ❈♦♠♣✉t❛❝✐♦♥❛✐s ♣✳ ✺✾

✻✳✶ ❆♠❜✐❡♥t❡ ❞❡ ❚❡st❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✾

✻✳✷ ●❡r❛çã♦ ❞♦s ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✾

✻✳✸ ❘❡s✉❧t❛❞♦s ❞♦ ▼ét♦❞♦ ❊①❛t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✶

✻✳✹ ❚❡st❡s ❞❡ ❙❡♥s✐❜✐❧✐❞❛❞❡ ❞❡ P❛râ♠❡tr♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✹

✻✳✹✳✶ ❆♣r❡s❡♥t❛çã♦ ❞♦s ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✺

✻✳✺ ❉❡s❡♠♣❡♥❤♦ ❞❛s ❆❜♦r❞❛❣❡♥s ▼♦♥♦✲♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✺

✻✳✻ ❉❡s❡♠♣❡♥❤♦ ❞♦s ▼ét♦❞♦s ▼✉❧t✐✲♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✵

✼ ❈♦♥❝❧✉sõ❡s ❡ P❡rs♣❡❝t✐✈❛s ♣✳ ✽✺

❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ♣✳ ✽✼

(17)

▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙

✶ ▼étr✐❝❛s ❞❡ ◗✉❛❧✐❞❛❞❡ ❞♦ P❆❆❙ ❞❛ ▲✐t❡r❛t✉r❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻

✷ ❉✐♠❡♥sõ❡s ✉t✐❧✐③❛❞❛s ♥❛s ■♥stâ♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✵

✸ ■♥stâ♥❝✐❛s ✉t✐❧✐③❛❞❛s ❡ s✉❛s ❝❛r❛❝t❡ríst✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✵

✹ P❡s♦s ♣❛r❛ ❛s ✺ ▼étr✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✶

✺ ❙♦❧✉çõ❡s ♦❜t✐❞❛s ❝♦♠ ♦ ❈P▲❊❳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✷

✻ P❛râ♠❡tr♦ ❞♦s ❆❧❣♦r✐t♠♦s Pr♦♣♦st♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✹

✼ ❉✐s❝r❡t✐③❛çã♦ ❞♦s P❛râ♠❡tr♦ ❞♦s ❆❧❣♦r✐t♠♦s Pr♦♣♦st♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✹

✽ ❉❡s❡❥❛❜✐❧✐❞❛❞❡ ❈♦♠♣♦st❛ ♣❛r❛ ❛s ❝♦♠❜✐♥❛çõ❡s ❞❡ ♣❛râ♠❡tr♦s ❞♦ ●❘❆❙P ♣✳ ✼✵

✾ ❈♦♠♣♦s✐t❡ ❉❡s✐r❛❜✐❧✐t② ♣❛r❛ ❛s ❝♦♠❜✐♥❛çõ❡s ❞❡ ♣❛râ♠❡tr♦s ❞♦ ❆●❈ ✳ ✳ ♣✳ ✼✷

✶✵ ❚❡st❡ ❞❡ ❚✉r❦❡② ♣❛r❡❛❞♦ ♣❛r❛ ❚❛①❛ ❞❡ ❈r♦ss♦✈❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✸

✶✶ ❚❡st❡ ❞❡ ❚✉r❦❡② ♣❛r❡❛❞♦ ♣❛r❛ ❚❛①❛ ❞❡ ▼✉t❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✹

✶✷ P❛râ♠❡tr♦s ❡s❝♦❧❤✐❞♦s ♣❛r❛ ❝❛❞❛ ✉♠ ❞♦s ♠ét♦❞♦s ♠♦♥♦✲♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ♣✳ ✼✺

(18)

(19)

▲■❙❚❆ ❉❊ ❋■●❯❘❆❙

✶ ■❧✉str❛çã♦ ❞❛ ❘❡♣r❡s❡♥t❛çã♦ ♣♦r ●r❛❢♦ ❞♦ P❆❆❙ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶

✷ ❊①❡♠♣❧♦ ❞♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❛ ❇✉s❝❛ ▲♦❝❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✷

✸ ❊①❡♠♣❧✐✜❝❛çã♦ ❞♦ ♠♦✈✐♠❡♥t♦ ❞❡ ❚r♦❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸

✹ ❊①❡♠♣❧✐✜❝❛çã♦ ❞♦ ♠♦✈✐♠❡♥t♦ ❞❡ ❆❧♦❝❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✸

✺ ❊①❡♠♣❧✐✜❝❛çã♦ ❞❛ ♥♦✈❛ ❱✐③✐♥❤❛♥ç❛ ♣r♦♣♦st❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✻

✻ ❊①❡♠♣❧♦ ❞♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❛ ❇✉s❝❛ ❚❛❜✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽

✼ ❘❡♣r❡s❡♥t❛çã♦ ❝♦❞✐✜❝❛❞❛ ❞❡ ✉♠❛ s♦❧✉çã♦ ♥♦ ❆● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✸

✽ ❖♣❡r❛❞♦r ❞❡ r❡❝♦♠❜✐♥❛çã♦ tr❛❞✐❝✐♦♥❛❧ ❞♦ ❆● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✸

✾ ❖♣❡r❛❞♦r ❞❡ ♠✉t❛çã♦ tr❛❞✐❝✐♦♥❛❧ ❞♦ ❆● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✸

✶✵ ❋❧✉①♦❣r❛♠❛ ❞♦ ❆● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✹

✶✶ ❈♦❞✐✜❝❛çã♦ ✉t✐❧✐③❛❞❛ ♣❛r❛ ♦ ❆● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✺

✶✷ ❘❡❝♦♠❜✐♥❛çã♦ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❧✐♥❤❛ ✈❡rt✐❝❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✻

✶✸ ❘❡❝♦♠❜✐♥❛çã♦ ✉t✐❧✐③❛♥❞♦ ✉♠❛ ❧✐♥❤❛ ❤♦r✐③♦♥t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✻

✶✹ Pr♦❝❡ss♦ ❞❡ ❢❛❝t✐❜✐❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✼

✶✺ ❘❡♣r❡s❡♥t❛çã♦ ❞♦ ♠♦❞❡❧♦ ♣r♦❜❛❜✐❧íst✐❝♦ P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✵

✶✻ Pr♦❝❡ss♦ ❞❡ ❛♠♦str❛❣❡♠ ❞❡ s♦❧✉çã♦ ♣❛r❛ ♦ ❆●❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✶

(20)

✶✽ ■❧✉str❛çã♦ ❞♦ ✐♠♣❛❝t♦ ❞❛ ❡s❝♦❧❤❛ ❞♦s ♣❡s♦s ♣❛r❛ ❛ ❛❜♦r❞❛❣❡♠ ♠♦♥♦✲

♦❜❥❡t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻

✶✾ ❘❡❧❛çã♦ ❞❡ ❉♦♠✐♥â♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✼

✷✵ ❊①❡♠♣❧♦ ❞❛ ❋r♦♥t❡✐r❛ ❞❡ P❛r❡t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✽

✷✶ ■❧✉str❛çã♦ ❞❛ ❛♣r♦①✐♠❛çã♦ ❞❛ ❋P❖ ♣❡❧♦s ❝♦♥❥✉♥t♦s ❞❡ s♦❧✉çã♦ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✾

✷✷ ■❧✉str❛çã♦ ❞❡ ❝♦♥❥✉♥t♦s ❞❡ s♦❧✉çã♦ ♣♦ssí✈❡❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✾

✷✸ ❊①❡♠♣❧♦s ❞❡ ❤✐♣❡r✈♦❧✉♠❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✵

✷✹ Pr♦❝❡ss♦ ❞❡ ■♥✐❝✐❛çã♦ ❞❛s ❚❛❜❡❧❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✸

✷✺ ●❆P ❞❡ ♦t✐♠❛❧✐❞❛❞❡ ♣❛r❛ ♦ ❈P▲❊❳ ❝♦♠ ✺ ♠✐♥✉t♦s ❝♦♠♣❛r❛❞♦ ❝♦♠ ♦

❧✐♠✐t❛♥t❡ ✐♥❢❡r✐♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✸

✷✻ ●❆P ❞❡ ♦t✐♠❛❧✐❞❛❞❡ ♣❛r❛ ♦ ❈P▲❊❳ ❝♦♠ ✶ ❤♦r❛ ❝♦♠♣❛r❛❞♦ ❝♦♠ ♦ ❧✐♠✐✲

t❛♥t❡ ✐♥❢❡r✐♦r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✸

✷✼ ❊✈✐❞ê♥❝✐❛ ❞❡ ◆ã♦ ◆♦r♠❛❧✐❞❛❞❡ ❞❡ ●❆P ♥♦s ❞❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✻

✷✽ ❆♥á❧✐s❡ ❞♦s ❘❡sí❞✉♦s ♣❛r❛ ♦ ▼♦❞❡❧♦ ❆❥✉st❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✼

✷✾ ❍✐st♦❣r❛♠❛s ❞❡ ●❆P ❝♦♠ ◆♦r♠❛✐s ❆❥✉st❛❞❛s ♣❛r❛ ♦ ●❘❆❙P ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✼

✸✵ ●rá✜❝♦ ❞❡ ❊❢❡✐t♦s Pr✐♥❝✐♣❛✐s ❞❡ ●❆P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✽

✸✶ ●rá✜❝♦ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ●❆P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✾

✸✷ ●rá✜❝♦s ❞❛ ❆♥á❧✐s❡ ❞❡ ❘❡sí❞✉♦s ❞❛ ❘❡❣r❡ssã♦ ▲✐♥❡❛r ▼ú❧t✐♣❧❛ ♣❛r❛ ♦

●❘❆❙P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✾

✸✸ ●rá✜❝♦ ❞❡ ❊❢❡✐t♦s Pr✐♥❝✐♣❛✐s s♦❜r❡ ❛s ▼é❞✐❛s ❞❡ ●❆P ♣❛r❛ ♦ ●❘❆❙PT ♣✳ ✼✶

✸✹ ❙❝❛tt❡r♣❧♦t ❞♦ ❡♥s❛✐♦ ❞♦ ❆●❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✷

✸✺ ●rá✜❝♦ ❞❡ ❊❢❡✐t♦s Pr✐♥❝✐♣❛✐s ♣❛r❛ ♦ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✸

✸✻ ●rá✜❝♦ ❞❡ ❊❢❡✐t♦s Pr✐♥❝✐❛♣❛✐s ♣❛r❛ ❛ ❇✉s❝❛ ❚❛❜✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✹

✸✼ ❚❡st❡ ❞❡ ❚✉r❦❡② P❛r❡❛❞♦ ♣❛r❛ T abu ♥❛ ♠❡t❛❤❡✉ríst✐❝❛ ❇✉s❝❛ ❚❛❜✉ ✳ ✳ ♣✳ ✼✺

✸✽ ❇♦①♣❧♦t ❞♦ ❡①♣❡r✐♠❡♥t♦ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♠ét♦❞♦s ♠♦♥♦✲♦❜❥❡t✐✈♦ ✳ ♣✳ ✼✻

✸✾ ❇♦①♣❧♦t ❞♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♠ét♦❞♦s s✉❜❞✐✈✐❞✐❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✼

✹✵ ❚❡st❡ ♣❛r❡❛❞♦ ❞❡ ●❛♠❡s✲❍♦✇❡❧❧ ♣❛r❛ ♦ ❞❡s❡♠♣❡♥❤♦ ❞♦s ♠ét♦❞♦s ♠♦♥♦✲

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✹✶ ❚❡st❡ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞❡ ❉♦❧❛♥✲▼♦ré ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✾

✹✷ ❇♦①♣❧♦t ❞♦ ❤✐♣❡r✈♦❧✉♠❡ ♣❛r❛ ❛s ❇✉s❝❛s ❆●❈✱ ❇▲ ❡ ❇❚ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✶

✹✸ ❇♦①♣❧♦t ❞❛ ❇✉s❝❛ ❆●❈ ❞✐✈✐❞✐❞❛ ❡♠ ❝❛t❡❣♦r✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽✷

