❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P▲❆◆❊❏❆▼❊◆❚❖ ❇❆❙❊❆❉❖ ❊▼ ❇❯❙❈❆ ❊
❆P❘❊◆❉■❩❆●❊▼
❘❆❯▲❈➱❩❆❘ ▼❆❳■▼■❆◆❖ ❋■●❯❊■❘❆ ❆▲❱❊❙
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❘❆❯▲❈➱❩❆❘ ▼❆❳■▼■❆◆❖ ❋■●❯❊■❘❆ ❆▲❱❊❙
P▲❆◆❊❏❆▼❊◆❚❖ ❇❆❙❊❆❉❖ ❊▼ ❇❯❙❈❆ ❊
❆P❘❊◆❉■❩❆●❊▼
❉✐ss❡rt❛çã♦ ❞❡ ▼❡str❛❞♦ ❛♣r❡s❡♥t❛❞❛ à ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥✲ ❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛✱ ▼✐♥❛s ●❡r❛✐s✱ ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ♦❜✲ t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
➪r❡❛ ❞❡ ❝♦♥❝❡♥tr❛çã♦✿ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧✳
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❈❛r❧♦s ❘♦❜❡rt♦ ▲♦♣❡s
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❖s ❛❜❛✐①♦ ❛ss✐♥❛❞♦s✱ ♣♦r ♠❡✐♦ ❞❡st❡✱ ❝❡rt✐✜❝❛♠ q✉❡ ❧❡r❛♠ ❡ r❡❝♦♠❡♥❞❛♠ ♣❛r❛ ❛ ❋❛✲ ❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❛ ❛❝❡✐t❛çã♦ ❞❛ ❞✐ss❡rt❛çã♦ ✐♥t✐t✉❧❛❞❛ ✏P❧❛♥❡❥❛♠❡♥t♦ ❇❛s❡❛❞♦ ❡♠ ❇✉s❝❛ ❡ ❆♣r❡♥❞✐③❛❣❡♠✑ ♣♦r ❘❛✉❧❝é③❛r ▼❛①✐♠✐❛♥♦ ❋✐❣✉❡✐r❛ ❆❧✈❡s ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ❡①✐❣✐❞♦s ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❯❜❡r❧â♥❞✐❛✱ ✶✵ ❞❡ ❋❡✈❡r❡✐r♦ ❞❡ ✷✵✶✹
❖r✐❡♥t❛❞♦r✿
Pr♦❢✳ ❉r✳ ❈❛r❧♦s ❘♦❜❡rt♦ ▲♦♣❡s ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❇❛♥❝❛ ❊①❛♠✐♥❛❞♦r❛✿
Pr♦❢✳ ❉r✳ ❏♦sé ❏❡❛♥✲P❛✉❧ ❩✳ ❞❡ ❙✳ ❚❛✈❛r❡s ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛
❯◆■❱❊❘❙■❉❆❉❊ ❋❊❉❊❘❆▲ ❉❊ ❯❇❊❘▲➶◆❉■❆ ❋❆❈❯▲❉❆❉❊ ❉❊ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
P❘❖●❘❆▼❆ ❉❊ PÓ❙✲●❘❆❉❯❆➬➹❖ ❊▼ ❈■✃◆❈■❆ ❉❆ ❈❖▼P❯❚❆➬➹❖
❉❛t❛✿ ❋❡✈❡r❡✐r♦ ❞❡ ✷✵✶✹
❆✉t♦r✿ ❘❛✉❧❝é③❛r ▼❛①✐♠✐❛♥♦ ❋✐❣✉❡✐r❛ ❆❧✈❡s
❚ít✉❧♦✿ P❧❛♥❡❥❛♠❡♥t♦ ❇❛s❡❛❞♦ ❡♠ ❇✉s❝❛ ❡ ❆♣r❡♥❞✐③❛❣❡♠ ❋❛❝✉❧❞❛❞❡✿ ❋❛❝✉❧❞❛❞❡ ❞❡ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦
●r❛✉✿ ▼❡str❛❞♦
❋✐❝❛ ❣❛r❛♥t✐❞♦ à ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❯❜❡r❧â♥❞✐❛ ♦ ❞✐r❡✐t♦ ❞❡ ❝✐r❝✉❧❛çã♦ ❡ ✐♠♣r❡ssã♦ ❞❡ ❝ó♣✐❛s ❞❡st❡ ❞♦❝✉♠❡♥t♦ ♣❛r❛ ♣r♦♣ós✐t♦s ❡①❝❧✉s✐✈❛♠❡♥t❡ ❛❝❛❞ê♠✐❝♦s✱ ❞❡s❞❡ q✉❡ ♦ ❛✉t♦r s❡❥❛ ❞❡✈✐❞❛♠❡♥t❡ ✐♥❢♦r♠❛❞♦✳
❆✉t♦r
❖ ❆❯❚❖❘ ❘❊❙❊❘❱❆ P❆❘❆ ❙■ ◗❯❆▲◗❯❊❘ ❖❯❚❘❖ ❉■❘❊■❚❖ ❉❊ P❯❇▲■❈❆➬➹❖ ❉❊❙❚❊ ❉❖❈❯▼❊◆❚❖✱ ◆➹❖ P❖❉❊◆❉❖ ❖ ▼❊❙▼❖ ❙❊❘ ■▼P❘❊❙❙❖ ❖❯ ❘❊P❘❖✲ ❉❯❩■❉❖✱ ❙❊❏❆ ◆❆ ❚❖❚❆▲■❉❆❉❊ ❖❯ ❊▼ P❆❘❚❊❙✱ ❙❊▼ ❆ P❊❘▼■❙❙➹❖ ❊❙❈❘■❚❆ ❉❖ ❆❯❚❖❘✳
❝
❉❡❞✐❝❛tór✐❛
❆❣r❛❞❡❝✐♠❡♥t♦s
❆❣r❛❞❡ç♦✳✳✳
❆ ❉❡✉s✱ ♣♦r ♠✐♥❤❛ ✈✐❞❛✳
❆♦s ♠❡✉s ♣❛✐s ❱❛❣♥❡t❡ ❋❛❣✉♥❞❡s ❋❡rr❡✐r❛ ❡ ❩♦r❛❡♥❡ ❈❛r♠❡♥ ❋✐❣✉❡✐r❛ ❋❛❣✉♥❞❡s ♣❡❧❛ ❞❡❞✐❝❛çã♦✱ ❝♦♥✜❛♥ç❛✱ ❛♣♦✐♦✱ ❝❛r✐♥❤♦ ❡ ❛♠♦r ✐♥❝♦♥❞✐❝✐♦♥❛❧ ❡♠ t♦❞♦s ♦s ♠♦♠❡♥t♦s✳
❆♦s ♠❡✉s ✐r♠ã♦s ❏♦③❛❡♥❡ ▼❛①✐♠✐❛♥♦ ❋✐❣✉❡✐r❛ ❆❧✈❡s ❋❛r✐❛ ❡ ❱✐❝t♦r ❋✐❣✉❡✐r❛ ❋❛❣✉♥❞❡s ♣❡❧❛ s❡r❡♥✐❞❛❞❡✱ ♣❛r❝❡r✐❛✱ ❝❛r✐♥❤♦ ❡ ❛♠♦r✳
❆ ♠✐♥❤❛ ♥❛♠♦r❛❞❛ ❈r✐st✐❛♥❡ ❙♦❛r❡s ❈❛♠♣♦s ♣♦r t❡r ♠❡ ❛♣♦✐❛❞♦ ❞✉r❛♥t❡ ❡st❡ ♣r♦❥❡t♦✳ ❱♦❝ê ♠❡ ❞❡✉ ♠✉✐t❛ ❢♦rç❛✱ ❛❧❡❣r✐❛ ❡ ❛♠♦r✳
❆ t♦❞♦s ❞❛ ♠✐♥❤❛ ❢❛♠í❧✐❛ q✉❡ s❡♠♣r❡ ♠❡ ❛♣♦✐❛r❛♠ ❡ ❛❝r❡❞✐t❛r❛♠ ❡♠ ♠✐♠✳
❆♦s ♠❡✉s ❛♠✐❣♦s ❞♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞❛ ❯❋❯ ♣♦r t❡r❡♠ ❢❡✐t♦ ❞❡ss❛ ❝❛♠✐♥❤❛❞❛ ❛❧❣♦ ♠❛✐s ❞❡s❝♦♥tr❛í❞♦ ❡ ♣r❛③❡r♦s♦✳
❆♦s ♠❡✉s ❛♠✐❣♦s ❞♦ ❈❡♥tr♦ ❞❡ ❚❡❝♥♦❧♦❣✐❛ ❞❛ ■♥❢♦r♠❛çã♦ ❞❛ ❯❋❯ ♣❡❧♦ ✐♥❝❡♥t✐✈♦ ❡ ❛♠✐③❛❞❡ ❛♦ ❧♦♥❣♦ ❞❡st❛ ❡t❛♣❛ ❞❛ ♠✐♥❤❛ ✈✐❞❛✳
❆ ♣r♦❢❡ss♦r❛ ▼ár❝✐❛ ❆♣❛r❡❝✐❞❛ ❋❡r♥❛♥❞❡s ♣❡❧♦ ❛♣♦✐♦✱ ♦r✐❡♥t❛çã♦ ❡ ❝❛r✐♥❤♦ ❞❡s❞❡ ❛ ♠✐♥❤❛ ❣r❛❞✉❛çã♦✳
❘❡s✉♠♦
❉✉r❛♥t❡ ❞é❝❛❞❛s✱ ✈ár✐♦s s✐st❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ✈ê♠ s❡♥❞♦ ♣r♦♣♦st♦s ❛ ✜♠ ❞❡ ❡♥❝♦♥✲ tr❛r s♦❧✉çõ❡s ♣❛r❛ ♦s ♠❛✐s ❞✐✈❡rs♦s ♣r♦❜❧❡♠❛s ❞♦ ❞✐❛✲❛✲❞✐❛✳ P♦ré♠✱ ❛♣❡♥❛s r❡❝❡♥t❡♠❡♥t❡✱ s✐st❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝♦♠❡ç❛r❛♠ ❛ ♦❜t❡r r❡s✉❧t❛❞♦s s❛t✐s❢❛tór✐♦s ❛tr❛✈és ❞❡ ♠ét♦❞♦s ❞❡ ❜✉s❝❛ ♣❛r❛ ❝♦♥str✉✐r s❡✉s ♣❧❛♥♦s✳ ❈♦♠♦ ❡①❡♠♣❧♦ ❞❡ ♣❧❛♥❡❥❛❞♦r ❞❡ s✉❝❡ss♦✱ ♣♦❞❡✲s❡ ❝✐✲ t❛r ♦ s✐st❡♠❛ ❋❛st ❋♦r✇❛r❞ q✉❡ ❝♦♠❜✐♥❛ ❛ ❡①❡❝✉çã♦ ❞❡ ❞♦✐s ♠ét♦❞♦s ❞❡ ❜✉s❝❛✱ ♦ ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ❡ ♦ ❇❡st ❋✐rst ❙❡❛r❝❤✳ ❚é❝♥✐❝❛s ✐♥tr♦❞✉③✐❞❛s ♣❡❧♦ ❋❛st ❋♦r✇❛r❞ t❡♠ s✐❞♦ t❛♠❜é♠ ❛♣❧✐❝❛❞❛s ❡♠ ♠✉✐t♦s ♦✉tr♦s ♣❧❛♥❡❥❛❞♦r❡s ♠❛✐s r❡❝❡♥t❡s✳