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▲■❙❚❆ ❉❊ ❆❇❘❊❱■❆❚❯❘❆❙ ❊ ❙■●▲❆❙

❆❇❚ ❆❧❣♦r✐t♠♦ ❞❡ ❇✉s❝❛ ❡♠ ❚❛❜❡❧❛s

❆❊❉ ❆❧❣♦r✐t♠♦s ❞❡ ❊st✐♠❛çã♦ ❞❡ ❉✐str✐❜✉✐çã♦

❆● ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦

❆●❈ ❆❧❣♦r✐t♠♦ ●❡♥ét✐❝♦ ❈♦♠♣❛❝t♦

❆◆❖❱❆ ❆♥❛❧②s✐s ♦❢ ❱❛r✐❛♥❝❡

❇❚ ❇✉s❝❛ ❚❛❜✉

❈❆P ❈❧❛ssr♦♦♠ ❆ss✐♥❣♠❡♥t Pr♦❜❧❡♠

❋P ❋r♦♥t❡✐r❛ ❞❡ P❛r❡t♦

❋P❖ ❋r♦♥t❡✐r❛ ❞❡ P❛r❡t♦ Ót✐♠❛

●❘❆❙P ●r❡❡❞② ❘❛♥❞♦♠✐③❡❞ ❆❞❛♣t✐✈❡ ❙❡❛r❝❤ Pr♦❝❡❞✉r❡

■❈▼❈ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ▼❛t❡♠át✐❝❛s ❡ ❞❡ ❈♦♠♣✉t❛çã♦

▲❚ ▲✐st❛ ❚❛❜✉

▼❊❆◆ ▼✉❧t✐♦❜❥❡❝t✐✈❡ ❊✈♦❧✉t✐♦♥❛r② ❆❧❣♦r✐t❤♠ ✇✐t❤ ◆♦❞❡✲❞❡♣t❤ ❡♥✲

❝♦❞✐♥❣

P❆❆❙ Pr♦❜❧❡♠❛ ❞❡ ❆❧♦❝❛çã♦ ❞❡ ❆✉❧❛s à ❙❛❧❛s

P❆❙ Pr♦❜❧❡♠❛ ❞❡ ❆❧♦❝❛çã♦ ❞❡ ❙❛❧❛s

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✶

❈❆P❮❚❯▲❖ ✶

■◆❚❘❖❉❯➬➹❖

❊st❡ tr❛❜❛❧❤♦ tr❛t❛ ♦ Pr♦❜❧❡♠❛ ❞❡ ❆❧♦❝❛çã♦ ❞❡ ❆✉❧❛s à ❙❛❧❛s ✭P❆❆❙✮ ❡ ❞✐s❝✉t❡ ❞✐✲ ❢❡r❡♥t❡s ❛❜♦r❞❛❣❡♥s ♣❛r❛ r❡s♦❧✈ê✲❧♦✳ ❖ P❆❆❙ ❝♦♥s✐st❡ ❡♠ ❡♥❝♦♥tr❛r ❛ ♠❡❧❤♦r ❢♦r♠❛ ❞❡ ❞✐str✐❜✉✐r ❛✉❧❛s ✭❡✈❡♥t♦s✮ ♥❛s s❛❧❛s ✭❡s♣❛ç♦s✮✱ ❛t❡♥❞❡♥❞♦ à ❡①✐❣ê♥❝✐❛s ❞♦s ❞❡❝✐s♦r❡s ❧♦❝❛✐s✳ ❊st❡ ♣r♦❜❧❡♠❛ ♣♦❞❡ s❡r ❛❜♦r❞❛❞♦ ❞✐r❡t❛♠❡♥t❡ ♦✉ ❝♦♠♦ ♣❛rt❡ ❝♦♥st✐t✉✐♥t❡ ❞♦s Pr♦❜❧❡♠❛s ❞❡ Pr♦❣r❛♠❛çã♦ ❞❡ ❈✉rs♦s ❯♥✐✈❡rs✐tár✐♦s✳

❖ Pr♦❜❧❡♠❛ ❞❡ Pr♦❣r❛♠❛çã♦ ❞❡ ❈✉rs♦s ❯♥✐✈❡rs✐tár✐♦s é ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❛❧♦❝❛çã♦ ❞❡ r❡❝✉rs♦s q✉❡ ❞❡✈❡ ❞❡✜♥✐r ♦s ❤♦rár✐♦s✱ ❞♦❝❡♥t❡s ❡ s❛❧❛s ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❛s ❛✉❧❛s✱ ❛t❡♥❞❡♥❞♦ à ❞❡♠❛♥❞❛ ❞✐❞át✐❝❛ ❞❛s ❯♥✐✈❡rs✐❞❛❞❡s✳ ❖ P❆❆❙ ♣♦rt❛♥t♦✱ é ✉♠❛ ♣❛rt❡ ❞❡st❡ ♣r♦❜❧❡♠❛✱ ♣♦✐s ❝♦♥s✐❞❡r❛ q✉❡ ♦s ❤♦rár✐♦s ❞❛s ❛✉❧❛s ❥á ❞❡✜♥✐❞♦s ❡ ❛❧♦❝❛♠✲s❡ s♦♠❡♥t❡ ❛s s❛❧❛s ♣❛r❛ ❡st❛s ❛✉❧❛s✳ ❖ P❆❆❙ ♣♦❞❡ s❡r r❡s♦❧✈✐❞♦ s❡♣❛r❛❞❛♠❡♥t❡ ♦✉ ❝♦♠♦ ♣❛rt❡ ❞♦

Pr♦❜❧❡♠❛ ❞❡ Pr♦❣r❛♠❛çã♦ ❞❡ ❈✉rs♦s ❯♥✐✈❡rs✐tár✐♦s ✭P❍■▲▲■P❙ ❡t ❛❧✳✱ ✷✵✶✺✮✳

◆❡st❛ ❞✐ss❡rt❛çã♦ s❡rá ❝♦♥s✐❞❡r❛❞♦ ♦ P❆❆❙ ❡♠ ✐♥st✐t✉✐çõ❡s ❞❡ ❡♥s✐♥♦ s✉♣❡r✐♦r ❝♦♠♦ ✉♠ ♣r♦❜❧❡♠❛ ❡s♣❡❝í✜❝♦✱ ♦✉ s❡❥❛✱ ♦s ❤♦rár✐♦s ❞❡ ✐♥í❝✐♦ ❡ tér♠✐♥♦ ❞❡ ❝❛❞❛ ❛✉❧❛ ❡ ♦s ❛❣❡♥t❡s ❞✐s❝❡♥t❡s ❡ ❞♦❝❡♥t❡s ❥á ❡stã♦ ❞❡✜♥✐❞♦s à ♣r✐♦r✐✳ ❈♦♥s✐❞❡r♦✉✲s❡ q✉❡ ♣❛r❛ ❡st❛s ✐♥st✐t✉✐çõ❡s ❡①✐st❛♠ ❝✉rs♦s ❡st❛❜❡❧❡❝✐❞♦s q✉❡ ♣♦ss✉❡♠ s✉❛ ❝❛r❣❛ ❞✐❞át✐❝❛ ♣r❡❞❡✜♥✐❞❛✱ ❛ss✐♠✱ ♣❛r❛ q✉❡ ✉♠ ❛❧✉♥♦ ♣♦ss❛ s❡ ❣r❛❞✉❛r ❝♦♠♦ ❊♥❣❡♥❤❡✐r♦ ❈✐✈✐❧✱ ♣♦r ❡①❡♠♣❧♦✱ ❞❡✈❡rá ❝✉rs❛r ❛❧❣✉♠❛s ❛✉❧❛s ❡s♣❡❝í✜❝❛s✱ ✐✳❡✳✱ ♦❜r✐❣❛tór✐❛s ♣❛r❛ ♦❜t❡♥çã♦ ❞❡st❡ tít✉❧♦✳

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✷ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦

• ❆✉❧❛✿ ❯♠ ❡✈❡♥t♦ s❡♠❛♥❛❧ ❝♦♠ ❤♦rár✐♦ ❞❡ ✐♥í❝✐♦✱ ❤♦rár✐♦ ❞❡ tér♠✐♥♦✱ ❞♦❝❡♥t❡ ❡

❛❧✉♥♦s ♣r❡❞❡✜♥✐❞♦s❀

• ❙❛❧❛✿ ❯♠ ❡s♣❛ç♦ ❛♣r♦♣r✐❛❞♦ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❛s ❛✉❧❛s❀

• ❚✉r♠❛✿ ❯♠ ❝♦♥❥✉♥t♦ ❞❡ ❛❧✉♥♦s ❝♦♠ ✉♠ ♣r♦❢❡ss♦r q✉❡ ♣♦ss✉✐ ✉♠❛ ♦✉ ♠❛✐s ❛✉❧❛s

s❡♠❛♥❛✐s✱ ♣♦r ❡①❡♠♣❧♦✱ ✉♠❛ t✉r♠❛ ❞❡ ■♥tr♦❞✉çã♦ à ❉✐❞át✐❝❛ q✉❡ ♣♦ss✉❛ ✷ ❛✉❧❛s s❡♠❛♥❛✐s❀

• ❈✉rrí❝✉❧♦✿ ❯♠ ❝♦♥❥✉♥t♦ ❞❡ ❛✉❧❛s ❛ss✐st✐❞❛s ♣♦r ✉♠ ❣r✉♣♦ ❞✐s❝❡♥t❡ ♣r❡❞❡✜♥✐❞♦✳

P♦r ❡①❡♠♣❧♦✱ ❛s ❛✉❧❛s ♦❜r✐❣❛tór✐❛s ❞♦ t❡r❝❡✐r♦ ♣❡rí♦❞♦ ❞♦ ❝✉rs♦ ❞❡ ▼❛t❡♠át✐❝❛❀

• ❘❡❝✉rs♦✿ ❖s r❡❝✉rs♦s sã♦ ❡❧❡♠❡♥t♦s ❛ss♦❝✐❛❞♦s às ❛✉❧❛s ♥❛ ❢♦r♠❛ ❞❡ ❡①✐❣ê♥❝✐❛s ❞✐✲

❞át✐❝❛s ♦✉ ❡r❣♦♥ô♠✐❝❛s✱ ❡♥q✉❛♥t♦ sã♦ ❛ss♦❝✐❛❞❛s à s❛❧❛s ♥❛ ❢♦r♠❛ ❞❡ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡✳ P♦r ❡①❡♠♣❧♦✱ ❛❝❡ss✐❜✐❧✐❞❛❞❡✱ ♣r♦❥❡t♦r✱ ♠❡s❛ ❞❡ ❞❡s❡♥❤♦✱ ❡t❝✳

❊st❡s ❡❧❡♠❡♥t♦s ❡stã♦ ♣r❡s❡♥t❡s ❡♠ q✉❛❧q✉❡r tr❛❜❛❧❤♦ r❡❧❛t✐✈♦ ❛♦ P❆❆❙✱ ♣♦✐s ❛♦ ♠❡♥♦s ♦ ♥ú♠❡r♦ ❞❡ ❛ss❡♥t♦s ❞❛ s❛❧❛ ❡ ♦ ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ♥❛ ❛✉❧❛ ♣♦❞❡♠ s❡r ✈✐st♦s ❝♦♠♦ r❡❝✉rs♦s ❡ ♦ ❛❣r✉♣❛♠❡♥t♦ ❞❡ ❛✉❧❛s ❡♠ ❣r✉♣♦s ❝✉rr✐❝✉❧❛r❡s ♦✉ t✉r♠❛s é ✉♠❛ ♣rát✐❝❛ ❝♦♠✉♠❡♥t❡ ❛❞♦t❛❞❛✳ ◆❡st❛ ❞✐ss❡rt❛çã♦✱ ♦s r❡❝✉rs♦s s❡rã♦ tr❛t❛❞♦s ❞❡ ❢♦r♠❛ ✐♠♣❡❞✐t✐✈❛✱ ♦✉ s❡❥❛✱ ❝❛s♦ ❛ s❛❧❛ ♥ã♦ ♣♦ss✉❛ ♦ r❡❝✉rs♦ ❡①✐❣✐❞♦ ♣❛r❛ ✉♠❛ ❛✉❧❛✱ s✉❛ ❛❧♦❝❛çã♦ ✜❝❛rá ✐♥✈✐❛❜✐❧✐③❛❞❛✳

❊①✐st❡♠ ❞✐✈❡rs❛s ❢♦r♠✉❧❛çõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ♥❛ ❧✐t❡r❛t✉r❛✱ ♣♦✐s ❡♠ ❝❛❞❛ ❧♦❝❛❧ ❡♠ q✉❡ ♦ tr❛❜❛❧❤♦ é ❝♦♥s✐❞❡r❛❞♦✱ ❝r✐❛✲s❡ ✉♠❛ ♥♦✈❛ ❢♦r♠✉❧❛çã♦✱ ❞❛❞♦ q✉❡ ♦s ❞✐❢❡r❡♥t❡s ❞❡❝✐s♦r❡s ♣♦ss✉❡♠ ❞✐st✐♥t❛s ♠❡❞✐❞❛s ❞❡ q✉❛❧✐❞❛❞❡ q✉❡ ❛❧♠❡❥❛♠ ❛♦ ❛❜♦r❞❛r ♦ ♣r♦❜❧❡♠❛✳ P♦ré♠ ❡①✐st❡♠ ❛❧❣✉♠❛s ❝❛r❛❝t❡ríst✐❝❛s q✉❡ sã♦ ✐♥trí♥s❡❝❛s ❛♦ P❆❆❙✱ q✉❡ sã♦ r❡s✉♠✐❞❛s ❡♠ três r❡str✐çõ❡s ❢♦rt❡s✿

✶✳ ❚♦❞❛s ❛s ❛✉❧❛s ❞❡✈❡♠ s❡r ❛❧♦❝❛❞❛s ❡♠ ❛❧❣✉♠❛ s❛❧❛❀

✷✳ ❆s ❛✉❧❛s ♥ã♦ ♣♦❞❡♠ t❡r ✐♥t❡rs❡❝çã♦ ❞❡ ❤♦rár✐♦ ♥❛s s❛❧❛s✱ ♦✉ s❡❥❛✱ ❞✉❛s ❛✉❧❛s ❝♦♠ s♦❜r❡♣♦s✐çã♦ ❞❡ ❤♦rár✐♦ ♥ã♦ ♣♦❞❡♠ s❡r s✐♠✉❧t❛♥❡❛♠❡♥t❡ ❛❧♦❝❛❞❛s ♥❛ ♠❡s♠❛ s❛❧❛❀

✸✳ ❆s ❛✉❧❛s s♦♠❡♥t❡ ♣♦❞❡rã♦ s❡r ❛❧♦❝❛❞❛s ❡♠ s❛❧❛s q✉❡ ❛t❡♥❞❛♠ s✉❛s ❞❡♠❛♥❞❛s ❞❡ r❡❝✉rs♦s ❡ ❝❛♣❛❝✐❞❛❞❡ ♣❛r❛ ❛❝♦♠♦❞❛r t♦❞♦s ♦s ♣❛rt✐❝✐♣❛♥t❡s✳

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❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦ ✸

❆s ❛❜♦r❞❛❣❡♥s ♠♦♥♦✲♦❜❥❡t✐✈♦ ❡ ♠✉❧t✐✲♦❜❥❡t✐✈♦ sã♦ ❝♦♥s✐❞❡r❛❞❛s ❡ ❛❧❣✉♥s ♠ét♦❞♦s ❞❡ r❡s♦❧✉çã♦ ❤❡✉ríst✐❝♦s ❡ ♠❡t❛❤❡✉ríst✐❝♦s ❢♦r❛♠ ♣r♦♣♦st♦s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳ ❋♦r❛♠ r❡❛❧✐✲ ③❛❞♦s ❡①♣❡r✐♠❡♥t♦s ❡st❛tíst✐❝♦s ♣❛r❛ ❛♥á❧✐s❡ ❞❛ ❡s❝♦❧❤❛ ❞♦s ♣❛râ♠❡tr♦s ❡ ❞❡ ❞❡s❡♠♣❡♥❤♦ ❞❡st❡s ♠ét♦❞♦s✳

❆♥á❧✐s❡s ❞❡ ❞❡s❡♠♣❡♥❤♦ ✐♥❞✐❝❛♠ q✉❡ ♦s ♠ét♦❞♦s ♣r♦♣♦st♦s sã♦ r♦❜✉st♦s✱ ♣♦ré♠ ❞✐✲ ✈❡r❣❡♠ ♥❛ q✉❛❧✐❞❛❞❡ ❞❛s s♦❧✉çõ❡s ♦❜t✐❞❛s✳ P❛r❛ ♦s ♠ét♦❞♦s ♠✉❧t✐✲♦❜❥❡t✐✈♦ ❛s s♦❧✉çõ❡s sã♦ ❛♥❛❧✐s❛❞❛s ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ♠❡❞✐❞❛ ✉♥ár✐❛ ❜❡♠ ❡st❛❜❡❧❡❝✐❞❛ ♥❛ ❧✐t❡r❛t✉r❛✱ ♦ ❤✐♣❡r✈♦❧✉♠❡✳ ❙ã♦ r❡❛❧✐③❛❞❛s ❛❧❣✉♠❛s ❛♥á❧✐s❡s ❡ ❛❧❣✉♥s ❝♦♠❡♥tár✐♦s s♦❜r❡ ❛ r❡❧❛çã♦ ❡♥tr❡ ❛s ❛❜♦r❞❛❣❡♥s ♠♦♥♦ ❡ ♠✉❧t✐ ♦❜❥❡t✐✈♦ sã♦ t❡❝✐❞♦s✳

❊st❛ ❞✐ss❡rt❛çã♦ ❡st❛ ❞✐✈✐❞✐❞❛ ❡♠ ❝❛♣ít✉❧♦s✳ ❖ ❈❛♣ít✉❧♦ ✷ tr❛③ ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐✲ ♦❣rá✜❝❛ ❞♦ ♣r♦❜❧❡♠❛✳ ◆♦ ❈❛♣ít✉❧♦ ✸ ❞✐s❝✉t❡✲s❡ ✉♠ ❡st✉❞♦ ❞❡ ❝❛s♦ ❡ ❛❧❣✉♥s ❡①❡♠♣❧♦s ❞❡ ❢♦r♠✉❧❛çã♦ ♣♦r ♠❡✐♦ ❞❡ ♠♦❞❡❧❛❣❡♠ ♠❛t❡♠át✐❝❛✳ ◆♦ ❈❛♣ít✉❧♦ ✹✱ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❞✐❢❡r❡♥t❡s ❛❜♦r❞❛❣❡♥s ♠♦♥♦✲♦❜❥❡t✐✈♦ ❡st✉❞❛❞❛s ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❡♥q✉❛♥t♦ ♦ ❈❛♣ít✉❧♦ ✺ ❛♣r❡s❡♥t❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♠✉❧t✐✲♦❜❥❡t✐✈♦✳

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(29)

✺

❈❆P❮❚❯▲❖ ✷

❘❊❱■❙➹❖ ❇■❇▲■❖●❘➪❋■❈❆

❖ P❆❆❙ é ✉♠ ♣r♦❜❧❡♠❛ q✉❡ ❛t✐♥❣❡ ✈ár✐❛s ✐♥st✐t✉✐çõ❡s ❞❡ ❡♥s✐♥♦ s✉♣❡r✐♦r ❛♦ r❡❞♦r ❞♦ ♠✉♥❞♦ ❞✉r❛♥t❡ ♦ ❝♦♠❡ç♦ ❞❡ s❡✉s ♣❡rí♦❞♦s ❧❡t✐✈♦s✳ P♦r ❡①❡♠♣❧♦✱ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡

❆✉❝❦❧❛♥❞ ✭❲❆❚❊❘❊❘✱ ✶✾✾✺✮ ❡ ✭P❍■▲▲■P❙ ❡t ❛❧✳✱ ✷✵✶✺✮✱ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ P✉r❞✉❡ ✭▼❖❖◆❊❨

❡t ❛❧✳✱ ✶✾✾✻✮ ❡ ❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙❢❛① ✭❊▲▲❖❯▼■ ❡t ❛❧✳✱ ✷✵✶✹✮✳ ❊①✐st❡♠ ♦✉tr♦s tr❛❜❛❧❤♦s

q✉❡ ❛❜♦r❞❛♠ ♦ ♣r♦❜❧❡♠❛ ❝♦♠♦ ♣❛rt❡ ✐♥t❡❣r❛♥t❡ ❞♦ Pr♦❜❧❡♠❛ ❞❡ Pr♦❣r❛♠❛çã♦ ❞❡ ❈✉rs♦s ❯♥✐✈❡rs✐tár✐♦s✱ q✉❡ ❢♦❣❡ ❞♦ ❡s❝♦♣♦ ❞❡st❛ ❞✐ss❡rt❛çã♦✱ ♣❛r❛ ♠❛✐s ✐♥❢♦r♠❛çõ❡s ✈❡r P✐❧❧❛② ✭✷✵✶✹✮✳

❱ár✐❛s ■♥st✐t✉✐çõ❡s ❞❡ ❊♥s✐♥♦ ❙✉♣❡r✐♦r ❞♦ ❇r❛s✐❧ ❛❜♦r❞❛♠ ♦ ♣r♦❜❧❡♠❛✳ ❆❧❣✉♥s ❡①❡♠✲

♣❧♦s q✉❡ ❢♦r❛♠ ❛♥❛❧✐s❛❞♦s ♣❛r❛ ❡st❛ ❞✐ss❡rt❛çã♦ sã♦ ♦s tr❛❜❛❧❤♦s ❞❡ ✭❙❖❯❩❆❀ ❙❈❆❘P■◆✱

✷✵✶✹✮ ♥❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞♦ P❛r❛♥á❀ ✭❙❖❯❩❆ ❡t ❛❧✳✱ ✷✵✵✷❛✮✱ ✭❙❖❯❩❆ ❡t ❛❧✳✱ ✷✵✵✷❜✮✱

✭❙■▲❱❆❀ ❙■▲❱❆✱ ✷✵✵✾✮ ❡ ✭P❘❆❉❖❀ ❙❖❯❩❆✱ ✷✵✶✹✮ ♥❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❖✉r♦ Pr❡t♦❀ ✭❙❯✲ ❇❘❆▼❆◆■❆◆ ❡t ❛❧✳✱ ✷✵✶✶✮ ♥❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❛ P❛r❛í❜❛❀ ✭❑❘■P❑❆❀ ❑❘■P❑❆✱ ✷✵✶✵✮

♥❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ P❛ss♦ ❋✉♥❞♦❀ ✭❈❖◆❙❚❆◆❚■◆❖ ❡t ❛❧✳✱ ✷✵✶✵✮ ♥❛ ❯♥✐✈❡rs✐❞❛❞❡ ❊st❛❞✉❛❧

❞❡ ▼❛r✐♥❣á✳

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✻ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦

❚❛❜❡❧❛ ✶✿ ▼étr✐❝❛s ❞❡ ◗✉❛❧✐❞❛❞❡ ❞♦ P❆❆❙ ❞❛ ▲✐t❡r❛t✉r❛

P✉❜❧✐❝❛çã♦ _M ▼étr✐❝❛s

1 M2 M3 M4 M5

▼✉❧✈❡② ❡t ❛❧✳ ✭✶✾✽✷✮ •

❲❛t❡r❡r ✭✶✾✾✺✮ • •

▼❛rt✐♥❡③✲❆❧❢❛r♦ ❡ ❋❧♦r❡s✲❚❡r❛♥ ✭✶✾✾✽✮ • •

❙♦✉③❛ ❡t ❛❧✳ ✭✷✵✵✷❛✮ • • •

❙♦✉③❛ ❡t ❛❧✳ ✭✷✵✵✷❜✮ • • • •

◆❛s❝✐♠❡♥t♦ ❡t ❛❧✳ ✭✷✵✵✺✮ • •

❙✐❧✈❛ ❡ ❙✐❧✈❛ ✭✷✵✵✾✮ • • •

❈♦♥st❛♥t✐♥♦ ❡t ❛❧✳ ✭✷✵✶✵✮ • • •

❑r✐♣❦❛ ❡ ❑r✐♣❦❛ ✭✷✵✶✵✮ •

❙✉❜r❛♠❛♥✐❛♥ ❡t ❛❧✳ ✭✷✵✶✶✮ • • •

❈✐r✐♥♦ ❡t ❛❧✳ ✭✷✵✶✸✮ • •

Pr❛❞♦ ❡ ❙♦✉③❛ ✭✷✵✶✹✮ • • • • •

❙♦✉③❛ ❡ ❙❝❛r♣✐♥ ✭✷✵✶✹✮ • • • •

❊❧❧♦✉♠✐ ❡t ❛❧✳ ✭✷✵✶✹✮ •

P❤✐❧❧✐♣s ❡t ❛❧✳ ✭✷✵✶✺✮ • • •

❊st❛ ❉✐ss❡rt❛çã♦ • • • • •

❆ ❚❛❜❡❧❛ ✶ s✉♠❛r✐③❛ ❛s ❞✐❢❡r❡♥t❡s ♠étr✐❝❛s ❞❡ q✉❛❧✐❞❛❞❡ ✉t✐❧✐③❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛✳ ❊❧❛s ❢♦r❛♠ ❞❡✜♥✐❞❛s ❞❡ ❢♦r♠❛ ❛ ❡♥❣❧♦❜❛r ❛s ❞✐❢❡r❡♥t❡s ♠❛♥❡✐r❛s ❝♦♠♦ sã♦ ❛♣r❡s❡♥t❛❞❛s ♥❛ ❧✐✲ t❡r❛t✉r❛✱ ♠❛s ♣r❡s❡r✈❛♥❞♦ ♦ ❢❛t♦r ❡ss❡♥❝✐❛❧ ❞❡ s✉❛ ♠❡❞✐çã♦✳ P♦r ❡①❡♠♣❧♦✱ ♣❛r❛ ❛ ♠étr✐❝❛

❘❡❞✉çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ✭M1✮ ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞♦s t❛♥t♦ ♦s ❝❛s♦s ❞❡ ❞❡s❧♦❝❛♠❡♥t♦

❞❡ ❞♦❝❡♥t❡ ✭P❘❆❉❖❀ ❙❖❯❩❆✱ ✷✵✶✹✮ q✉❛♥t♦ ♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞❡ ❞✐s❝❡♥t❡s ✭❑❘■P❑❆❀ ❑❘■P❑❆✱

✷✵✶✵✮ ❡ q✉❡ ♥❛ ♣rát✐❝❛ tr❛♥s❝r❡✈❡♠✲s❡ ❡♠ ✈❡r✐✜❝❛r s❡ ✉♠ ❝♦♥❥✉♥t♦ ♣r❡✈✐❛♠❡♥t❡ ❡st❛❜❡❧❡✲ ❝✐❞♦ ❞❡ ❛✉❧❛s ❡stá ❞✐s♣❡rs♦ s❡❣✉♥❞♦ ❛s ♠étr✐❝❛s ❡st❛❜❡❧❡❝✐❞❛s✱ ♥♦r♠❛❧♠❡♥t❡ ❛ ❞✐stâ♥❝✐❛✳

❈♦♠ ❛ ♠étr✐❝❛ ❞❡ ❊st❛❜✐❧✐❞❛❞❡ ❞❡ ❙❛❧❛ ✭M2✮✱ t❡♥t❛✲s❡ ♠❛♥t❡r ❡♠ ❞❡t❡r♠✐♥❛❞❛s

s❛❧❛s✱ ♦✉ ❝♦♥❥✉♥t♦s ❞❡ s❛❧❛s✱ ✉♠ ❝♦♥❥✉♥t♦ ♣r❡✈✐❛♠❡♥t❡ ❡s♣❡❝✐✜❝❛❞♦ ❞❡ ❛✉❧❛s✳ ❆ss✐♠✱ tr❛❜❛❧❤♦s q✉❡ ❝♦♥s✐❞❡r❛♠ q✉❡ ❛✉❧❛s ❞❡ ✉♠ ♠❡s♠♦ ❈✉rrí❝✉❧♦ ❞❡✈❡♠ ♣❡r♠❛♥❡❝❡r ❡♠

✉♠ ♠❡s♠♦ ❜❧♦❝♦ ❞✐❞át✐❝♦ ✭❙❯❇❘❆▼❆◆■❆◆ ❡t ❛❧✳✱ ✷✵✶✶✮ ♦✉ tr❛❜❛❧❤♦s q✉❡ ❝♦♥s✐❞❡r❛♠ q✉❡

❛✉❧❛s ❞❡ ✉♠❛ ♠❡s♠❛ ❚✉r♠❛ ❞❡✈❡♠ s❡r ❛❧♦❝❛❞❛s ♥❛ ♠❡s♠❛ s❛❧❛ ✭P❍■▲▲■P❙ ❡t ❛❧✳✱ ✷✵✶✺✮

❝♦♥st✐t✉❡♠ ❛ ♠❡s♠❛ ❝❛t❡❣♦r✐❛✳

❘❡ss❛❧t❛✲s❡ q✉❡ ❛ ♠étr✐❝❛ ❘❡str✐çã♦ ❞❡ ❯t✐❧✐③❛çã♦ ❞❡ ❙❛❧❛s ✭M3✮ é ❝♦♥s✐❞❡r❛❞❛

t❛♥t♦ ♥❛ s✉❛ ❢♦r♠❛ ♣❛r❝✐❛❧✱ ✐✳❡✳ ❤á ❛❧❣✉♥s ❤♦rár✐♦s ✐♥❞❡s❡❥á✈❡✐s ♣❛r❛ s✉❛ ✉t✐❧✐③❛çã♦ ♦✉

❡✈✐t❛✲s❡ ❛ s✉❜✲✉t✐❧✐③❛çã♦ ❞♦s r❡❝✉rs♦s ❞❛s s❛❧❛s ✭❙❯❇❘❆▼❆◆■❆◆ ❡t ❛❧✳✱ ✷✵✶✶✮✱ ❛té s✉❛ ❢♦r♠❛

t♦t❛❧✱ ✐✳❡✳ é ✐♥❞❡s❡❥á✈❡❧ ❛ ✉t✐❧✐③❛çã♦ ❞❛ s❛❧❛ ❡♠ q✉❛❧q✉❡r ❤♦rár✐♦ ✭◆❆❙❈■▼❊◆❚❖ ❡t ❛❧✳✱

✷✵✵✺✮✱ ✭❈■❘■◆❖ ❡t ❛❧✳✱ ✷✵✶✺✮✳

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❈❛♣ít✉❧♦ ✷✳ ❘❡✈✐sã♦ ❇✐❜❧✐♦❣rá✜❝❛ ✼

♥ú♠❡r♦ ❞❡ ❛ss❡♥t♦s ❧✐✈r❡s ♥❛s s❛❧❛s ❛♣ós ❛ ❛❧♦❝❛çã♦ ❞❡ ✉♠❛ ❛✉❧❛✱ ♥♦r♠❛❧♠❡♥t❡ t❡♥t❛♥❞♦ r❡❞✉③✐r ❡st❡ ♥ú♠❡r♦✳ ❊♥q✉❛♥t♦ ❛ ♠étr✐❝❛ ❆t❡♥❞✐♠❡♥t♦ ❞❡ Pr❡❢❡rê♥❝✐❛s ♣♦r ❙❛❧❛s

✭M5✮ ✐♥❝❧✉✐ t❛♥t♦ ❛s ♣r❡❢❡rê♥❝✐❛s ❞❡ ❞♦❝❡♥t❡s ♣♦r s❛❧❛s ✭P❘❆❉❖❀ ❙❖❯❩❆✱ ✷✵✶✹✮ q✉❛♥t♦

♣r❡❢❡rê♥❝✐❛s ❞❡ ❞✐s❝❡♥t❡s ✭P❍■▲▲■P❙ ❡t ❛❧✳✱ ✷✵✶✺✮✳

❆s ❛❜♦r❞❛❣❡♥s ❞❡ s♦❧✉çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞✐st✐♥❣✉❡♠✲s❡ ♠✉✐t♦ ♥❛ ❧✐t❡r❛t✉r❛✱ ❞❡st❛❝❛♥❞♦✲

s❡ ♦ ✉s♦ ❞❛ ♠❡t❛✲❤❡✉ríst✐❝❛ ❘❡❝♦③✐♠❡♥t♦ ❙✐♠✉❧❛❞♦ ✭❙✐♠✉❧❛t❡❞ ❆♥♥❡❛❧✐♥❣✮ ❡♠ ✭❑❘■P❑❆❀

❑❘■P❑❆✱ ✷✵✶✵✮ ✭❙❖❯❩❆ ❡t ❛❧✳✱ ✷✵✵✷❛✮ ✭▼❆❘❚■◆❊❩✲❆▲❋❆❘❖❀ ❋▲❖❘❊❙✲❚❊❘❆◆✱ ✶✾✾✽✮ ✭◆❆❙❈■✲ ▼❊◆❚❖ ❡t ❛❧✳✱ ✷✵✵✺✮❀ ❞❛ ♠❡t❛✲❤❡✉ríst✐❝❛ ❇✉s❝❛ ❚❛❜✉ ✭❙❖❯❩❆ ❡t ❛❧✳✱ ✷✵✵✷❛✮ ✭❙❯❇❘❆▼❆◆■❆◆ ❡t ❛❧✳✱ ✷✵✶✶✮ ✭❙❖❯❩❆ ❡t ❛❧✳✱ ✷✵✵✹✮❀ ❛❧é♠ ❞❡ ❛❜♦r❞❛❣❡♥s ❞✐st✐♥t❛s ❝♦♠♦ ❈♦❧♦r❛çã♦ ❞❡ ●r❛❢♦s

✭❙■▲❱❆❀ ❙■▲❱❆✱ ✷✵✵✾✮✱ ❤❡✉ríst✐❝❛s ❝♦♥str✉t✐✈❛s ✭▲❖P❊❙❀ ❙❈❍❖❊❋❋❊▲✱ ✷✵✵✷✮ ❡ té❝♥✐❝❛s ❞❡

❣❡r❛çã♦ ❞❡ ❝♦❧✉♥❛s ♣❛r❛ ❛♣r♦①✐♠❛çã♦ ❞❛ s♦❧✉çã♦ ❞♦ ♠♦❞❡❧♦ ✐♥t❡✐r♦ ✭❈❖◆❙❚❆◆❚■◆❖ ❡t ❛❧✳✱

✷✵✶✵✮✳

❋✐♥❛❧♠❡♥t❡✱ ❤á ❞❡ s❡ ❝♦♥s✐❞❡r❛r q✉❡ ♦ P❆❆❙ ♥ã♦ é ✉♠ ♣r♦❜❧❡♠❛ ú♥✐❝♦✱ ♣♦✐s ♠❛✲ t❡♠❛t✐❝❛♠❡♥t❡ é ♦ ♠❡s♠♦ ♣r♦❜❧❡♠❛ ❞❡ ❛❧♦❝❛r q✉❛rt♦s ❞❡ ❤♦t❡❧✱ ❛❧♦❝❛çã♦ ❞❡ ♥❛✈✐♦s ❡♠ ❞♦❝❛s✱ ❛❧♦❝❛çã♦ ❞❡ ♣♦rtõ❡s ❞❡ ❡♠❜❛rq✉❡s ♣❛r❛ ❛❡r♦♥❛✈❡s ❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❞❡ t❛r❡❢❛s ♣❛r❛