❆♣❡s❛r ❞❛ ❡str❛té❣✐❛ ❞♦ ❋❛st ❋♦r✇❛r❞ ❛♣r❡s❡♥t❛r ✉♠ ❞❡s❡♠♣❡♥❤♦ s✉♣❡r✐♦r q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❛ ♦✉tr♦s ♠ét♦❞♦s✱ ❡❧❛ t❛♠❜é♠ ♠♦str❛ ❛❧❣✉♠❛s ❢r❛❣✐❧✐❞❛❞❡s✳ P❛r❛ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ♦ ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ♥ã♦ ❝♦♥s❡❣✉❡ ❡s❝❛♣❛r ❞❡ ♠á①✐✲ ♠♦s✴♠í♥✐♠♦s ❧♦❝❛✐s✱ ♦ q✉❡ ♦ ❧❡✈❛ ❛ ✜❝❛r ♣r❡s♦ ❡♠ ✏❜❡❝♦s s❡♠ s❛í❞❛✑✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ❡❧❡ ❢❛❧❤❡✳ ❈❛s♦ ✐ss♦ ♦❝♦rr❛✱ ✉♠❛ ❜✉s❝❛ ❝♦♠♣❧❡t❛ é r❡❛❧✐③❛❞❛ ♣❡❧♦ ❇❡st ❋✐rst ❙❡❛r❝❤✱ q✉❡ ♣♦❞❡ ❢❛❧❤❛r ♣♦r ❢❛❧t❛ ❞❡ ❡s♣❛ç♦ ❞❡ ♠❡♠ór✐❛✳ ◆♦t❡ q✉❡ ❡ss❡s ♣r♦❜❧❡♠❛s ♣♦❞❡♠ ❛❢❡t❛r q✉❛❧q✉❡r ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛✳
❊st❡ tr❛❜❛❧❤♦ ❞❡s❝r❡✈❡ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ ✉♠ ♣❧❛♥❡❥❛❞♦r✱ ❝❤❛♠❛❞♦ ❞❡ ❙▲P❧❛♥✱ ❜❛s❡❛❞♦ ❡♠ ✈❡rsõ❡s ♦t✐♠✐③❛❞❛s ❞♦s ❛❧❣♦r✐t♠♦s ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ❡ ▲❡❛r♥✐♥❣ ❘❡❛❧✲ ❚✐♠❡ ❆✯ q✉❡ t❡♥t❛♠ r❡❞✉③✐r ♦ ✐♠♣❛❝t♦ ❞♦s ♣r♦❜❧❡♠❛s ❞❡s❝r✐t♦s ❛❝✐♠❛ ♣❛r❛ ❝♦♥str✉✐r ♣❧❛♥♦s ❞❡ ❢♦r♠❛ ♠❛✐s ❡✜❝✐❡♥t❡✳
❆❧é♠ ❞✐ss♦✱ ❛ ❛♣❧✐❝❛çã♦ ❞❡ té❝♥✐❝❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ♥❛ s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s r❡❧❡✈❛♥t❡s é t❡♠❛ ❞❡ ❡s♣❡❝✐❛❧ ✐♥t❡r❡ss❡ ♣❡❧❛ ❝♦♠✉♥✐❞❛❞❡ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳ ❆ ❣❡r❛çã♦ ❞❡ ♣r♦❝❡ss♦s ❞❡ ♥❡❣ó❝✐♦ ✭✇♦r❦✢♦✇✮ é ✉♠❛ ❞❛s ár❡❛s q✉❡ ♣♦❞❡♠ s❡ ❜❡♥❡✜❝✐❛r ❞♦ ✉s♦ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳ ◆❡st❛ ❞✐ss❡rt❛çã♦ ❡s♣❡❝✐✜❝❛✲s❡ t❛♠❜é♠ ❝♦♠♦ ♦ ♣❧❛♥❡❥❛❞♦r ❞❡s❡♥✈♦❧✈✐❞♦ ❢♦✐ ❛♣❧✐❝❛❞♦ ♥❛ ❣❡r❛çã♦ ❛✉t♦♠át✐❝❛ ❞❡ ♠♦❞❡❧♦s ❞❡ ♣r♦❝❡ss♦s ❞❡ ♥❡❣ó❝✐♦✳
❆❜str❛❝t
❋♦r ❞❡❝❛❞❡s✱ s❡✈❡r❛❧ ♣❧❛♥♥✐♥❣ s②st❡♠s ❤❛✈❡ ❜❡❡♥ ♣r♦♣♦s❡❞ ✐♥ ♦r❞❡r t♦ ✜♥❞ s♦❧✉t✐♦♥s t♦ ♠❛♥② ♦❢ t❤❡ ❞✐✛❡r❡♥t ♣r♦❜❧❡♠s ❡♥❝♦✉♥t❡r❡❞ ✐♥ ❡✈❡r②❞❛② ❧✐❢❡✳ ❍♦✇❡✈❡r✱ ♦♥❧② ✐♥ r❡❝❡♥t ②❡✲ ❛rs✱ ❤❛✈❡ ♣❧❛♥♥✐♥❣ s②st❡♠s st❛rt❡❞ t♦ ♦❜t❛✐♥ s❛t✐s❢❛❝t♦r② r❡s✉❧ts t❤r♦✉❣❤ t❤❡ ✉s❡ ♦❢ s❡❛r❝❤ ♠❡t❤♦❞s ❢♦r ❜✉✐❧❞✐♥❣ ♣❧❛♥s✳ ❆s ❛ s✉❝❝❡ss❢✉❧ ♣❧❛♥♥❡r✱ ❋❛st ❋♦r✇❛r❞ ❝♦♠❜✐♥❡s t❤❡ ❡①❡❝✉✲ t✐♦♥ ♦❢ t✇♦ s❡❛r❝❤ ♠❡t❤♦❞s✱ ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ❛♥❞ ❇❡st ❋✐rst ❙❡❛r❝❤✳ ❚❡❝❤♥✐q✉❡s ✐♥tr♦❞✉❝❡❞ ❜② ❋❛st ❋♦r✇❛r❞ ❤❛✈❡ ❛❧s♦ ❜❡❡♥ ❛♣♣❧✐❡❞ ✐♥ ♠❛♥② ♦t❤❡r r❡❝❡♥t ♣❧❛♥♥❡rs✳
❆❧t❤♦✉❣❤ ❋❛st ❋♦r✇❛r❞ str❛t❡❣② ♣r❡s❡♥ts ❛♥ ❡♥❤❛♥❝❡❞ ♣❡r❢♦r♠❛♥❝❡ ✇❤❡♥ ❝♦♠♣❛r❡❞ t♦ ❛❧t❡r♥❛t✐✈❡ ♠❡t❤♦❞s✱ ✐t s❤♦✇s s♦♠❡ ✇❡❛❦♥❡ss❡s✳ ❋♦r s♦♠❡ ♣❧❛♥♥✐♥❣ ♣r♦❜❧❡♠s ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ❝❛♥♥♦t ❡s❝❛♣❡ ❢r♦♠ ❧♦❝❛❧ ♠❛①✐♠❛✴♠✐♥✐♠❛✱ ✇❤✐❝❤ ♠❡❛♥s ✐t ♠✐❣❤t ❣❡t st✉❝❦ ❛t ❞❡❛❞ ❡♥❞s✱ t❤✉s ❧❡❛❞✐♥❣ t♦ ❛ ❢❛✐❧✉r❡✳ ■♥ t❤❡ ❡✈❡♥t ♦❢ s✉❝❤ ♦❝❝✉rr❡♥❝❡s✱ ❛ ❝♦♠♣❧❡t❡ s❡❛r❝❤ ✐s ♣❡r❢♦r♠❡❞ ❜② ❇❡st ❋✐rst ❙❡❛r❝❤✱ ✇❤✐❝❤ ♠❛② ❢❛✐❧ ❞✉❡ t♦ ❧❛❝❦ ♦❢ ♠❡♠♦r② s♣❛❝❡✳ ◆♦t❡ t❤❛t t❤❡s❡ tr♦✉❜❧❡s ❝♦✉❧❞ ❛✛❡❝t ❛♥② s❡❛r❝❤ ❛❧❣♦r✐t❤♠✳
❚❤✐s ♣❛♣❡r ❞❡s❝r✐❜❡s t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ❛ ♣❧❛♥♥❡r✱ ❝❛❧❧❡❞ ❙▲P❧❛♥✱ ❜❛s❡❞ ♦♥ ♦♣t♠✐③❡❞ ✈❡rs✐♦♥s ♦❢ t❤❡ ❛❧❣♦r✐t❤♠s ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ❛♥❞ ▲❡❛r♥✐♥❣ ❘❡❛❧✲❚✐♠❡ ❆✯ t❤❛t ❛✐♠ t♦ r❡❞✉❝❡ t❤❡ ✐♠♣❛❝t ♦❢ t❤❡ tr♦✉❜❧❡s ❝✐t❡❞ ❜❡❢♦r❡ ✐♥ ♦r❞❡r t♦ ❜✉✐❧❞ ♣❧❛♥s ♠♦r❡ ❡✣❝✐❡♥t❧②✳ ❇❡s✐❞❡s✱ t❤❡ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ♣❧❛♥♥✐♥❣ t❡❝❤♥✐q✉❡s ✐♥ s♦❧✈✐♥❣ r❡❧❡✈❛♥t ♣r♦❜❧❡♠s ✐s ♦❢ ♣❛r✲ t✐❝✉❧❛r ❝♦♥❝❡r♥ ❢♦r t❤❡ ♣❧❛♥♥✐♥❣ ❝♦♠♠✉♥✐t②✳ ❚❤❡ ❣❡♥❡r❛t✐♦♥ ♦❢ ❜✉s✐♥❡ss ♣r♦❝❡ss❡s ✭✇♦r❦✲ ✢♦✇✮ ✐s ♦♥❡ ♦❢ t❤❡ ❛r❡❛s t❤❛t ❝❛♥ ❜❡♥❡✜t ❢r♦♠ t❤❡ ✉s❡ ♦❢ ♣❧❛♥♥✐♥❣✳ ❚❤✐s ❞✐ss❡rt❛t✐♦♥ ❛❧s♦ s♣❡❝✐✜❡s ❤♦✇ ❙▲P❧❛♥ ✇❛s ❛♣♣❧✐❡❞ t♦ t❤❡ ❛✉t♦♠❛t✐❝ ❣❡♥❡r❛t✐♦♥ ♦❢ ❜✉s✐♥❡ss ♣r♦❝❡ss❡s ♠♦❞❡❧s✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐①
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①①✐
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ❡ ❙✐❣❧❛s ①①✐✐✐
✶ ■♥tr♦❞✉çã♦ ✷✺
✶✳✶ ❈♦♥tr✐❜✉✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻ ✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
✷ ❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ❡ ❚r❛❜❛❧❤♦s ❈♦rr❡❧❛t♦s ✷✼
✷✳✶ ❇✉s❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷✳✶✳✶ ❇✉s❝❛ ❈❡❣❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✷✳✶✳✷ ❇✉s❝❛ ❍❡✉ríst✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✷ P❧❛♥❡❥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✷✳✶ P❧❛♥❡❥❛❞♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✷✳✷ ❍❡✉ríst✐❝❛ ❡♠ P❧❛♥❡❥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✻ ✷✳✷✳✸ ▲✐♥❣✉❛❣❡♥s ❞❡ ❉❡✜♥✐çã♦ ❞❡ ❉♦♠í♥✐♦s ❡ Pr♦❜❧❡♠❛s ❞❡ P❧❛♥❡❥❛♠❡♥t♦ ✺✷ ✷✳✷✳✹ ❈♦♠♣❡t✐çã♦ ❡♠ P❧❛♥❡❥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺
✸ ❙✐st❡♠❛ ❙▲P❧❛♥ ✻✶
✸✳✶ ▼♦t✐✈❛çã♦ ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞♦ ♠ét♦❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✸✳✷ ❊str❛té❣✐❛ ❞❡ ❇✉s❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✸✳✷✳✶ ❍❇✲❊❍❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✷✳✷ ❆❞❛♣t✐✈❡✲▲❘❚❆✯ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶
✹ ❊①♣❡r✐♠❡♥t♦s ❡ ❉✐s❝✉ssõ❡s ✽✸
✹✳✶ ▼❡t♦❞♦❧♦❣✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✹✳✷ ❇❡♥❝❤♠❛r❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✹✳✸ ❘❡s✉❧t❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✹✳✸✳✶ ❘❡s✉❧t❛❞♦s ♣❛r❝✐❛✐s✿ ❍❇✲❊❍❈ ❡ ❆❞❛♣t✐✈❡✲▲❘❚❆✯ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✹✳✸✳✷ ❘❡s✉❧t❛❞♦s ❣❡r❛✐s✿ P❧❛♥❡❥❛❞♦r ❙▲P❧❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵
①✈✐✐✐ ❙✉♠ár✐♦
✺ ❆♣❧✐❝❛♥❞♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❡♠ ♣r♦❝❡ss♦s ❞❡ ♥❡❣ó❝✐♦ ✾✺
✺✳✶ ❈♦♥❝❡✐t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✺ ✺✳✷ ▼❡t❛♣❧❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✺✳✸ ■♥t❡❣r❛çã♦ ❡♥tr❡ ❙▲P❧❛♥ ❡ ▼❡t❛♣❧❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾
✻ ❈♦♥❝❧✉sã♦ ❡ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✶✶✸
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✷✳✶ ❍❡✉ríst✐❝❛ ❝♦♠♦ ❡st✐♠❛t✐✈❛ ❞❛ ❞✐stâ♥❝✐❛ ❛té ❛ ♠❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✷ ❊①❡♠♣❧♦✿ ✐♥stâ♥❝✐❛ ❞♦ ♣r♦❜❧❡♠❛ ✏▼✉♥❞♦ ❞♦s ❇❧♦❝♦s✑ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✸ ❊①❡♠♣❧♦✿ ❛♣❧✐❝❛♥❞♦ ✉♠❛ ❛çã♦ s♦❜r❡ ♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✷✳✹ ❊①❡♠♣❧♦✿ s✉❝❡ss✐✈❛s ❡①♣❛♥sõ❡s ❛té ❡♥❝♦♥tr❛r ❛ ♠❡t❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵ ✷✳✺ ❊①❡♠♣❧♦✿ ♣r♦❜❧❡♠❛ ❞❡ ❧♦❣íst✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✽ ✷✳✻ ❊①❡♠♣❧♦✿ ❣❡r❛çã♦ ❞♦ ❘P● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✷✳✼ ❊①❡♠♣❧♦✿ r❡❣r❡ssã♦ ♥♦ ❘P● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✵ ✷✳✽ ❊①❡♠♣❧♦✿ ✈❛❧♦r ❤❡✉ríst✐❝♦ ❡①tr❛í❞♦ ❞♦ ❘P● ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✷✳✾ ❍✐stór✐❛ ❞❛ ■♥t❡r♥❛t✐♦♥❛❧ P❧❛♥♥✐♥❣ ❈♦♠♣❡t✐t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✶ ❍❇✲❊❍❈✿ ❤❡❛♣s ◗♠❛① ❡ ◗♠✐♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✸✳✷ ❍❇✲❊❍❈✿ ❡s❝❛♣❛♥❞♦ ❞❡ ót✐♠♦s ❧♦❝❛✐s ♠❛✐s rá♣✐❞♦ ❛tr❛✈és ❞♦ ❤❡❛♣ Qmin✳ ✳ ✻✺
✸✳✸ ❍❇✲❊❍❈✿ ❛♥t❡❝✐♣❛♥❞♦ ❛ ❜✉s❝❛ ❝♦♠♣❧❡t❛ ❛♦ ❡①❝❡❞❡r ❛ ❝❛♣❛❝✐❞❛❞❡ ♠á①✐♠❛ ❞❡ Qmin✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻
✸✳✹ ❍❇✲❊❍❈✿ r❡tr♦❝❡❞❡♥❞♦ ♣❛r❛ s❛✐r ❞❡ ❜❡❝♦s s❡♠ s❛í❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✸✳✺ ❆❞❛♣t✐✈❡✲▲❘❚❆✯✿ ❛r♠❛③❡♥❛♠❡♥t♦ ❞❡ ❡st❛❞♦s ❡ s❡✉s ✈❛❧♦r❡s ❤❡✉ríst✐❝♦s✳ ✳ ✳ ✼✷ ✸✳✻ ❆❞❛♣t✐✈❡✲▲❘❚❆✯✿ ♣♦❞❛ ❞❡ s✉❝❡ss♦r❡s ❞✉r❛♥t❡ ❛ ❡①♣❛♥sã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✸✳✼ ❆❞❛♣t✐✈❡✲▲❘❚❆✯✿ ♣r♦❝❡ss♦ ❞❡ ❛♣r❡♥❞✐③❛❣❡♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✸✳✽ ❆❞❛♣t✐✈❡✲▲❘❚❆✯✿ ❡s❝❛♣❛♥❞♦ ❞❡ ♠á①✐♠♦s✴♠í♥✐♠♦s ❧♦❝❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✸✳✾ ❆❞❛♣t✐✈❡✲▲❘❚❆✯✿ ❜❛❧❛♥❝❡❛♠❡♥t♦ ❞♦ ❤❡❛♣ Qmax✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺
✸✳✶✵ ❆❞❛♣t✐✈❡✲▲❘❚❆✯✿ ❡♥❝♦♥tr❛♥❞♦ ❛ s♦❧✉çã♦ ❛ ♣❛rt✐r ❞❡ ✐t❡r❛çõ❡s ❣✉❧♦s❛s✳ ✳ ✳ ✳ ✼✻ ✸✳✶✶ ❆❞❛♣t✐✈❡✲▲❘❚❆✯✿ ❛❝❡❧❡r❛♥❞♦ ❛ ❝♦♥✈❡r❣ê♥❝✐❛ ❝♦♠ ✐t❡r❛çõ❡s ❣✉❧♦s❛s✳ ✳ ✳ ✳ ✳ ✼✼ ✹✳✶ ❚❛①❛ ❞❡ ❝♦♠♣❧❡t✉❞❡✿ ❍❈✱ ❊❍❈ ❡ ❍❇✲❊❍❈✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✽ ✹✳✷ ❚❡♠♣♦ ♠é❞✐♦✿ ▲❘❚❆✯✱▲❘❚❆✯✲❑ ❡ ❆❞❛♣t✐✈❡✲▲❘❚❆✯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✵ ✹✳✸ ❚❡♠♣♦ ♠é❞✐♦✿ ❋❋ ❡ ❙▲P❧❛♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✸ ✺✳✶ Pr✐♥❝✐♣❛✐s sí♠❜♦❧♦s ❞❛ ♥♦t❛çã♦ ❇P▼◆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✺✳✷ ❊①❡♠♣❧♦ ❞❡ ♠♦❞❡❧❛❣❡♠ ❞❡ ✇♦r❦✢♦✇✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✺✳✸ ❆rq✉✐t❡t✉r❛ ❞♦ ❙✐st❡♠❛ ▼❡t❛♣❧❛♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✺✳✹ ❚❡♠♣♦ ♠é❞✐♦✿ ▼❡t❛♣❧❛♥✲❋❋ ❡ ▼❡t❛♣❧❛♥✲❙▲P❧❛♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✷✳✶ ❉✐❢❡r❡♥ç❛s ❡♥tr❡ ❙❚❘■P❙ ❡ ❆❉▲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✷✳✷ ❈♦♠♣❡t✐❞♦r❡s ■P❈✲✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✷✳✸ ❘❡s✉❧t❛❞♦s ■P❈✲✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✷✳✹ ❱❡♥❝❡❞♦r❡s ■P❈✲✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✶ ❉♦♠í♥✐♦s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❞♦ ❜❡♥❝❤♠❛r❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✹✳✷ ❚❛①❛ ❞❡ ❝♦♠♣❧❡t✉❞❡ ❡ t❡♠♣♦ ♠é❞✐♦ ❞❡ ❡①❡❝✉çã♦✿ ❍❈✱ ❊❍❈ ❡ ❍❇✲❊❍❈✳ ✳ ✳ ✽✻ ✹✳✸ ❚❛①❛ ❞❡ ❢❛❧❤❛ ✭❢❛❧t❛ ❞❡ ❡s♣❛ç♦✮ ❡ t❡♠♣♦ ♠é❞✐♦ ❞❡ ❡①❡❝✉çã♦✿ ▲❘❚❆✯✱
▲❘❚❆✯✲❑ ❡ ❆❞❛♣t✐✈❡✲▲❘❚❆✯✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✹✳✹ ❚❛①❛ ❞❡ ❢❛❧❤❛ ❡ t❡♠♣♦ ♠é❞✐♦ ❞❡ ❡①❡❝✉çã♦✿ ❋❋ ❡ ❙▲P❧❛♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ❡ ❙✐❣❧❛s
❆✯ ❆❧❣♦r✐t♠♦ ♣❛r❛ ❜✉s❝❛ ❞❡ ❝❛♠✐♥❤♦s ót✐♠♦s ❡♠ ❣r❛❢♦s ❆❉▲ ❆❝t✐♦♥ ❉❡s❝r✐♣t✐♦♥ ▲❛♥❣✉❛❣❡
❆■P❙ ❆rt✐✜❝✐❛❧ ■♥t❡❧❧✐❣❡♥❝❡ P❧❛♥♥✐♥❣ ❙②st❡♠s ❇❋❙ ❇❡st ❋✐rst ❙❡❛r❝❤
❇P▼◆ ❇✉s✐♥❡ss Pr♦❝❡ss ▼♦❞❡❧✐♥❣ ◆♦t❛t✐♦♥ ❊❍❈ ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣
❋❋ ❋❛st ❋♦r✇❛r❞ ❍❈ ❍✐❧❧ ❈❧✐♠❜✐♥❣
■❆ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧
■❈❆P❙ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❆✉t♦♠❛t❡❞ P❧❛♥♥✐♥❣ ❙❝❤❡❞✉❧✐♥❣ ■P❈ ■♥t❡r♥❛t✐♦♥❛❧ P❧❛♥♥✐♥❣ ❈♦♠♣❡t✐t✐♦♥
▲❘❚❆✯ ▲❡❛r♥✐♥❣ ❘❡❛❧✲❚✐♠❡ ❆✯
P❉❉▲ P❧❛♥♥✐♥❣ ❉♦♠❛✐♥ ❉❡✜♥✐t✐♦♥ ▲❛♥❣✉❛❣❡ ❙❚❘■P❙ ❙❚❛♥❢♦r❞ ❘❡s❡❛r❝❤ ■♥st✐t✉t❡ Pr♦❜❧❡♠ ❙♦❧✈❡r ❲❢▼❈ ❲♦r❦✢♦✇ ▼❛♥❛❣❡♠❡♥t ❈♦❛❧✐t✐♦♥
❳▼▲ ❡❳t❡♥s✐❜❧❡ ▼❛r❦✉♣ ▲❛♥❣✉❛❣❡ ❳P❉▲ ❳▼▲ Pr♦❝❡ss ❉❡✜♥✐t✐♦♥ ▲❛♥❣✉❛❣❡
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
P❧❛♥❡❥❛♠❡♥t♦ é ✉♠ ❝❛♠♣♦ ❞❛ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧ q✉❡ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ❝♦♥tr♦❧❛r s✐st❡♠❛s ❝♦♠♣❧❡①♦s ❞❡ ❢♦r♠❛ ❛✉tô♥♦♠❛✳ ❊st❛ ❛❜♦r❞❛❣❡♠ s❡ t♦r♥♦✉ ♠✉✐t♦ ✉s❛❞❛ ♣❛r❛ r❡✲ s♦❧✈❡r ♣r♦❜❧❡♠❛s ♣rát✐❝♦s ❝♦♠♦ ♦s ❡♥❝♦♥tr❛❞♦s ♥❛s ár❡❛s ❞❡✿ ❧♦❣íst✐❝❛✱ ❡①♣❧♦r❛çã♦ ❡s♣❛❝✐❛❧✱ ❥♦❣♦s✱ ♣r♦❥❡t♦s✱ r♦❜ót✐❝❛✱ ❡t❝✳ ❙✐st❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ♦✉ s✐♠♣❧❡s♠❡♥t❡ ♣❧❛♥❡❥❛❞♦r❡s✱ ✈✐s❛♠ ❣❡r❛r ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❛çõ❡s✱ ❞❡♥♦♠✐♥❛❞❛ ♣❧❛♥♦✱ ♥❡❝❡ssár✐❛ ♣❛r❛ ❛❧❝❛♥ç❛r ❛ ♠❡t❛✱ s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❝♦♥✜❣✉r❛çã♦ ✐♥✐❝✐❛❧ ❞♦ ♠❡s♠♦✳
❖s ♣❧❛♥❡❥❛❞♦r❡s ❛t✉❛✐s ✉s❛♠ té❝♥✐❝❛s ❞❡ ❜✉s❝❛ ♣❛r❛ s❡❧❡❝✐♦♥❛r ❛çõ❡s ♣❛r❛ ❝♦♥str✉✐r s❡✉s ♣❧❛♥♦s✳ ❖s ❣r❛♥❞❡s ❞❡s❛✜♦s ❞❡ss❡s ♣❧❛♥❡❥❛❞♦r❡s ❡♥✈♦❧✈❡♠ ♦ ♠❡❧❤♦r❛♠❡♥t♦ ❞❡ ❛❧✲ ❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ❡ ❛ ❝♦♥str✉çã♦ ❞❡ ❤❡✉ríst✐❝❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ✉s❛❞❛s ♣❛r❛ ❣✉✐❛r t❛✐s ❛❧❣♦r✐t♠♦s✳ ❯♠ ♣❧❛♥❡❥❛❞♦r ❞❡ r❡❢❡rê♥❝✐❛ q✉❡ ❢❛③ ✉s♦ ❞❡ss❛ ❛❜♦r❞❛❣❡♠ é ♦ ❋❛st ❋♦r✇❛r❞ ✭❋❋✮ ❬❍♦✛♠❛♥♥ ❡ ◆❡❜❡❧ ✷✵✵✶❪✳ ❊❧❡ é ❝♦♠♣♦st♦ ♣♦r ❞♦✐s ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛✱ ♦ ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ✭❊❍❈✮ ❬❍♦✛♠❛♥♥ ❡ ◆❡❜❡❧ ✷✵✵✶❪ ❡ ♦ ❇❡st ❋✐rst ❙❡❛r❝❤ ✭❇❋❙✮ ❬❈♦♣♣✐♥ ✷✵✵✹❪✳ ❊ss❡s ❛❧❣♦r✐t♠♦s sã♦ ❣✉✐❛❞♦s ♣♦r ✉♠❛ ❤❡✉ríst✐❝❛ ❞❡r✐✈❛❞❛ ❞❡ ❣r❛❢♦s ❞❡ ♣❧❛♥♦s r❡❧❛①❛❞♦s✱ ❡①tr❛í❞♦s ❛ ♣❛rt✐r ❞♦s ♣r♦❜❧❡♠❛s ❛ s❡r❡♠ r❡s♦❧✈✐❞♦s✳
❖ ❋❋ ♦❜t❡✈❡ ♦ ♣r✐♠❡✐r♦ ❧✉❣❛r ♥❛ s❡❣✉♥❞❛ ❝♦♠♣❡t✐çã♦ ✐♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳ ❱ár✐♦s ♣❧❛♥❡❥❛❞♦r❡s ❞❡ s✉❝❡ss♦ s✉r❣✐r❛♠ ❛ ♣❛rt✐r ❞❛s ✐❞❡✐❛s ♣r♦♣♦st❛s ♣❡❧♦ ❋❋✱ ❝♦♠♦✿ ▼❡tr✐❝✲❋❋ ❬❍♦✛♠❛♥♥ ✷✵✵✷❪✱ ❈♦♥❢♦r♠❛♥t✲❋❋ ❬❍♦✛♠❛♥♥ ❡ ❇r❛❢♠❛♥ ✷✵✵✻❪✱ ❈♦♥t✐♥❣❡♥t✲❋❋ ❬❆❧❜♦r❡ ❡t ❛❧✳ ✷✵✵✾❪✱ Pr♦❜❛❜✐❧✐st✐❝✲❋❋ ❬❉♦♠s❤❧❛❦ ❡ ❍♦✛♠❛♥♥ ✷✵✵✼❪✱ ▼❆❈❘❖✲❋❋ ❬❇♦t❡❛ ❡t ❛❧✳ ✷✵✵✺❪✱ ▼❆❘❱■◆ ❬❈♦❧❡s ❡ ❙♠✐t❤ ✷✵✵✼❪✱ P❖◆❉ ❬❉❡♣❛rt♠❡♥t ✷✵✵✻❪✱ ❏❛✈❛❋❋ ❬❈♦❧❡s ❡t ❛❧✳ ✷✵✵✽❪✱ ❋❉ ❬❍❡❧♠❡rt ✷✵✵✻❪ ❡ ▲❆▼❆ ❬❘✐❝❤t❡r ❡ ❲❡st♣❤❛❧ ✷✵✶✵❪✳
❆♣ós ❡①❡❝✉t❛r ❡①♣❡r✐♠❡♥t♦s ✉t✐❧✐③❛♥❞♦ ♦ ♠ét♦❞♦ ♣r♦♣♦st♦ ♣❡❧♦ ❋❋✱ ❡♠ ❛❧❣✉♥s ♣r♦✲ ❜❧❡♠❛s ✉s❛❞♦s ♥❛s ❝♦♠♣❡t✐çõ❡s ✐♥t❡r♥❛❝✐♦♥❛✐s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ❢♦✐ ♣♦ssí✈❡❧ ✐❞❡♥t✐✜❝❛r ❛❧❣✉♠❛s s✐t✉❛çõ❡s q✉❡ ♣♦❞❡♠ ♣r❡❥✉❞✐❝❛r ❛ ❡①❡❝✉çã♦ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛s ❡✱ ❝♦♥s❡q✉❡♥✲ t❡♠❡♥t❡✱ ❞❡❣r❛❞❛r ❛ ♣❡r❢♦r♠❛♥❝❡ ❞❡ s✐st❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✳ P❛r❛ ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ♦ ❊❍❈ ♥ã♦ ❝♦♥s❡❣✉❡ ❡s❝❛♣❛r ❞❡ ♠á①✐♠♦s✴♠í♥✐♠♦s ❧♦❝❛✐s✱ ✜❝❛♥❞♦ ♣r❡s♦ ❡♠ ✏❜❡❝♦s s❡♠ s❛í❞❛✑✱ ♦ q✉❡ ❢❛③ ❝♦♠ q✉❡ ❡❧❡ ✈❡♥❤❛ ❛ ❢❛❧❤❛r✳ ◗✉❛♥❞♦ ✐ss♦ ♦❝♦rr❡✱ ✉♠❛ ❜✉s❝❛ ❝♦♠♣❧❡t❛ é r❡❛❧✐③❛❞❛ ♣❡❧♦ ❇❋❙ q✉❡ ♣♦❞❡ ✈✐r ❛ ❢❛❧❤❛r ♣♦r ❢❛❧t❛ ❞❡ ❡s♣❛ç♦ ❞❡ ♠❡♠ór✐❛✳
✷✻ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
❞✐ss♦✱ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ♦ ♣❧❛♥❡❥❛❞♦r ❙❡❛r❝❤✐♥❣ ❛♥❞ ▲❡❛r♥✐♥❣ ✲ P❧❛♥♥❡r ✭❙▲P❧❛♥✮✱ ❞❡s❝r✐t♦ ♥❡st❡ tr❛❜❛❧❤♦✱ q✉❡ ✉t✐❧✐③❛ ❞♦✐s ♠ét♦❞♦s ❞❡ ❜✉s❝❛ ❜❛s❡❛❞♦s ♥♦s ❛❧❣♦r✐t♠♦s ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ✭❊❍❈✮ ❡ ▲❡❛r♥✐♥❣ ❘❡❛❧✲❚✐♠❡ ❆✯ ✭▲❘❚❆✯✮ ❬❑♦r❢ ✶✾✾✵❪✳ ❊ss❡s ♠ét♦❞♦s s♦❢r❡r❛♠ ❛❞❛♣t❛çõ❡s ❛ ✜♠ ❞❡ ♠✐t✐❣❛r ♦s ✐♠♣❛❝t♦s ❝❛✉s❛❞♦s ♣❡❧♦s ♣r♦❜❧❡♠❛s ✐❞❡♥t✐✜❝❛❞♦s ❞✉r❛♥t❡ ♦s ❡①♣❡r✐♠❡♥t♦s✳ ❉❡ss❡ ♠♦❞♦✱ ✉♠ ❞♦s ♦❜❥❡t✐✈♦s ❞❡st❡ tr❛❜❛❧❤♦ é ❛♥❛❧✐s❛r ❛ ❡✜❝✐ê♥❝✐❛ ❞♦ ♣❧❛♥❡❥❛❞♦r ❞❡s❡♥✈♦❧✈✐❞♦✱ ♣❛r❛ q✉❡ ❡❧❡ ♣♦ss❛ s❡r ✉t✐❧✐③❛❞♦ ♥❛ r❡s♦❧✉çã♦ ❞❡ ♣r♦❜❧❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ✐♥❞❡♣❡♥❞❡♥t❡ ❞♦ ❞♦♠í♥✐♦✳
❈♦♠♦ r❡s✉❧t❛❞♦ ❞❡st❛ ❛♥á❧✐s❡✱ ❢♦✐ ♣♦ssí✈❡❧ ❝♦♥st❛t❛r ✉♠❛ r❡❞✉çã♦ s✐❣♥✐✜❝❛t✐✈❛ ♥♦ t❡♠♣♦ ♠é❞✐♦ ❡ ♥❛ t❛①❛ ❞❡ ❢❛❧❤❛s ♣♦r ❢❛❧t❛ ❞❡ ❡s♣❛ç♦ ❡♠ ♠❡♠ór✐❛✱ ❞✉r❛♥t❡ ❛ ❣❡r❛çã♦ ❞♦s ♣❧❛♥♦s✱ ✉t✐❧✐③❛♥❞♦ ♦s ♠ét♦❞♦s ❞❡s❡♥✈♦❧✈✐❞♦s ♥❡st❡ tr❛❜❛❧❤♦✳
❆t✉❛❧♠❡♥t❡✱ ♦✉tr♦ ♣r♦❜❧❡♠❛ ❝♦♠✉♠ ❞❡ ❡①tr❡♠❛ r❡❧❡✈â♥❝✐❛✱ q✉❡ ✈❡♠ s❡♥❞♦ ❛❜♦r❞❛❞♦ ♥❛s ♦r❣❛♥✐③❛çõ❡s é ❛ ♠♦❞❡❧❛❣❡♠ ❞❡ ♣r♦❝❡ss♦s ❞❡ ♥❡❣ó❝✐♦ ✭✇♦r❦✢♦✇✮✱ ❡st✉❞❛❞♦ ♥♦ ●❡r❡♥❝✐✲ ❛♠❡♥t♦ ❞❡ Pr♦❝❡ss♦s ❞❡ ◆❡❣ó❝✐♦ ✭❞♦ ✐♥❣❧ês ❇✉s✐♥❡ss Pr♦❝❡ss ▼❛♥❛❣❡♠❡♥t ✭❇P▼✮✮ ❬❲❡s❦❡ ✷✵✵✼❪✳ Pr♦❝❡ss♦s ❞❡ ✇♦r❦✢♦✇ ♣♦❞❡♠ s❡r ❢❛❝✐❧♠❡♥t❡ r❡❧❛❝✐♦♥❛❞♦s ❛ ♣r♦❜❧❡♠❛s ❞❡ ♣❧❛♥❡❥❛✲ ♠❡♥t♦✱ ♦♥❞❡ s❡ t❡♠ ✐♥✐❝✐❛❧♠❡♥t❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ t❛r❡❢❛s✴❛çõ❡s q✉❡ ❞❡✈❡♠ s❡r ❝♦❧♦❝❛❞❛s ❡♠ ✉♠❛ s❡q✉ê♥❝✐❛ ❧ó❣✐❝❛ ✭✇♦r❦✢♦✇✴♣❧❛♥♦✮ ❛ ✜♠ ❞❡ s❛t✐s❢❛③❡r ✉♠ ❞❛❞♦ ♦❜❥❡t✐✈♦ ❬❈❛s❛t✐ ❡t ❛❧✳ ✶✾✾✻❪✳ ●❡r❛❧♠❡♥t❡✱ ♣r♦❝❡ss♦s ❞❡ ♥❡❣ó❝✐♦ sã♦ ♠♦❞❡❧❛❞♦s ♠❛♥✉❛❧♠❡♥t❡ ❝♦♠ ❛❥✉❞❛ ❞❡ ✉♠ ❡❞✐t♦r✱ ♣♦ré♠ ❡st❛ ❛❜♦r❞❛❣❡♠ ❞❡♠❛♥❞❛ t❡♠♣♦ ❡ é ♣❛ssí✈❡❧ ❞❡ ❡rr♦s✳ ❊♥tã♦✱ ❧❡✈❛♥❞♦ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❛ ♣❛rt❡ ♣rát✐❝❛ ❞♦ ✉s♦ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ♦✉tr♦ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ ❢♦✐ ❛♣❧✐❝❛r ♦ ♣❧❛♥❡❥❛❞♦r ❙▲P❧❛♥ ♥❛ ❣❡r❛çã♦ ❛✉t♦♠át✐❝❛ ❞❡ ✇♦r❦✢♦✇s✳
✶✳✶ ❈♦♥tr✐❜✉✐çã♦
❆s ♣r✐♥❝✐♣❛✐s ❝♦♥tr✐❜✉✐çõ❡s ❞❡st❡ tr❛❜❛❧❤♦ sã♦✿
• ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ ♣❧❛♥❡❥❛❞♦r ❙▲P❧❛♥ ❜❛s❡❛❞♦ ♥♦s ❛❧❣♦r✐t♠♦s ❊❍❈ ❡ ▲❘❚❆✯❀ • ✉t✐❧✐③❛çã♦ ❞♦ ♣❧❛♥❡❥❛❞♦r ❙▲P❧❛♥ ❝♦♠♦ ♠♦t♦r ❞❡ ❣❡r❛çã♦ ❛✉t♦♠át✐❝❛ ❞❡ ✇♦r❦✢♦✇✳
✶✳✷ ❖r❣❛♥✐③❛çã♦ ❞❛ ❉✐ss❡rt❛çã♦
❖ ❈❛♣ít✉❧♦ ✷ ❛♣r❡s❡♥t❛ ❝♦♥❝❡✐t♦s ❜ás✐❝♦s ❞❡ ❜✉s❝❛ ❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❡♠ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦s ♣r✐♥❝✐♣❛✐s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s ❛♦ ❝♦♥t❡①t♦ ❞❛ ❞✐ss❡rt❛çã♦✳ ❖ ❈❛♣ít✉❧♦ ✸ ♣r♦♣õ❡ ✉♠ ♥♦✈♦ ♣❧❛♥❡❥❛❞♦r✱ ❞❡s❝r❡✈❡♥❞♦ s✉❛ ✐♠♣❧❡♠❡♥t❛çã♦✱ ❛❧é♠ ❞♦s ❛❧❣♦r✐t♠♦s ✉s❛❞♦s ♣♦r ❡❧❡✳
◆❛ ♣r✐♠❡✐r❛ ♣❛rt❡ ❞♦ ❈❛♣ít✉❧♦ ✹ é ❞❡s❝r✐t♦ ♦ ❡st✉❞♦ ❝♦♠♣❛r❛t✐✈♦ r❡❛❧✐③❛❞♦ ❡♥tr❡ ♦s ❛❧❣♦r✐t♠♦s ❞❡s❡♥✈♦❧✈✐❞♦s ❡ ✈❡rsõ❡s s❡♠❡❧❤❛♥t❡s ❛ ❡❧❡s✳ ❏á ♥❛ s❡❣✉♥❞❛ ♣❛rt❡✱ ❢♦✐ ❢❡✐t❛ ✉♠❛ ❝♦♠♣❛r❛çã♦ ❡♥tr❡ ♦ ♣❧❛♥❡❥❛❞♦r ❞❡s❡♥✈♦❧✈✐❞♦ ❡ ♦ ♣❧❛♥❡❥❛❞♦r ❋❋✳
❈❛♣ít✉❧♦ ✷
❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ❡ ❚r❛❜❛❧❤♦s
❈♦rr❡❧❛t♦s
◆❡st❡ ❝❛♣ít✉❧♦ sã♦ ❞✐s❝✉t✐❞♦s ♦s ❢✉♥❞❛♠❡♥t♦s t❡ór✐❝♦s ❡ tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s✱ ♦❜❥❡✲ t✐✈❛♥❞♦ ♣r♦♣✐❝✐❛r ✉♠❛ ♠❡❧❤♦r ❝♦♠♣r❡❡♥sã♦ ❞♦ tr❛❜❛❧❤♦ ❞❡s❡♥✈♦❧✈✐❞♦✳ ❈♦♠♦ ♦ tr❛❜❛❧❤♦ ❝♦♥s✐st✐✉ ♥❛ ❝♦♥str✉çã♦ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦ ❝♦♠♣♦st♦ ♣♦r ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛✱ ❡st❡ ❝❛♣ít✉❧♦ ❢♦✐ ❡str✉t✉r❛❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿ ♥❛ ❙❡çã♦ ✷✳✶ sã♦ ❞❡s❝r✐t♦s ❝♦♥❝❡✐t♦s ❡ ❛❧✲ ❣✉♥s ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ r❡❧❛❝✐♦♥❛❞♦s ❛♦ t❡♠❛❀ ♥❛ ❙❡çã♦ ✷✳✷ sã♦ ❛♣r❡s❡♥t❛❞♦s ❝♦♥❝❡✐t♦s ❡ ❛❧❣✉♥s s✐st❡♠❛s ❞❡ ♣❧❛♥❡❥❛♠❡♥t♦✱ ❜❡♠ ❝♦♠♦ s❡✉s ❛✈❛♥ç♦s ♦❜t✐❞♦s ❛♦ ❧♦♥❣♦ ❞❛ ❤✐stór✐❛✳