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✾

❈❆P❮❚❯▲❖ ✸

❈❆❙❖❙ ❉❊ ❊❙❚❯❉❖

❖ P❆❆❙ t❡♠ ❢♦r♠✉❧❛çã♦ ♠❛t❡♠át✐❝❛ s✐♠♣❧❡s ♣❛r❛ ❣❡r❛r s♦❧✉çõ❡s ❢❛❝tí✈❡✐s✱ ♦✉ s❡❥❛✱ s♦❧✉çõ❡s q✉❡ ❛t❡♥❞❛♠ à ❞❡♠❛♥❞❛ ❞❛s r❡str✐çõ❡s ❢♦rt❡s ❞♦ ♣r♦❜❧❡♠❛✿ ❝♦♠♣❧❡t✉❞❡ ❞❡ ❛❧♦✲ ❝❛çã♦✱ ♥ã♦ s♦❜r❡♣♦s✐çã♦ ❞❡ ❤♦rár✐♦s ❡ ❛t❡♥❞✐♠❡♥t♦ ❞❡ r❡q✉✐s✐t♦s✳ P♦ré♠ ❞❛❞❛ ❛ ❛❧t❛ ❞❡♣❡♥❞ê♥❝✐❛ ❞❛s ♠étr✐❝❛s ❞❡ q✉❛❧✐❞❛❞❡ ❝♦♠ ♦ ❧♦❝❛❧ ❡♠ q✉❡ ♦ ♣r♦❜❧❡♠❛ é r❡s♦❧✈✐❞♦✱ ♦s ❡st✉❞♦s ❞❡ ❝❛s♦ ✐rã♦ ❞❡s❡♥✈♦❧✈❡r ♠♦❞❡❧♦s ❞❡ ❢♦r♠❛ ❛ ❛t❡♥❞❡r ❡st❡s r❡q✉✐s✐t♦s ✭✈❡r ❚❛❜❡❧❛ ✶ ♥♦ ❈❛♣ít✉❧♦ ✷✮✳

P❛r❛ ❡st❛ ❞✐ss❡rt❛çã♦ ❢♦✐ ❡st✉❞❛❞♦ ♦ ❝❛s♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ▼❛t❡♠át✐❝❛s ❡ ❞❡ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦ ✲ ❈❛♠♣✉s ❙ã♦ ❈❛r❧♦s ✭■❈▼❈✮✳ ❖ ■❈▼❈ ♣♦ss✉✐ s❡✐s ❝✉rs♦s ❞❡ ❣r❛❞✉❛çã♦ ❡ é ❝♦✲r❡s♣♦♥sá✈❡❧ ♣♦r ♠❛✐s ❞♦✐s✱ ❛❧é♠ ❞❡ ♦❢❡r❡❝❡r q✉❛tr♦ ♣r♦❣r❛♠❛s ❞❡ ♣ós✲❣r❛❞✉❛çã♦ ❡ ♣♦ss✉✐r ✈✐♥t❡ ❡ três s❛❧❛s ❞✐❞át✐❝❛s ❞✐s♣♦st❛s ❡♠ ✹ ❜❧♦❝♦s ❞❡ ❛✉❧❛✳ ❙♦♠❡♥t❡ ❛s ❛✉❧❛s q✉❡ ✉t✐❧✐③❛♠ ♦s ❡s♣❛ç♦ ❢ís✐❝♦ ❞♦ ■❈▼❈ sã♦ ❝♦♥s✐❞❡r❛❞❛s ♣❛r❛ ♦ tr❛❜❛❧❤♦✳

❖s r❡s♣♦♥sá✈❡✐s ♣♦r r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ♥♦ ■❈▼❈✱ ❝❤❛♠❛❞♦s ❞♦r❛✈❛♥t❡ ❞❡ ❞❡❝✐s♦r❡s✱ r❡s♦❧✈❡♠ ♦ ♣r♦❜❧❡♠❛ ♠❛♥✉❛❧♠❡♥t❡ ❡ ✉t✐❧✐③❛♠ s♦❧✉çõ❡s ❤✐stór✐❝❛s ❝♦♠♦ ❜❛s❡ ♣r✐♥❝✐♣❛❧✳ ❊st❛ ♠❡t♦❞♦❧♦❣✐❛ ♠♦str♦✉✲s❡ ✐♥❛❞❡q✉❛❞❛ ♣❛r❛ ❛❧❣✉♥s ❡st✉❞♦s ❞❡ ❡①♣❛♥sã♦✱ ♣♦✐s ❛❞✐❝✐♦♥❛r ✉♠❛ ❛✉❧❛ ♥♦✈❛ ♦✉ ♠✉❞❛r ♦ ❤♦rár✐♦ ❞❡ ❛✉❧❛s ❛♥t✐❣❛s✱ ❛❧t❡r❛r✐❛ ❛ s♦❧✉çã♦ ❤✐stór✐❝❛ ❛ ♣♦♥t♦ ❞❡ s❡r ♥❡❝❡ssár✐❛ ✉♠❛ ♥♦✈❛ s♦❧✉çã♦ ✲ s♦❧✉çã♦ ❡st❛ q✉❡ ♣♦❞❡r✐❛ ❞❡♠♦r❛r ✈ár✐❛s ❤♦r❛s ♣❛r❛ s❡r ♦❜t✐❞❛✳

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✶✵ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦

❧✉çõ❡s ❡ ❝❛❞❛ ❧♦❝❛❧ ❡st❛❜❡❧❡❝❡ s❡✉s ❝r✐tér✐♦s✳ P♦r ✈❡③❡s ❡ss❡s ❝r✐tér✐♦s ♥ã♦ sã♦ ❡①♣❧í❝✐t♦s✱ ♣♦✐s ♦s ❞❡❝✐s♦r❡s ♥♦r♠❛❧♠❡♥t❡ ❛tr✐❜✉❡♠ q✉❛❧✐❞❛❞❡ à s♦❧✉çã♦ ♣♦r ♠❡✐♦ ❞❡ ❡①♣❡r✐ê♥❝✐❛s ❛♥t❡r✐♦r❡s ♦✉ r❡s♣♦st❛s ❞♦s ❞✐s❝❡♥t❡s ♦✉ ❞♦❝❡♥t❡s✳ ❆ss✐♠ ♣♦r ♠❡✐♦ ❞❡ ❡♥tr❡✈✐st❛s ❝♦♠ ♦s ❞❡❝✐s♦r❡s ❢♦✐✲s❡ ❡st❛❜❡❧❡❝✐❞❛ ♦ ♣r✐♠❡✐r♦ ♠♦❞❡❧♦ ♣❛r❛ ♦ ■❈▼❈ ❝♦♠ s♦♠❡♥t❡ ❞✉❛s ♠étr✐❝❛s ❞❡ q✉❛❧✐❞❛❞❡ ✭❙❡çã♦ ✸✳✶✮✳

❖s r❡s✉❧t❛❞♦s ♦❜t✐❞♦s ❝♦♠ ♦ ♣r✐♠❡✐r♦ ♠♦❞❡❧♦ ♣❛r❛ ♦ ■❈▼❈ s❡r✈✐r❛♠ ❝♦♠♦ ❜❛s❡ ♣❛r❛ ❝♦♠♣r❡❡♥❞❡r ❛s ♦✉tr❛s ❢♦r♠❛s ❞❡ ♠❡❞✐r q✉❛❧✐❞❛❞❡ q✉❡ ♥ã♦ ❤❛✈✐❛♠✱ ❛té ❡♥tã♦✱ s✐❞♦ ❢♦r♠✉✲ ❧❛❞❛s ♠❛t❡♠❛t✐❝❛♠❡♥t❡✳ ❚❡♥❞♦ ❡♠ ✈✐st❛ q✉❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❛❞q✉✐r✐❞♦ ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ é t♦t❛❧♠❡♥t❡ ❡♠♣ír✐❝♦✱ ❞✐✜❝✉❧t❛♥❞♦ ♣♦rt❛♥t♦ ❛ tr❛♥s❝r✐çã♦ ❞♦s r❡❛✐s ✐♥t✉✐t♦s ❞♦s ❞❡❝✐s♦r❡s✳ P♦r ♠❡✐♦ ❞♦ ♣r♦❝❡ss♦ ❞❡ ✐❞❡♥t✐✜❝❛çã♦ ❞♦s ♣r♦❜❧❡♠❛s ♥❛ s♦❧✉çã♦ ❞♦ ♣r✐✲ ♠❡✐r♦ ♠♦❞❡❧♦ ❡ ❞❡ ♥♦✈❛s r❡✉♥✐õ❡s ❝♦♠ ♦s ❞❡❝✐s♦r❡s✱ ✜❝♦✉ ❡st❛❜❡❧❡❝✐❞♦ ✉♠ ♥♦✈♦ ♠♦❞❡❧♦✱ ❡st❡ ❛❣♦r❛ ❝♦♠ ❝✐♥❝♦ ♠étr✐❝❛s✱ ♣❛r❛ ♦ P❆❆❙ ♥♦ ■❈▼❈ ✭❙❡çã♦ ✸✳✷✮✳

✸✳✶ ▼♦❞❡❧❛❣❡♠ ❝♦♠ ❞✉❛s ♠étr✐❝❛s ❞❡ q✉❛❧✐❞❛❞❡

P❛r❛ ❛ ❢♦r♠✉❧❛çã♦ ❞♦ P❆❆❙ ❝♦♠ ❞✉❛s ♠étr✐❝❛s ♥♦ ■❈▼❈ ❛s ❛✉❧❛s s❡rã♦ tr❛t❛❞❛s ✐♥❞❡♣❡♥❞❡♥t❡ ❞❛ ❣r❛❞❡ ❤♦rár✐❛✳ ❆ ❣r❛❞❡ ❤♦rár✐❛ s❡r✈✐rá s♦♠❡♥t❡ ♣❛r❛ ❡st❛❜❡❧❡❝❡r ❛s r❡❧❛çõ❡s ♣❡rt✐♥❡♥t❡s ❡♥tr❡ ❛s ❛✉❧❛s ❡ s❛❧❛s✱ ♣♦r ❡①❡♠♣❧♦✱ ❞❡✜♥✐r ❛s r❡❧❛çõ❡s ❞❡ s♦❜r❡♣♦s✐çã♦ ❞❡ ❤♦rár✐♦ ❡♥tr❡ ❛s ❛✉❧❛s✳ ❊❧✐♠✐♥❛✲s❡ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ tr❛t❛r ♦s s❧♦ts ❞❡ ❤♦rár✐♦ ♥❛s ✈❛r✐á✈❡✐s ❞❡ ❞❡❝✐sã♦✳

❖ t❡♠♣♦ ❞❡ ✉♠❛ s❡♠❛♥❛ é ❞✐s❝r❡t✐③❛❞♦ ♣♦r ♠❡✐♦ ❞❡ s❧♦ts ❞❡ ❤♦rár✐♦ ❡ ❝❛❞❛ ❛✉❧❛ ❞❡✈❡rá ❡st❛r ❛ss♦❝✐❛❞❛ ❛ ✉♠ ♦✉ ♠❛✐s ❞❡st❡s s❧♦ts ❝♦♥s❡❝✉t✐✈♦s✳ ❉❡st❛❝❛✲s❡ q✉❡ ❡st❡s s❧♦ts ♣♦❞❡♠ ♣♦ss✉✐r ❞✉r❛çõ❡s ❞✐❢❡r❡♥t❡s✱ ❜❛st❛♥❞♦ ❝♦❜r✐r t♦❞♦s ♦s ❤♦rár✐♦s ❞❛ s❡♠❛♥❛✳ ❆ r❡❧❛çã♦ ❡♥tr❡ ❛s ❛✉❧❛s ❞❛s t✉r♠❛s ❡ ♦s s❧♦ts ❞❡ ❤♦rár✐♦ é ❡st❛❜❡❧❡❝✐❞❛ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ♠❛tr✐③ ❜✐♥ár✐❛

ρ✱ s❡♥❞♦ ✉♠ ❞❛❞♦ ❞❡ ❡♥tr❛❞❛ ❞♦ ♣r♦❜❧❡♠❛✳

◆❡ss❡ ♠♦❞❡❧♦ ❝❛❞❛ ❛✉❧❛ s❡rá ✉♠ ❡♥✈❡❧♦♣❛♠❡♥t♦ ❞❡ s❡✉s ❞❛❞♦s✱ ♦✉ ✉♠ ♠❡t❛❞❛❞♦✱ ❝♦♥t❡♥❞♦ ❤♦rár✐♦ ❞❡ ✐♥í❝✐♦✱ ❤♦rár✐♦ ❞❡ tér♠✐♥♦✱ ❞♦❝❡♥t❡✱ ♥ú♠❡r♦ ❞❡ ✐♥s❝r✐t♦s✱ r❡❝✉rs♦s r❡q✉❡r✐❞♦s ❡ t✉r♠❛✳ ❖s ❝♦♥❥✉♥t♦s ❞❡ ❛✉❧❛ ❡♠ s♦❜r❡♣♦s✐çã♦ ♣♦❞❡♠ s❡r ❡①tr❛í❞♦s ❞♦s ❞❛❞♦s ❡ ❛❞✐❝✐♦♥❛❞♦s ♥❛s r❡str✐çõ❡s✳ ❖♣t♦✉✲s❡ ♣♦r ♠♦❞❡❧❛r ♦ ♣r♦❜❧❡♠❛ ❛❧♦❝❛♥❞♦ ❛✉❧❛s ❛ s❛❧❛s✱ ♠❛♥t❡♥❞♦✲s❡ ❛s três r❡str✐çõ❡s ❢♦rt❡s✱ ♦✉ s❡❥❛✱ ❝♦♠♣❧❡t✉❞❡ ❞❛ s♦❧✉çã♦✱ ♥ã♦ s♦❜r❡♣♦s✐çã♦ ❞❡ ❤♦rár✐♦s ❡ ❛t❡♥❞✐♠❡♥t♦ ❞❡ r❡q✉✐s✐t♦s ❞❡ r❡❝✉rs♦s✳

P♦❞❡✲s❡ r❡♣r❡s❡♥t❛r ♣❛r❝✐❛❧♠❡♥t❡ ♦ P❆❆❙ ♣♦r ♠❡✐♦ ❞❡ ✉♠ ❣r❛❢♦✱ ❛tr✐❜✉✐♥❞♦ ❝❛❞❛ ❛✉❧❛ à ✉♠ ✈ért✐❝❡ ❞❡st❡ ❣r❛❢♦ ❡ ❛❞✐❝✐♦♥❛♥❞♦ ❛r❡st❛s ♣❛r❛ ❝❛❞❛ ♣❛r ❞❡ ❛✉❧❛ ❝♦♠ s♦❜r❡♣♦s✐çã♦

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❈❛♣ít✉❧♦ ✸✳ ❈❛s♦s ❞❡ ❊st✉❞♦ ✶✶

❞❡ ❝♦♥✢✐t♦s ❞❡ ❛✉❧❛s✮ ❡ ♠♦❞❡❧❛✲s❡ ❛ r❡str✐çã♦ ❞❡ ♥ã♦✲s♦❜r❡♣♦s✐çã♦ ❞❡ ❤♦rár✐♦s ❝♦♠♦ ❡♠ ❋❡r❧❛♥❞ ❡ ❘♦② ✭✶✾✽✺✮✳ ❆ ❋✐❣✉r❛ ✶ ✐❧✉str❛ ✉♠ ❣r❛❢♦ r❡♣r❡s❡♥t❛♥❞♦ ♣❛r❝✐❛❧♠❡♥t❡ ✉♠ P❆❆❙✳ ◆♦ ❡①❡♠♣❧♦✱ ❛s ❛✉❧❛s ❆✼ ❡ ❆✻ ♣♦ss✉❡♠ s♦❜r❡♣♦s✐çã♦ ❞❡ ❤♦rár✐♦✳

❋✐❣✉r❛ ✶✿ ■❧✉str❛çã♦ ❞❛ ❘❡♣r❡s❡♥t❛çã♦ ♣♦r ●r❛❢♦ ❞♦ P❆❆❙

❖s r❡❝✉rs♦s ❝♦♥s✐❞❡r❛❞♦s ♣❛r❛ ❡st❡ ♠♦❞❡❧♦ sã♦✿ s❛❧❛ ❞❡ ❛✉❧❛ ❝♦♠✉♠✱ q✉❛❞r♦ ❣r❛♥❞❡✱ ♣r♦❥❡t♦r✱ ❧❛❜♦r❛tór✐♦ ❞❡ ✐♥❢♦r♠át✐❝❛ ❡ ❧❛❜♦r❛tór✐♦ ❞❡ ♠❛t❡♠át✐❝❛✳ P❛r❛ ❝❛❞❛ t✉r♠❛ ♦s ❞♦❝❡♥t❡s ❞❡t❡r♠✐♥❛♠ ♦s r❡q✉❡r✐♠❡♥t♦s ❞✐❞át✐❝♦s ❞❡ r❡❝✉rs♦s✱ ❡st❛❜❡❧❡❝❡♥❞♦ ✉♠❛ r❡❧❛çã♦

❜✐♥ár✐❛ ❡♥tr❡ ❛s t✉r♠❛s ❡ ♦s r❡❝✉rs♦s ✭♠❛tr✐③τ✮ q✉❡ é ✉♠ ❞❛❞♦ ❞❡ ❡♥tr❛❞❛ ❞♦ ♣r♦❜❧❡♠❛✳

P❛r❛ ❝❛❞❛ s❛❧❛ ♦s ❞❡❝✐s♦r❡s s❛❜❡♠ q✉❛✐s ♦s r❡❝✉rs♦s ❡stã♦ ❛ss♦❝✐❛❞♦s ✭♠❛tr✐③ ❜✐♥ár✐❛ σ✮

q✉❡ é t❛♠❜é♠ ❞❛❞♦ ❞❡ ❡♥tr❛❞❛✳

P❛r❛ ♠♦❞❡❧❛r ❛ r❡str✐çã♦ ❞❡ ❛t❡♥❞✐♠❡♥t♦ ❞❡ r❡q✉✐s✐t♦s ❢♦✐ ♣r♦♣♦st❛ ✉♠❛ ♠❛tr✐③ ❜✐♥ár✐❛

η r❡❧❛❝✐♦♥❛♥❞♦ ❛✉❧❛s ❡ s❛❧❛s✳ P❛r❛ ❝♦♥str✉✐r ❡st❛ ♠❛tr✐③ ✉t✐❧✐③❛✲s❡ ♦ ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ♥❛

t✉r♠❛ ✭T AMt✮✱ ❛ ❝❛♣❛❝✐❞❛❞❡ ❞❛s s❛❧❛s ✭CAPs✮ ❡ ❛s ♠❛tr✐③❡s τ ❡ σ✳ ❊st❛❜❡❧❡❝❡✲s❡ q✉❡

✉♠❛ ❛✉❧❛ a ♣♦❞❡rá ❡st❛ ❛❧♦❝❛❞❛ ♥❛ s❛❧❛ s ❝❛s♦ ❡st❛ ♣♦ss✉❛ ♥ú♠❡r♦ ❞❡ ❛ss❡♥t♦s ✐❣✉❛❧ ♦✉

s✉♣❡r✐♦r ❛♦ ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ❡ ❞✐s♣♦♥✐❜✐❧✐③❡✱ ❛♦ ♠❡♥♦s✱ t♦❞♦s ♦s r❡❝✉rs♦s r❡q✉❡r✐❞♦s ♣❡❧❛

❛✉❧❛✳ P♦rt❛♥t♦ ηas s❡rá ✶ ♣❛r❛ t♦❞❛s ❛s s❛❧❛s s q✉❡ ♣♦❞❡♠ ❛❧♦❝❛r ❛ ❛✉❧❛ a ❡ ✵ ♣❛r❛ ❛s

❞❡♠❛✐s✳

◆❡st❛ ❡t❛♣❛ ✐♥✐❝✐❛❧ ❞♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ♠♦❞❡❧♦✱ ♦s ❞❡❝✐s♦r❡s ❞♦ ■❈▼❈ s❛❧✐❡♥t❛r❛♠ s♦♠❡♥t❡ ❞✉❛s ♠étr✐❝❛s ❞❡ q✉❛❧✐❞❛❞❡ ♣❛r❛ ❛❢❡r✐r ✉♠❛ s♦❧✉çã♦ ♦❜t✐❞❛✳ ❊st❛s ❞✉❛s ♠étr✐❝❛s sã♦✿ ✉t✐❧✐③❛r s❛❧❛s ❝♦♠ ❝❛♣❛❝✐❞❛❞❡ ♦ ♠❛✐s ♣ró①✐♠❛ ♣♦ssí✈❡❧ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❛❧✉♥♦s ❞❛ t✉r♠❛✱ ♦✉ s❡❥❛✱ r❡❞✉③✐r ♦ ♥ú♠❡r♦ ❞❡ ❛ss❡♥t♦s ✈❛③✐♦s ❡♠ ❝❛❞❛ s❛❧❛❀ ♣❛r❛ ✉♠❛ ♦✉ ♠❛✐s ❛✉❧❛s q✉❡ s❡❥❛♠ ❞❛ ♠❡s♠❛ t✉r♠❛✱ t❡♥t❛r ❛❧♦❝á✲❧❛s ♥❛ ♠❡s♠❛ s❛❧❛✱ ♦✉ s❡❥❛✱ r❡❞✉③✐r ♦ ♥ú♠❡r♦ ❞❡ tr♦❝❛s ❞❡ s❛❧❛ ❞❛s t✉r♠❛s✳

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✶✷ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦

❛♦ ♣❛r ❛✉❧❛✲s❛❧❛ ✉♠ ❝✉st♦ r❡❧❛t✐✈♦ ❝❛s♦ ❛ ❛✉❧❛ s❡❥❛ ❛❧♦❝❛❞❛ ♥❛ s❛❧❛✳ ❈♦♠ ♦ ✐♥t✉✐t♦ ❞❡

r❡❞✉③✐r ♦ ♥ú♠❡r♦ ❞❡ ❛ss❡♥t♦s ❧✐✈r❡s ♥❛s s❛❧❛s✱ ❞❡✜♥❡✲s❡ ♦ U SOas = 100.

1−T AMta

CAPs

✱

❡♠ q✉❡ T AMta é ♦ ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ✐♥s❝r✐t♦s ♥❛ ❛✉❧❛✳ ❖ U SOas ♣♦rt❛♥t♦ ✐rá s❡r ✉♠

✈❛❧♦r ♣❡r❝❡♥t✉❛❧ ❞❡ ❛ss❡♥t♦s ✈❛③✐♦s ♥❛ s❛❧❛ s ❝❛s♦ ❛ ❛✉❧❛ a s❡❥❛ ❛❧♦❝❛❞❛ ♥❛ ♠❡s♠❛✳

❖s ❞❛❞♦s ❞✐s♣♦♥✐❜✐❧✐③❛❞♦s ♣❡❧♦s ❞❡❝✐s♦r❡s s♦❜r❡ ❛s t✉r♠❛s✱ r❡❝✉rs♦s ❡ s❛❧❛s ♣❛ss❛♠ ♣♦r ♣r❡♣r♦❝❡ss❛♠❡♥t♦✱ ♣❛r❛ r❡❞✉③✐r ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ✐♥❢♦r♠❛çã♦ ❡ ❡①tr❛✐r ❛s r❡❧❛çõ❡s ✐♠♣♦rt❛♥t❡ ❡♥tr❡ ❛✉❧❛s ❡ s❛❧❛s✳ ❋✐♥❛❧♠❡♥t❡ ❝❛❜❡ ❛♦ ❞❡❝✐s♦r ❛ ❡s❝♦❧❤❛ ❛♣r♦♣r✐❛❞❛ ❞♦s

♣❛râ♠❡tr♦s α ❡β q✉❡ ♣♦♥❞❡r❛♠ ❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦✱ ❞❡✜♥✐♥❞♦ ❝♦♠❡♥s✉r❛❜✐❧✐❞❛❞❡ ❡♥tr❡ ❛s

♠étr✐❝❛s✳ ❖ ♠♦❞❡❧♦ ❞♦ P❆❆❙ ♣❛r❛ ♦ ■❈▼❈ ❝♦♠ ❞✉❛s ♠étr✐❝❛s é ❡♥tã♦ ♣r♦♣♦st♦✿

❈♦♥❥✉♥t♦s ❡ ❮♥❞✐❝❡s

H ❈♦♥❥✉♥t♦ ❞❡ s❧♦ts ❞❡ ❤♦rár✐♦ ✭h∈ {1, . . . ,|H|}✮❀

T ❈♦♥❥✉♥t♦ ❞❡ t✉r♠❛s ✭t∈ {1, . . . ,|T|}✮❀

S ❈♦♥❥✉♥t♦ ❞❡ s❛❧❛s ✭s∈ {1, . . . ,|S|}✮❀

R ❈♦♥❥✉♥t♦ ❞❡ r❡❝✉rs♦s ✭r ∈ {1, . . . ,|R|}✮✳

❉❛❞♦s ❞❡ ❊♥tr❛❞❛

ρ ρth= 1 s❡ t✉r♠❛ t∈T t❡♠ ❛✉❧❛ ♥♦ s❧♦t ❞❡ ❤♦rár✐♦h∈H✱ ✵ ❝✳❝✳❀

σ σsr= 1 s❡ s❛❧❛s ∈S ♣♦ss✉✐ r❡❝✉rs♦ r ∈R✱ ✵ ❝✳❝✳❀

τ τtr = 1 s❡ t✉r♠❛ t ∈T r❡q✉❡r r❡❝✉rs♦ r∈R✱ ✵ ❝✳❝✳❀

CAP CAPs =♥ú♠❡r♦ ❞❡ ❛ss❡♥t♦s ♥❛ s❛❧❛ s∈S❀

T AM T AMt=♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ✐♥s❝r✐t♦s ♥❛ t✉r♠❛ t∈T❀

❉❛❞♦s ❞❡ Pr❡♣r♦❝❡ss❛♠❡♥t♦

A ❈♦♥❥✉♥t♦ ❞❡ ❆✉❧❛s ✭a ∈ {1, . . . ,|A|}✮ ❀

At _{❙✉❜❝♦♥❥✉♥t♦ ❞❛s ❆✉❧❛s}_a_∈_A _{❞❛ t✉r♠❛} _t _∈_T

η ηas = 1 s❡ s❛❧❛ s∈S ♣♦❞❡ ❛❧♦❝❛r ❛ ❛✉❧❛a ∈A✱ ✵ ❝✳❝✳❀

Θ _Θ_aa′ = 1 s❡ ❛s ❛✉❧❛s a, a′ ∈A ♣♦ss✉❡♠ s♦❜r❡♣♦s✐çã♦ ❞❡ ❤♦rár✐♦✱ ✵ ❝✳❝✳❀

U SO U SOas= ❝✉st♦ ❞❡ ❛❧♦❝❛r ❛✉❧❛a ♥❛ s❛❧❛ s✳

❱❛r✐á✈❡✐s ❞❡ ❉❡❝✐sã♦

xas xas= 1 s❡ ❛✉❧❛ a∈A é ❛❧♦❝❛❞❛ ♥❛ s❛❧❛ s∈S✱ ✵ ❝✳❝✳❀

yt yt =♥ú♠❡r♦ ❞❡ tr♦❝❛s ❞❛ t✉r♠❛ t∈T✳

(37)

❈❛♣ít✉❧♦ ✸✳ ❈❛s♦s ❞❡ ❊st✉❞♦ ✶✸

min F =α· X

s∈S

X

a∈A

U SOas·xas

!

+β· X

t∈T yt

!

✭✸✳✶✮

s✉❥❡✐t♦ ❛✿ X

s_∈S

xas = 1 a∈A ✭✸✳✷✮

xas ≤ηsa s∈S ❡ a∈A ✭✸✳✸✮

xas+xa′_s≤1 s∈S ❡a, a′ ∈A|Θ_aa′ = 1 ✭✸✳✹✮

|At_|

X

n=1

xansn ≤1 +yt t∈T✱an∈A

t _❡

s1, ..., s|At_| ⊂S ✭✸✳✺✮

xas∈ {0,1} a ∈A ✱s∈S ✭✸✳✻✮

yt∈Z+ t ∈T ✭✸✳✼✮

❆ ❋✉♥çã♦ ❖❜❥❡t✐✈♦ ✭✸✳✶✮ ♠✐♥✐♠✐③❛ ♦ ♣❡r❝❡♥t✉❛❧ ❞❡ ❛ss❡♥t♦s ❧✐✈r❡s ♥❛s s❛❧❛s ✭t❡r♠♦

♠✉❧t✐♣❧✐❝❛❞♦ ♣♦rα✮ ❡ ♦ ♥ú♠❡r♦ ❞❡ tr♦❝❛s ❞❡ s❛❧❛s ❞❛s t✉r♠❛s ✭t❡r♠♦ ♠✉❧t✐♣❧✐❝❛❞♦ ♣♦rβ✮✳

❖ ❝♦♥❥✉♥t♦ ❞❡ r❡str✐çõ❡s ✭✸✳✷✮ ❛ss❡❣✉r❛ q✉❡ t♦❞❛s ❛s ❛✉❧❛s ❞❡✈❡♠ s❡r ❛❧♦❝❛❞❛s ❡♠ ✉♠❛✱ ❡ s♦♠❡♥t❡ ✉♠❛✱ s❛❧❛✳ ❆s r❡str✐çõ❡s ✭✸✳✸✮ ❣❛r❛♥t❡♠ q✉❡ só s❡rã♦ ❛❧♦❝❛❞❛s ❛✉❧❛s ❡♠ s❛❧❛s q✉❡ ❝✉♠♣r❛♠ ❛s ❡①✐❣ê♥❝✐❛s ❞❡ ❡s♣❛ç♦ ❡ r❡❝✉rs♦s✳ ❆s r❡str✐çõ❡s ✭✸✳✹✮ ✐♠♣❡❞❡♠ q✉❡ ❞✉❛s ❛✉❧❛s ❝♦♠ ❝♦♥✢✐t♦ ❞❡ ❤♦rár✐♦ s❡❥❛♠ ❛❧♦❝❛❞❛s ♥❛ ♠❡s♠❛ s❛❧❛✱ ❡♥q✉❛♥t♦ ❛s r❡str✐çõ❡s ✭✸✳✺✮ ✐rã♦ ♠❡❞✐r ❛ q✉❛♥t✐❞❛❞❡ ❞❡ tr♦❝❛s ❞❡ s❛❧❛s ❞❛s t✉r♠❛s✳ ❖ ❝♦♥❥✉♥t♦ ❞❡ r❡str✐çõ❡s ✭✸✳✻✮ ❡ ✭✸✳✼✮ sã♦ ❞❡ ❞♦♠í♥✐♦ ❞❡ ✈❛r✐á✈❡✐s✳

✸✳✷ ▼♦❞❡❧❛❣❡♠ ❝♦♠ ❝✐♥❝♦ ♠étr✐❝❛s ❞❡ q✉❛❧✐❞❛❞❡

❆s s♦❧✉çõ❡s ♦❜t✐❞❛s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❝♦♠ ❞✉❛s ♠étr✐❝❛s ♣❛r❛ ♦ ■❈▼❈ ❢♦r❛♠ ❝♦♥❢❡r✐❞❛s ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦s ❞❡❝✐s♦r❡s ❞♦ P❆❆❙ ❡ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ♥❛ s♦❧✉çã♦ ❢♦r❛♠ ❧❡✈❛♥t❛❞❛s ♣❡❧♦s ♠❡s♠♦s✳ ▼❡❞✐❞❛s ❞❡ q✉❛❧✐❞❛❞❡ q✉❡ ❡r❛♠ ❝♦♥s✐❞❡r❛❞❛s ✐♠♣❧✐❝✐t❛♠❡♥t❡ ♣♦r ❡❧❡s ♥ã♦ ❤❛✈✐❛♠ s✐❞♦ tr❛♥s♣♦st❛s ♣❛r❛ ♦ ♠♦❞❡❧♦ ❛té ❡♥tã♦✱ ♦ q✉❡ ❧❡✈♦✉ ❛ s♦❧✉çõ❡s ❞❡ ❜❛✐①❛ q✉❛❧✐❞❛❞❡ s❡❣✉♥❞♦ ❛s ♠étr✐❝❛s ♥ã♦ ❝♦♥s✐❞❡r❛❞❛s✳

❖ ♥♦✈♦ ♠♦❞❡❧♦ ✉t✐❧✐③❛ ❛s ♠❡s♠❛s ♣r❡♠✐ss❛s ❞♦ ♠♦❞❡❧♦ ❛♥t❡r✐♦r✱ ❝♦♠ ❛ ❛❞✐çã♦ ❞❡ ♥♦✈♦s ❞❛❞♦s ❞❡ ❡♥tr❛❞❛ ❡ ❞❡ ♣r❡♣r♦❝❡ss❛♠❡♥t♦✳ ❖ ❝♦♥❥✉♥t♦ ❞❡ ❝✉rrí❝✉❧♦s✱ ❛❞✐❝✐♦♥❛❞♦ ♣❛r❛ ❡st❡ ♠♦❞❡❧♦✱ ❞✐③ r❡s♣❡✐t♦ ❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞✐s❝✐♣❧✐♥❛s q✉❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❣r✉♣♦ ❞✐s❝❡♥t❡✱ ♣♦r ❝♦♥t❛ ❞♦ ❝✉rs♦ ❡s❝♦❧❤✐❞♦ ❡ ❛♥♦ ❞❡ ✐♥❣r❡ss♦✱ ❞❡✈❡rá ❢❛③❡r✳ ❆ss♦❝✐❛✲s❡ ❡♥tã♦ ♣❛r❛ ❝❛❞❛

t✉r♠❛t ∈T✱ ♦s ❝✉rrí❝✉❧♦s {c1, . . . , cn} ⊂C✱ ♣♦r ♠❡✐♦ ❞❛ ♠❛tr✐③ ❜✐♥ár✐❛ Υ✳ ❯♠❛ ♠❡s♠❛

(38)

✶✹ ❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦

❆s s♦❧✉çõ❡s ❞♦ ♣r✐♠❡✐r♦ ♠♦❞❡❧♦ ✉t✐❧✐③❛✈❛♠ ❞❡♠❛s✐❛❞❛♠❡♥t❡ ❛s s❛❧❛s ♠❡♥♦r❡s ❞♦ ■❈▼❈ ♣❛r❛ t✉r♠❛s ♣❡q✉❡♥❛s✱ ♣♦ré♠ ❡st❛s s❛❧❛s sã♦ ❣❡r❛❧♠❡♥t❡ ✉t✐❧✐③❛❞❛s ♣❛r❛ ❞❡❢❡s❛s ❡ s❡✉ ✉s♦ ♣❛r❛ ❛✉❧❛s s❡♠❛♥❛✐s ❞❡✈❡ s❡r ❡✈✐t❛❞♦✳ ❊①✐st❡✱ ♣♦rt❛♥t♦✱ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ s❛❧❛s q✉❡ ❞❡✈❡♠ ♣❡r♠❛♥❡❝❡r ♣r❡❢❡r❡♥❝✐❛❧♠❡♥t❡ ✈❛③✐❛s ❛♦ ❧♦♥❣♦ ❞♦ s❡♠❡str❡✳ ❊st❡ ❝♦♥❥✉♥t♦ ❞❡ s❛❧❛s s❡rá

❞❛❞♦ ♣❡❧♦ ✈❡t♦rP V AZ✱ ❡♠ q✉❡ ♦ ✈❛❧♦r ✶ ✐♥❞✐❝❛ q✉❡ ❛ s❛❧❛s é ♣r❡❢❡r❡♥❝✐❛❧♠❡♥t❡ ✈❛③✐❛✳

❯♠ ♦✉tr♦ ♣r♦❜❧❡♠❛ ❞❡t❡❝t❛❞♦ ♥❛ s♦❧✉çã♦ ❛♥t❡r✐♦r ❡r❛ ❛ ❜❛✐①❛ ❛❧♦❝❛çã♦ ❞❡ ❛✉❧❛s ❞❡ ❛❧❣✉♥s ❝✉rrí❝✉❧♦s ❡s♣❡❝í✜❝♦s à s❛❧❛s ♣r❡❞❡✜♥✐❞❛s✳ P♦rt❛♥t♦ ♦✉tr❛ ♠étr✐❝❛ ❞❡✜♥✐❞❛ é ♣r❡✲ s❡r✈❛r ✉♠❛ r❡❧❛çã♦ ♣ré✲❡st❛❜❡❧❡❝✐❞❛ ❡♥tr❡ ❝✉rrí❝✉❧♦s ❡ s❛❧❛s ❞❡ ❛✉❧❛✳ ❊st❛ r❡❧❛çã♦ s❡rá

❞❛❞❛ ♣❡❧❛ ♠❛tr✐③ ❞❡ ♣r❡t❡rê♥❝✐❛s P RET✱ q✉❡ ❛ss♦❝✐❛rá ❛ ❝❛❞❛ ♣❛r ❝✉rrí❝✉❧♦✲s❛❧❛ ✉♠

✈❛❧♦r ❡♥tr❡ ✵ ❡ ✶✵✱ ❡♠ q✉❡ ✵ sã♦ ❛s s❛❧❛s ♠❛✐s ✐♥❞✐❝❛❞❛s ♣❛r❛ ♦ ❝✉rrí❝✉❧♦ ❡ ✶✵ sã♦ ❛s s❛❧❛s ♠❡♥♦s ✐♥❞✐❝❛❞❛s✳ ➚ ❣✉✐s❛ ❞❡ ❡①❡♠♣❧♦✱ ♦s ✐♥❣r❡ss❛♥t❡s ❞❛ ✉♥✐✈❡rs✐❞❛❞❡ t❡♠ ♣r❡❢❡rê♥❝✐❛ ♣♦r ✉t✐❧✐③❛r ❛s s❛❧❛s ❞❡ ❛✉❧❛ ♠❛✐s ♣ró①✐♠❛s ❞♦ ♣ré❞✐♦ ❞❛ ❛❞♠✐♥✐str❛çã♦✱ ♣♦rt❛♥t♦ ♦ ✈❛❧♦r ❞❡P RET ❞❡st❡ ❝✉rrí❝✉❧♦ s❡rá ✵ ♣❛r❛ ❡st❛s s❛❧❛s✳

❖s ❞❡❝✐s♦r❡s ✐♥❞✐❝❛r❛♠ ❡♥tã♦ ❛ ú❧t✐♠❛ ❞❛s ♠étr✐❝❛s q✉❡ ❛✐♥❞❛ ♥ã♦ ❤❛✈✐❛ s✐❞♦ ❝♦♥s✐❞❡✲ r❛❞❛✱ ❛ r❡❞✉çã♦ ❞♦ ❞❡s❧♦❝❛♠❡♥t♦ ❞♦s ❛❧✉♥♦s✳ P❛r❛ ♠♦❞❡❧❛r ❡st❛ ♠étr✐❝❛ r❡q✉❡r ❞♦ ❞❡❝✐s♦r

♦s ❞❛❞♦s s♦❜r❡ ❛s ❞✐stâ♥❝✐❛s ❡♥tr❡ ❛s s❛❧❛s ✭♠❛tr✐③DIS✮✳ ❘❡❞✉③✲s❡ ❡♥tã♦ ♦ ❞❡s❧♦❝❛♠❡♥t♦

❞❡ ❝❛❞❛ ✉♠ ❞♦s ❝✉rrí❝✉❧♦s✱ ✐✳❡✳✱ ❛s ❛✉❧❛s ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❝✉rrí❝✉❧♦ ❞❡✈❡♠ s❡r ❛❧♦❝❛❞❛s

❡♠ s❛❧❛s ♣ró①✐♠❛s✱ s❡❣✉♥❞♦ ❛ ♠❛tr✐③ ❞❡ ❞✐stâ♥❝✐❛ DIS✳

❉❡st❛❝❛✲s❡ ♣♦ré♠ q✉❡ ❛s ❞✉❛s ♠étr✐❝❛s ✉t✐❧✐③❛❞❛s ♥♦ ♠♦❞❡❧♦ ❞❛ ❙t❡çã♦ ✸✳✶ sã♦ ♠❛♥✲ t✐❞❛s✱ ❛❝r❡s❝❡♥t❛♥❞♦✲s❡ ♦✉tr❛s três ♠étr✐❝❛s✱ t♦t❛❧✐③❛♥❞♦ ❛s ❝✐♥❝♦ ♠étr✐❝❛s ♣❛r❛ ♦ ♥♦✈♦ ♠♦❞❡❧♦ ❞♦ ■❈▼❈✿

✶✳ ❆❧♦❝❛r ❛✉❧❛s ❡♠ s❛❧❛s q✉❡ t❡♥❤❛♠ ❛ ❝❛♣❛❝✐❞❛❞❡ ♠❛✐s ♣ró①✐♠❛ ❞♦ ♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s❀

✷✳ ❊✈✐t❛r tr♦❝❛s ❞❡ s❛❧❛ ♣❛r❛ ❛✉❧❛s ❞❡ ✉♠❛ ♠❡s♠❛ ❞✐s❝✐♣❧✐♥❛❀

✸✳ ❘❡❞✉③✐r ❛ ❞✐stâ♥❝✐❛ ♣❡r❝♦rr✐❞❛ ♣♦r ✉♠ ❝✉rrí❝✉❧♦✱ ❝♦♥s✐❞❡r❛♥❞♦ t♦❞❛s ❛s s✉❛s ❛✉❧❛s❀

✹✳ ❊✈✐t❛r ❛ ✉t✐❧✐③❛çã♦ ❞❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ❝♦♥❥✉♥t♦ ❞❡ s❛❧❛s ❞❡ ❛✉❧❛❀

✺✳ ❆t❡♥❞❡r às ♣r❡❢❡rê♥❝✐❛s ♣ré✲❡st❛❜❡❧❡❝✐❞❛s ❡♥tr❡ ❝✉rrí❝✉❧♦ ❡ s❛❧❛s ❞❡ ❛✉❧❛✳

❆♥❛❧♦❣❛♠❡♥t❡ ❛♦ ♠♦❞❡❧♦ ❝♦♠ ❞✉❛s ♠étr✐❝❛s ❝❛❜❡ ❛♦ ❞❡❝✐s♦r ❡st✐♣✉❧❛r ♦s ♣❡s♦s ❞♦s ♣❛râ♠❡tr♦s ❞❡ ♣♦♥❞❡r❛çã♦ ❞❛ ❢✉♥çã♦ ♦❜❥❡t✐✈♦✱ ✐✳❡✳✱ ❡st❛❜❡❧❡❝❡r ❛ ❝♦♠❡♥s✉r❛❜✐❧✐❞❛❞❡ ❡♥tr❡ ❛s ♠étr✐❝❛s ❛ s❡r❡♠ ♠✐♥✐♠✐③❛❞❛s✳ P♦rt❛♥t♦✱ ❝❛❞❛ ✉♠❛ ❞❛s ♠étr✐❝❛s ❡st❛rá ❛ss♦❝✐❛❞❛ ❛

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❈❛♣ít✉❧♦ ✸✳ ❈❛s♦s ❞❡ ❊st✉❞♦ ✶✺

❈♦♥❥✉♥t♦s ❡ ❮♥❞✐❝❡s

H ❈♦♥❥✉♥t♦ ❞❡ s❧♦ts ❞❡ ❤♦rár✐♦ ✭h∈ {1, . . . ,|H|}✮❀

T ❈♦♥❥✉♥t♦ ❞❡ t✉r♠❛s ✭t∈ {1, . . . ,|T|}✮❀

S ❈♦♥❥✉♥t♦ ❞❡ s❛❧❛s ✭s∈ {1, . . . ,|S|}✮❀

R ❈♦♥❥✉♥t♦ ❞❡ r❡❝✉rs♦s ✭r∈ {1, . . . ,|R|}✮❀

C ❈♦♥❥✉♥t♦ ❞❡ ❝✉rrí❝✉❧♦s ✭c∈ {1, . . . ,|C|}✮✳

❉❛❞♦s ❞❡ ❊♥tr❛❞❛

ρ ρth= 1 s❡ t✉r♠❛ t∈T t❡♠ ❛✉❧❛ ♥♦ s❧♦t ❞❡ ❤♦rár✐♦h∈H✱ ✵ ❝✳❝✳❀

σ σsr= 1 s❡ s❛❧❛s ∈S ♣♦ss✉✐ r❡❝✉rs♦ r ∈R✱ ✵ ❝✳❝✳❀

τ τtr = 1 s❡ t✉r♠❛ t ∈T r❡q✉❡r r❡❝✉rs♦ r∈R✱ ✵ ❝✳❝✳❀

Υ _Υ_tc _{= 1} s❡ t✉r♠❛ _t_∈_T ♣❡rt❡♥❝❡ ❛♦ ❝✉rrí❝✉❧♦ _c_∈_C✱ ✵ ❝✳❝✳❀

CAP CAPs =♥ú♠❡r♦ ❞❡ ❛ss❡♥t♦s ♥❛ s❛❧❛ s∈S❀

T AM T AMt=♥ú♠❡r♦ ❞❡ ❛❧✉♥♦s ✐♥s❝r✐t♦s ♥❛ t✉r♠❛ t∈T❀

DIS DISss′ = ❞✐stâ♥❝✐❛ ❡♥tr❡ ❛s s❛❧❛ss∈S ❡ s′ ∈S❀

P V AZ P V AZs= 1 s❡ s❛❧❛s ∈S é ♣r❡❢❡r❡♥❝✐❛❧♠❡♥t❡ ✈❛③✐❛✱ ✵ ❝✳❝✳❀

P RET P RETcs = ♣r❡t❡rê♥❝✐❛ ❞♦ ❝✉rrí❝✉❧♦ c∈C ♣❡❧❛ s❛❧❛ s∈S✳

❉❛❞♦s ❞❡ Pr❡♣r♦❝❡ss❛♠❡♥t♦

A ❈♦♥❥✉♥t♦ ❞❡ ❆✉❧❛s ✭a ∈ {1, . . . ,|A|}✮❀

At _{❙✉❜❝♦♥❥✉♥t♦ ❞❛s ❆✉❧❛s}_a _∈_A _{❞❛ t✉r♠❛} _t_∈_T_❀

Λc _{❙✉❜❝♦♥❥✉♥t♦ ❞❡ ❆✉❧❛s}_a _∈_A _{❞♦ ❝✉rrí❝✉❧♦}_c_∈_C_❀

η ηas = 1 s❡ s❛❧❛ s∈S ♣♦❞❡ ❛❧♦❝❛r ❛ ❛✉❧❛a ∈A✱ ✵ ❝✳❝✳❀

Θ _Θ_aa′ = 1 s❡ ❛s ❛✉❧❛s a, a′ ∈A ♣♦ss✉❡♠ s♦❜r❡♣♦s✐çã♦ ❞❡ ❤♦rár✐♦✱ ✵ ❝✳❝✳❀

U SO U SOas= ❝✉st♦ ❞❡ ❛❧♦❝❛r ❛✉❧❛a ♥❛ s❛❧❛ s✳

❱❛r✐á✈❡✐s ❞❡ ❉❡❝✐sã♦

xas xas= 1 s❡ ❛✉❧❛ a∈A é ❛❧♦❝❛❞❛ ♥❛ s❛❧❛ s ∈S✱ ✵ ❝✳❝✳❀

yt yt =♥ú♠❡r♦ ❞❡ tr♦❝❛s ❞❛ t✉r♠❛ t∈T❀

wcs wcs = 1 s❡ ❝✉rrí❝✉❧♦c∈C t❡♠ ❛♦ ♠❡♥♦s ✶ ❛✉❧❛ ♥❛ s❛❧❛s∈S✱ ✵ ❝✳❝✳❀

vcss′ v_css′ = 1 s❡ ❝✉rrí❝✉❧♦c∈C t❡♠ ❛♦ ♠❡♥♦s ✶ ❛✉❧❛ ♥❛s s❛❧❛s s, s′ ∈S✱ ✵ ❝✳❝✳