✷✳✶ ❇✉s❝❛
❯♠❛ ❜✉s❝❛ ❝♦♥s✐st❡ ❡♠ ❞❡t❡r♠✐♥❛r ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ♣❛ss♦s q✉❡ ❧❡✈❛ ❞❡ ✉♠ ❡st❛❞♦ ✐♥✐❝✐❛❧ ❛té ✉♠ ❡st❛❞♦ ♠❡t❛✱ ❝✉❥❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❡stá r❡❧❛❝✐♦♥❛❞❛ ❛♦ t❛♠❛♥❤♦ ❞♦ ❡s♣❛ç♦ ❞❡ ❜✉s❝❛✳ ❆❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ sã♦ ❢✉♥❞❛♠❡♥t❛✐s ♣❛r❛ ❛ s♦❧✉çã♦ ❞❡ ♠✉✐t♦s ♣r♦❜❧❡♠❛s ❞❡ ■♥t❡❧✐❣ê♥❝✐❛ ❆rt✐✜❝✐❛❧ ✭■❆✮✳
❆ s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❜✉s❝❛ é ❝♦♠♣♦st❛ ♣♦r ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❡st❛❞♦s✱ s❡♥❞♦ q✉❡ ❝❛❞❛ ❡st❛❞♦ r❡♣r❡s❡♥t❛ ♣❛rt❡ ❞❛ s♦❧✉çã♦✳ ❊st❡s ❡st❛❞♦s sã♦ ❞✐✈✐❞✐❞♦s ❡♠✿ ❡st❛❞♦ ✐♥✐✲ ❝✐❛❧✱ ❡st❛❞♦s ✐♥t❡r♠❡❞✐ár✐♦s ❡ ❡st❛❞♦ ♠❡t❛✳ P❛r❛ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❡st❛❞♦s ❞❛❞♦ ❝♦♠♦ s♦❧✉çã♦ ❞❡ ✉♠ ♣r♦❜❧❡♠❛✱ ❛ ♣❛rt✐r ❞♦ ❡st❛❞♦ ✐♥✐❝✐❛❧✱ ♦s ❡st❛❞♦s ✐♥t❡r♠❡❞✐ár✐♦s sã♦ ♣❡r❝♦rr✐❞♦s ❛té ❛❧❝❛♥ç❛r ♦ ❡st❛❞♦ ♠❡t❛✳ ❊♥tr❡ ❝❛❞❛ ❡st❛❞♦ ♣♦❞❡✲s❡ ❛ss♦❝✐❛r ✉♠ ❝✉st♦✴❞✐stâ♥❝✐❛✳ ◆♦r♠❛❧✲ ♠❡♥t❡✱ ❛ ♠❡❧❤♦r s♦❧✉çã♦ ❝♦♥s✐st❡ ♥♦ s♦♠❛tór✐♦ ♠á①✐♠♦ ♦✉ ♠í♥✐♠♦ ❞❡st❡ ♣❛râ♠❡tr♦✳
❯♠ ❛❧❣♦r✐t♠♦ ❞❡ ❜✉s❝❛ ❣❡r❛ ♠ú❧t✐♣❧❛s ❡s❝♦❧❤❛s ❞❡ ❝❛♠✐♥❤♦✱ ❞❡♥tr❡ ❛s q✉❛✐s ❡❧❡ ♦♣t❛ ♣♦r ✉♠❛ ❞❡❧❛s ❡ ❞❡✐①❛ ❛s ♦✉tr❛s ♣❛r❛ s❡r❡♠ ❛♥❛❧✐s❛❞❛s ♣♦st❡r✐♦r♠❡♥t❡✱ ♦♥❞❡ ❛ ❞❡❝✐sã♦ ❞❡ q✉❛❧ s❡rá ❡s❝♦❧❤✐❞❛ ♣r✐♠❡✐r♦ ❞❡✜♥❡ ❛ ❡str❛té❣✐❛ ❞❡ ❜✉s❝❛✳
❊①✐st❡♠ ❛❧❣✉♥s ❝r✐tér✐♦s ♣❛r❛ s❡ ❛✈❛❧✐❛r ✉♠❛ ❡str❛té❣✐❛ ❞❡ ❜✉s❝❛✱ ❝♦♠♦✿
• ❈♦♠♣❧❡t✉❞❡✿ s❡ ❡①✐st❡ ✉♠❛ s♦❧✉çã♦ ❛ ❡str❛té❣✐❛ s❡rá ❝❛♣❛③ ❞❡ ❡♥❝♦♥trá✲❧❛❄ • ◗✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦✿ ❛ s♦❧✉çã♦ ❡♥❝♦♥tr❛❞❛ é ❛ s♦❧✉çã♦ ót✐♠❛❄
✷✽ ❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ❡ ❚r❛❜❛❧❤♦s ❈♦rr❡❧❛t♦s
• ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✿ q✉❛♥t♦ t❡♠♣♦ ❡❧❛ ❞❡♠♦r❛ ♣❛r❛ ♦❜t❡r ❛ s♦❧✉çã♦❄
• ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦✿ ❞❡ q✉❛♥t❛ ♠❡♠ór✐❛ ❡❧❛ ♥❡❝❡ss✐t❛ ♣❛r❛ r❡❛❧✐③❛r ❛ ❜✉s❝❛❄
❖ ♣r♦❝❡ss♦ ❞❡ ❜✉s❝❛ ♣♦❞❡ s❡r ❝♦♠♣❛r❛❞♦ ❛♦ ♣r♦❝❡ss♦ ❞❡ s❡ ❝♦♥str✉✐r ✉♠❛ ár✈♦r❡ ❞❡ ❜✉s❝❛ ❝✉❥❛ r❛✐③ é ♦ ❡st❛❞♦ ✐♥✐❝✐❛❧✱ ♦s ❡st❛❞♦s ❢♦❧❤❛s ❝♦rr❡s♣♦♥❞❡♠ ❛ ❡st❛❞♦s q✉❡ ♥ã♦ ♣♦ss✉❡♠ s✉❝❡ss♦r❡s ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡ ♥ã♦ t❡r❡♠ s✐❞♦ ❡①♣❛♥❞✐❞♦s ❛✐♥❞❛ ♦✉ ♣♦rq✉❡ ❢♦r❛♠ ❡①♣❛♥❞✐❞♦s ❡ ❣❡r❛r❛♠ ✉♠ ❝♦♥❥✉♥t♦ ✈❛③✐♦✳ ❊ ❛ ❝❛❞❛ ♣❛ss♦✱ ♦ ❛❧❣♦r✐t♠♦ ❜✉s❝❛ ✉♠ ❡st❛❞♦ ❢♦❧❤❛ ♣❛r❛ ❡①♣❛♥❞✐r✱ ❛té q✉❡ ❛ ♠❡t❛ s❡❥❛ ❡♥❝♦♥tr❛❞❛ ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳
✷✳✶✳✶ ❇✉s❝❛ ❈❡❣❛
❆ ❜✉s❝❛ ❝❡❣❛✱ t❛♠❜é♠ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❜✉s❝❛ ♥ã♦✲✐♥❢♦r♠❛❞❛✱ ♥ã♦ ♣♦ss✉✐ ♥❡♥❤✉♠❛ ✐♥❢♦r♠❛çã♦ ❛❞✐❝✐♦♥❛❧ s♦❜r❡ ♦ ♣r♦❜❧❡♠❛ q✉❡ ❛❥✉❞❡ ❛ ❣✉✐❛r ❛ ❜✉s❝❛✳ P♦rt❛♥t♦✱ t✉❞♦ q✉❡ s❡ ♣♦❞❡ ❢❛③❡r é ❡①♣❛♥❞✐r ✉♠ ❡st❛❞♦✱ ♦✉ s❡❥❛✱ ❣❡r❛r ❡st❛❞♦s s✉❝❡ss♦r❡s ❛ ♣❛rt✐r ❞❡ ✉♠ ♦✉tr♦ ❡st❛❞♦ q✉❛❧q✉❡r✱ ❡ ❞✐st✐♥❣✉✐r ✉♠ ❡st❛❞♦ ♠❡t❛ ❞❡ ✉♠ ♥ã♦✲♠❡t❛✳ ❖s ❛❧❣♦r✐t♠♦s ♠❛✐s ❝♦♥❤❡❝✐❞♦s q✉❡ ❢❛③❡♠ ✉s♦ ❞❡ss❛ ❡str❛té❣✐❛ sã♦✿
• ❇✉s❝❛ ❡♠ ❧❛r❣✉r❛✿ é ✉♠❛ ❡str❛té❣✐❛ s✐♠♣❧❡s ♦♥❞❡ ♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ é ❡①♣❛♥❞✐❞♦ ♣r✐✲
♠❡✐r♦✱ ❡ ❞❡♣♦✐s s❡✉s s✉❝❡ss♦r❡s✱ ♦s s✉❝❡ss♦r❡s ❞❡ s❡✉s s✉❝❡ss♦r❡s✱ ❡ ❛ss✐♠ ♣♦r ❞✐❛♥t❡✱ ❛té q✉❡ s❡ ❡♥❝♦♥tr❡ ❛ ♠❡t❛✳ ❖s ❡st❛❞♦s ❡①♣❛♥❞✐❞♦s sã♦ ❛r♠❛③❡♥❛❞♦s ❡♠ ✉♠ ✜❧❛ ❋■❋❖✱ ♦♥❞❡ ❛♦ s❡r❡♠ ❣❡r❛❞♦s✱ sã♦ ❝♦❧♦❝❛❞♦s ♥♦ ✜♠ ❞❛ ✜❧❛✱ ❡ ♦ ♣r✐♠❡✐r♦ ✭❝❛❜❡ç❛✮ é ❡s❝♦❧❤✐❞♦ ♣❛r❛ s❡r ❡①♣❛♥❞✐❞♦ ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳
✕ ❈♦♠♣❧❡t✉❞❡✿ é ❝♦♠♣❧❡t❛ s❡ ♦ ❡st❛❞♦ ♠❡t❛ ❡st✐✈❡r ❡♠ ✉♠❛ ♣r♦❢✉♥❞✐❞❛❞❡ ✜♥✐t❛ ❞✳
✕ ◗✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦✿ é ót✐♠❛ s❡ ♦s ❝✉st♦s ❞❛s tr❛♥s✐çõ❡s ❡♥tr❡ ♦s ❡st❛❞♦s sã♦ t♦❞♦s ✐❣✉❛✐s✳
✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✿ ❝♦♥s✐❞❡r❛♥❞♦ q✉❡ ❛ ❝❛❞❛ ♥í✈❡❧ ❞❛ ár✈♦r❡ ❞❡ ❜✉s❝❛✱ ✉♠ ❡st❛❞♦ ❣❡r❡ ❜ s✉❝❡ss♦r❡s ✭❢❛t♦r ❞❡ r❛♠✐✜❝❛çã♦✮✱ t❡♠✲s❡ ✉♠❛ s❡q✉ê♥❝✐❛ ❞❡ ❝✉st♦s ♥♦s ♥í✈❡✐s ❞❡✿ b+b2 +b3 +...+bd = O(bd)✱ ♦♥❞❡ ❞ é ♦ ♥í✈❡❧ ♦♥❞❡ s❡ ❡♥❝♦♥tr❛ ❛ ♠❡t❛ ❡ ♦ ❛❧❣♦r✐t♠♦ ♣❛r❛✳ ■ss♦ s❡ ❞❡✈❡ ❛♦ ❢❛t♦ ❞❡ q✉❡ ✉♠ ❡st❛❞♦ é ❛✈❛❧✐❛❞♦ s❡ é ♠❡t❛ ♦✉ ♥ã♦ ❛♣ós s✉❛ ❣❡r❛çã♦✱ ♦✉ s❡❥❛✱ ❛ ❝❛❞❛ s✉❝❡ss♦r ❣❡r❛❞♦ ❞✉r❛♥t❡ ❛ ❡①♣❛♥sã♦ é ❢❡✐t♦ ✉♠ t❡st❡ ❞❡ ♠❡t❛ s♦❜r❡ ❡❧❡✱ ❝♦♠ ✐ss♦ ❛ ❜✉s❝❛ s❡♠♣r❡ é ✐♥t❡rr♦♠♣✐❞❛ ♥♦ ♥í✈❡❧ ❡♠ q✉❡ ❛ ♠❡t❛ é ❡♥❝♦♥tr❛❞❛✳
✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦✿ ❞❛ ♠❡s♠❛ ❢♦r♠❛ q✉❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✱ t❛♠❜é♠ s❡ ❣❛st❛O(bd) ♣❛r❛ s❡ ❛r♠❛③❡♥❛r ♦s ❡st❛❞♦s ❣❡r❛❞♦s ❞✉r❛♥t❡ ❛ ❜✉s❝❛✳
• ❇✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡✿ ♦s ❡st❛❞♦s ❡①♣❛♥❞✐❞♦s ♥❡ss❛ ❡str❛té❣✐❛ sã♦ ❛r♠❛③❡♥❛❞♦s ❡♠
✷✳✶✳ ❇✉s❝❛ ✷✾
✕ ❈♦♠♣❧❡t✉❞❡✿ ❛ ✈❡rsã♦ ❞❛ ❜✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ❡♠ ❣r❛❢♦s é ❝♦♠♣❧❡t❛✱ s❡♥❞♦ ♦ ❡s♣❛ç♦ ❞❡ ❡st❛❞♦s ✜♥✐t♦✱ ❥á q✉❡ ❡❧❛ ❡✈✐t❛ ❡st❛❞♦s r❡♣❡t✐❞♦s ❡ ❝❛♠✐♥❤♦s r❡❞✉♥✲ ❞❛♥t❡s✱ ♣♦✐s ❡✈❡♥t✉❛❧♠❡♥t❡ t♦❞♦s ♦s ❡st❛❞♦s ♣♦❞❡♠ s❡r ❡①♣❛♥❞✐❞♦s✳ ▼❛s ❡ss❛ ❜✉s❝❛ ❡♠ ár✈♦r❡ ♥ã♦ é ❝♦♠♣❧❡t❛✱ ❞❡✈✐❞♦ ❛ ♣♦ssí✈❡❧ ♦❝♦rrê♥❝✐❛ ❞❡ ❝✐❝❧♦s✱ q✉❡ ❛té ♣♦❞❡♠ s❡r ❡✈✐t❛❞♦s ❝♦♠ ✉s♦ ❞❡ ♠❡♠ór✐❛ ♣❛r❛ ♦ ❛❧❣♦r✐t♠♦✱ ♠❛s q✉❡ ♥ã♦ ✐♠♣❡❞❡ ♦ ❛♣❛r❡❝✐♠❡♥t♦ ❞❡ ❝❛♠✐♥❤♦s r❡❞✉♥❞❛♥t❡s✳
✕ ◗✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦✿ ♠❡s♠♦ q✉❡ ❛ ❜✉s❝❛ s❡❥❛ ❝♦♠♣❧❡t❛✱ ❡❧❛ ♣♦❞❡ s❡r ♦❜r✐❣❛❞❛ ❛ ❞❡s❝❡r ♣♦r r❛♠♦s ♠❛✐s ♣r♦❢✉♥❞♦s à ❡sq✉❡r❞❛✱ ❛♥t❡s ❞❡ ❡♥❝♦♥tr❛r ❛ ♠❡t❛ ❡♠ ✉♠ r❛♠♦ ♠❛✐s ❛ ❞✐r❡✐t❛✱ ❞❡ss❛ ❢♦r♠❛ ❛♠❜❛s ❛s ✈❡rsõ❡s ♥ã♦ ♣♦❞❡♠ s❡r ót✐♠❛s✳ ✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✿ ❝♦♥s✐❞❡r❛♥❞♦ ❛ s✐t✉❛çã♦ ❛❝✐♠❛✱ ❛ ❜✉s❝❛ t❡rá ♥♦ ♠á✲ ①✐♠♦ O(bm) ❞❡ t❡♠♣♦✱ s❡♥❞♦ q✉❡ m é ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ♠á①✐♠❛ ❞❛ ár✈♦r❡ ❞❡ ❜✉s❝❛✳
✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦✿ ❛♣ós ❛✈❛❧✐❛r t♦❞♦s ♦s ❡st❛❞♦s ❞❡ ✉♠ r❛♠♦ ❛ ❡sq✉❡r❞❛ ❡ ♥ã♦ ❡♥❝♦♥tr❛r ❛ s♦❧✉çã♦✱ ♦ ❛❧❣♦r✐t♠♦ ♣♦❞❡ ✐r ♣❛r❛ ✉♠ r❛♠♦ ❞❛ ❞✐r❡✐t❛ ❡ r❡t✐r❛r ♦s ❡st❛❞♦s ❞♦ ♦✉tr♦ r❛♠♦ ❞❛ ♠❡♠ór✐❛✱ ❥á q✉❡ ❡❧❡s ♥ã♦ s❡rã♦ ♠❛✐s ♥❡❝❡ssár✐♦s ♣❛r❛ ❛ ❜✉s❝❛✳ ▲♦❣♦ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ é O(b×m)✳
• ❇✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ❧✐♠✐t❛❞❛✿ ❛ ❢❛❧❤❛ ❞❛ ❜✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ❡♠ ❡s♣❛ç♦ ❞❡
❡st❛❞♦s ✐♥✜♥✐t♦✱ ♣♦❞❡ s❡r ❝♦♥t♦r♥❛❞❛ ✜①❛♥❞♦ ✉♠ ❧✐♠✐t❡ ❧ ♠á①✐♠♦ ❞❡ ♣r♦❢✉♥❞✐❞❛❞❡✳ ▼❛s ❡①✐st❡ ✉♠ ✐♥❝♦♥✈❡♥✐❡♥t❡ q✉❡ é q✉❛♥❞♦ ❛ ♠❡t❛ s❡ ❡♥❝♦♥tr❛ ❡♠ ♥í✈❡✐s ✐♥❢❡r✐♦r❡s ❛♦ ❧✐♠✐t❡ ❡st✐♣✉❧❛❞♦✱ ♦✉ s❡❥❛✱ d > l✳ ❆ ❜✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ❝♦♥✈❡♥❝✐♦♥❛❧ ♣♦❞❡
s❡r ✈✐st❛ ❝♦♠♦ ✉♠❛ ♣❛rt✐❝✉❧❛r✐❞❛❞❡ ❞❛ ❜✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ❧✐♠✐t❛❞❛ ♦♥❞❡ l=∞
❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳
✕ ❈♦♠♣❧❡t✉❞❡✿ ❞❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❛ ♠❡t❛ ♣♦❞❡r ❡st❛r ❡♠ ♥í✈❡✐s ✐♥❢❡r✐♦r❡s ❛♦ ❧✐♠✐t❡
l✱ ❛ ❜✉s❝❛ ♥ã♦ é ❝♦♥s✐❞❡r❛❞❛ ❝♦♠♣❧❡t❛✳
✕ ◗✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦✿ ♣♦r ❡❧❛ ♥ã♦ s❡r ❝♦♠♣❧❡t❛✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡ ❡❧❛ ♥ã♦ ♣♦❞❡ s❡r ót✐♠❛ t❛♠❜é♠✳
✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✿ ❝♦♠♦ l ❢✉♥❝✐♦♥❛ ❝♦♠♦ ♣r♦❢✉♥❞✐❞❛❞❡ ♠á①✐♠❛ ♣❛r❛ ❛
❜✉s❝❛✱ ♦ t❡♠♣♦ é ❞❡ O(bl)✳
✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦✿ ♣❡❧♦ ♠❡s♠♦ ♠♦t✐✈♦ q✉❡ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✱ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦ é ♥♦ ♠á①✐♠♦O(b×l)✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛s ♣♦❞❛s ❢❡✐t❛s
❡♠ r❛♠♦s ♠❛✐s ❛ ❡sq✉❡r❞❛✳
• ❇✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ✐t❡r❛t✐✈❛✿ ❢❛③ ✉♠ ✐♥❝r❡♠❡♥t♦ ❣r❛❞✉❛❧ ♥♦ ❧✐♠✐t❡ ❞❛ ♣r♦❢✉♥❞✐✲
❞❛❞❡ ❞❛ ❜✉s❝❛ ❛té q✉❡ ❛ s♦❧✉çã♦ s❡❥❛ ❡♥❝♦♥tr❛❞❛✱ q✉❡ ♦❝♦rr❡ q✉❛♥❞♦ ♦ ❧✐♠✐t❡ ❝❤❡❣❛ ❡♠ d✱ ♦✉ s❡❥❛✱ ♥♦ ♥í✈❡❧ ♦♥❞❡ s❡ ❡♥❝♦♥tr❛ ❛ ♠❡t❛✳ ❊❧❛ ❝♦♠❜✐♥❛ ♦s ❜❡♥❡❢í❝✐♦s ❞❛s
❜✉s❝❛s ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ❡ ❧❛r❣✉r❛ ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳
✸✵ ❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ❡ ❚r❛❜❛❧❤♦s ❈♦rr❡❧❛t♦s
✕ ◗✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦✿ é ót✐♠❛ s❡ ♦s ❝✉st♦s sã♦ ♥ã♦ ❞❡❝r❡s❝❡♥t❡s✳
✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✿ ❝♦♥s♦♠❡ O(bd) ❞❡ t❡♠♣♦ ❝♦♠♦ ❛ ❜✉s❝❛ ❡♠ ❧❛r❣✉r❛✳
✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦✿ ❝♦♥s♦♠❡ O(b ×d) ❝♦♠♦ ❛ ❜✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡
❝♦♥✈❡♥❝✐♦♥❛❧✱ s❡♥❞♦ q✉❡ d ♥❡st❡ ❝❛s♦ é s❡♠♣r❡ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ♠á①✐♠❛ ❞❛
❜✉s❝❛✳
• ❇✉s❝❛ ❜✐❞✐r❡❝✐♦♥❛❧✿ sã♦ ❢❡✐t❛s ❞✉❛s ❜✉s❝❛s s✐♠✉❧tâ♥❡❛s✱ ✉♠❛ ♣r♦❣r❡ss✐✈❛ ♣❛rt✐♥❞♦
❞♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ ❡ ♦✉tr❛ r❡❣r❡ss✐✈❛ ♣❛rt✐♥❞♦ ❞❛ ♠❡t❛✱ ❡ s❡ ❡s♣❡r❛ q✉❡ ❛s ❞✉❛s s❡ ❡♥❝♦♥tr❡♠ ♥♦ ✏♠❡✐♦✑✳ ❆ ♠♦t✐✈❛çã♦ ♣❛r❛ ✐ss♦ é q✉❡✱bd÷2 ❞❡ ❝❛❞❛ ❜✉s❝❛ é ♠❡❧❤♦r q✉❡ bd ❞❡ ✉♠❛ ❜✉s❝❛ ❝♦♠♣❧❡t❛ ❞❡ ✉♠ ❧❛❞♦ ❛♦ ♦✉tr♦✳ ❊❧❛ é ✐♠♣❧❡♠❡♥t❛❞❛ s✉❜st✐t✉✐♥❞♦
♦ t❡st❡ ❞❡ ♠❡t❛ ♣♦r ✉♠ t❡st❡ q✉❡ ✈❡r✐✜❝❛ q✉❛♥❞♦ ❛s ❢r♦♥t❡✐r❛s ❞❛s ❞✉❛s ❜✉s❝❛s s❡ ✐♥t❡r❝❡♣t❛♠✳ ❆ ❞✐✜❝✉❧❞❛❞❡ ❞❡ s❡ ✉s❛r ❡ss❛ ❜✉s❝❛ é q✉❡✱ ❞❡♣❡♥❞❡♥❞♦ ❞♦ ♣r♦❜❧❡♠❛✱ ❛ ♠❡t❛ ♥❡♠ s❡♠♣r❡ é ❜❡♠ ❝♦♥❤❡❝✐❞❛ ❡ ❝❧❛r❛✱ ❡ t❛❧✈❡③ ❛s tr❛♥s✐çõ❡s ♣❛r❛ ❡st❛❞♦s ♣r❡❞❡❝❡ss♦r❡s ♥❛ ❜✉s❝❛ r❡❣r❡ss✐✈❛ ♣♦❞❡♠ s❡r ❞✐❢í❝❡✐s ❞❡ s❡r❡♠ ❞❡t❡r♠✐♥❛❞❛s ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳
✕ ❈♦♠♣❧❡t✉❞❡✿ é ❝♦♠♣❧❡t❛ s❡ ♦ ❢❛t♦r ❞❡ r❛♠✐✜❝❛çã♦ é ✜♥✐t♦ ❡ ❛♠❜❛s ❛s ❞✐r❡çõ❡s ✉s❛♠ ❜✉s❝❛ ❡♠ ❧❛r❣✉r❛✳
✕ ◗✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦✿ é ót✐♠❛ s❡ ♦s ❝✉st♦s sã♦ ✐❣✉❛✐s ❡ ❛♠❜❛s ❛s ❞✐r❡çõ❡s ✉s❛♠ ❜✉s❝❛ ❡♠ ❧❛r❣✉r❛✳
✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✿ ❝♦♥s♦♠❡O(bd÷2)❞❡ t❡♠♣♦ ❝♦♠ ❛s ❜✉s❝❛s ❡♠ ❧❛r❣✉r❛✳ ✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦✿ ❛ss✐♠ ❝♦♠♦ ♥❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✱ ❝♦♥s♦♠❡✲s❡
O(bd÷2) ♣❛r❛ ❛s ❜✉s❝❛s ❡♠ ❧❛r❣✉r❛✳
• ❇✉s❝❛ ❞❡ ❝✉st♦ ✉♥✐❢♦r♠❡✿ ❡①♣❛♥❞❡ ♦ ❡st❛❞♦ ❝♦♠ ♠❡♥♦r ❝✉st♦ ❛té ♦ ♠♦♠❡♥t♦✱ ✐ss♦
é ❢❡✐t♦ ❛r♠❛③❡♥❛♥❞♦ ♦s ❡st❛❞♦s ❡♠ ✉♠❛ ✜❧❛ ❞❡ ♣r✐♦r✐❞❛❞❡ ♦r❞❡♥❛❞❛ ♣❡❧♦ ❝✉st♦ ❛❝✉♠✉❧❛❞♦ g(n) ♣❛r❛ s❡ ❝❤❡❣❛r ❡♠ ❝❛❞❛ ❡st❛❞♦✳ ❯♠ ❞♦s ♣r✐♠❡✐r♦s ❛❧❣♦r✐t♠♦s ❛
✉s❛r ❡ss❛ ❡str❛té❣✐❛ ❢♦✐ ♦ ❛❧❣♦r✐t♠♦ ❞❡ ❉✐❥❦str❛ ❬❉✐❥❦str❛ ✶✾✺✾❪ ❬❘✉ss❡❧❧ ❡ ◆♦r✈✐❣ ✷✵✵✾❪✳
✕ ❈♦♠♣❧❡t✉❞❡✿ é ❝♦♠♣❧❡t❛ s❡ ♦ ❢❛t♦r ❞❡ r❛♠✐✜❝❛çã♦ é ✜♥✐t♦ ❡ ♦s ❝✉st♦s≥ℓ✭s❡♥❞♦ ℓ ♣♦s✐t✐✈♦✮✳
✕ ◗✉❛❧✐❞❛❞❡ ❞❛ s♦❧✉çã♦✿ é ót✐♠❛✱ ♣♦✐s ❞✐❢❡r❡♥t❡♠❡♥t❡ ❞❛ ❜✉s❝❛ ❡♠ ❧❛r❣✉r❛✱ ❛ ❜✉s❝❛ ❞❡ ❝✉st♦ ✉♥✐❢♦r♠❡ ❢❛③ ♦❜r✐❣❛t♦r✐❛♠❡♥t❡ ♦ t❡st❡ ❞❡ ♠❡t❛ ❛♦ s❡❧❡❝✐♦♥❛r ✉♠ ❡st❛❞♦ ♣❛r❛ s❡r ❡①♣❛♥❞✐❞♦✱ ❡ ♥ã♦ ❞✉r❛♥t❡ s✉❛ ❝r✐❛çã♦✳ ■ss♦ ✐♠♣❡❞❡ q✉❡ ♦ ❛❧❣♦r✐t♠♦ ❡s❝♦❧❤❛ s♦❧✉çõ❡s s✉❜✲ót✐♠❛s✳
✷✳✶✳ ❇✉s❝❛ ✸✶
❝❛♠✐♥❤♦s ❞♦ q✉❡ ♦ ♥❡❝❡ssár✐♦✱ ♣♦✐s ❛ ❜✉s❝❛ é ❣✉✐❛❞❛ ♣❡❧♦s ❝✉st♦s ❞♦s ❡st❛❞♦s✱ ❡ ♥ã♦ ❡stá ❞✐r❡t❛♠❡♥t❡ ❧✐❣❛❞❛ ❛ ♣r♦❢✉♥❞✐❞❛❞❡ ♦♥❞❡ ❛ ♠❡t❛ s❡ ❡♥❝♦♥tr❛✳ ❙❡♥❞♦
C∗ ♦ ❝✉st♦ ♣❛r❛ s❡ ❝❤❡❣❛r ❛ s♦❧✉çã♦ ót✐♠❛✱ ❡ ❝❛❞❛ tr❛♥s✐çã♦ ♣❛r❛ s❡ ❝❤❡❣❛r ❛té ❛ ♠❡t❛ t❡♠ ✉♠ ❝✉st♦ ❞❡ ℓ✱ t❡♠✲s❡ ✉♠ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦ ✐❣✉❛❧ ❛ O(b1+⌊C∗÷ℓ⌋)✳
✕ ❈♦♠♣❧❡①✐❞❛❞❡ ❞❡ ❡s♣❛ç♦✿ ❛ss✐♠ ❝♦♠♦ ♥❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ t❡♠♣♦✱ ❝♦♥s♦♠❡✲s❡
O(b1+⌊C∗÷ℓ⌋) ❞❡ ❡s♣❛ç♦✳
✷✳✶✳✷ ❇✉s❝❛ ❍❡✉ríst✐❝❛
❆ ❜✉s❝❛ ❤❡✉ríst✐❝❛✱ ♦✉ ❜✉s❝❛ ✐♥❢♦r♠❛❞❛✱ ✉t✐❧✐③❛ ✉♠ ❝♦♥❤❡❝✐♠❡♥t♦ ❡s♣❡❝í✜❝♦ ❞♦ ♣r♦✲ ❜❧❡♠❛ ♥❛ ❡s❝♦❧❤❛ ❞♦ ♣ró①✐♠♦ ❡st❛❞♦ ❛ s❡r ❡①♣❛♥❞✐❞♦✳ ❊ss❡ ❝♦♥❤❡❝✐♠❡♥t♦ ♣♦❞❡ s❡r r❡✲ ♣r❡s❡♥t❛❞♦ ♣♦r ✉♠❛ ❢✉♥çã♦ ❤❡✉ríst✐❝❛ q✉❡ ❡st✐♠❛ ♦ ❝✉st♦ ❞❡ s❡ ❝❤❡❣❛r ❛♦ ❡st❛❞♦ ♠❡t❛ ❛ ♣❛rt✐r ❞❡ ✉♠ ❡st❛❞♦ q✉❛❧q✉❡r✳ ❊ss❛ ❡st✐♠❛t✐✈❛ ♣♦❞❡ s❡r ♦❜t✐❞❛ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ✈❡rsã♦ r❡❧❛①❛❞❛ ❞♦ ♣r♦❜❧❡♠❛✱ ♦✉ s❡❥❛✱ ✉♠❛ s♦❧✉çã♦ q✉❡ ❝♦♥té♠ ♠❡♥♦s r❡str✐çõ❡s ❞♦ q✉❡ ✉♠❛ s♦❧✉çã♦ ✐❞❡❛❧✳ ❯♠❛ ❤❡✉ríst✐❝❛ h(s) s❡r✈❡ ♣❛r❛ ❡st✐♠❛r ❛ ❞✐stâ♥❝✐❛ ❞❡ ✉♠ ❡st❛❞♦ s ❛té ❛
♠❡t❛✱ ♦♥❞❡ ❛❧❣♦r✐t♠♦s ❞❡ ❜✉s❝❛ ♣r✐♦r✐③❛♠ ♣♦r ❡①♣❛♥❞✐r ❡st❛❞♦s q✉❡ t❡♠ ♠❡♥♦r ✈❛❧♦r ❞❡
h✱ ♦✉ s❡❥❛✱ ❡st❛❞♦s q✉❡ ❛❝r❡❞✐t❛✲s❡ ❡st❛r❡♠ ♠❛✐s ♣ró①✐♠♦s à ♠❡t❛ ♣❛r❛ q✉❡ ❛ ❜✉s❝❛ s❡❥❛
❡①❡❝✉t❛❞❛ ♦ ♠❛✐s rá♣✐❞♦ ♣♦ssí✈❡❧✳
❋✐❣✉r❛ ✷✳✶✿ ❍❡✉ríst✐❝❛ ❝♦♠♦ ❡st✐♠❛t✐✈❛ ❞❛ ❞✐stâ♥❝✐❛ ❛té ❛ ♠❡t❛
✸✷ ❈❛♣ít✉❧♦ ✷✳ ❋✉♥❞❛♠❡♥t♦s ❚❡ór✐❝♦s ❡ ❚r❛❜❛❧❤♦s ❈♦rr❡❧❛t♦s
❡ss❡ ♣r♦❝❡ss♦ ❛té q✉❡ ♥❡♥❤✉♠❛ ♠❡❧❤♦r✐❛ s❡❥❛ ❡♥❝♦♥tr❛❞❛✳ ❖ ❍❈ ❢r❡q✉❡♥t❡♠❡♥t❡ ♣r♦❞✉③ ♠❡❧❤♦r❡s r❡s✉❧t❛❞♦s ❞♦ q✉❡ ♦✉tr♦s ❛❧❣♦r✐t♠♦s q✉❛♥❞♦ s❡ t❡♠ ✉♠ t❡♠♣♦ r❡str✐t♦ ♣❛r❛ s❡ ❡①❡❝✉t❛r ❛ ❜✉s❝❛✱ ❝♦♠♦ ♥♦ ❝❛s♦ ❞❡ s✐st❡♠❛s ❞❡ t❡♠♣♦ r❡❛❧✳ ❊st❡ ♠ét♦❞♦ é ❜♦♠ ♣❛r❛ ❡♥✲ ❝♦♥tr❛r ót✐♠♦s ❧♦❝❛✐s✱ ♠❛s ♥ã♦ s❡ t❡♠ ❣❛r❛♥t✐❛s ❞❡ s❡ ❡♥❝♦♥tr❛r ❛ ♠❡❧❤♦r s♦❧✉çã♦ ❞❡♥tr❡ t♦❞❛s ❛s ♣♦ssí✈❡✐s s♦❧✉çõ❡s ♣❛r❛ ♦ ♣r♦❜❧❡♠❛✳ ❊st❡ ❛❧❣♦r✐t♠♦ ♥ã♦ é ❝♦♠♣❧❡t♦✱ ♣♦✐s ❡❧❡ ♣❛r❛ q✉❛♥❞♦ ♥❡♥❤✉♠ s✉❝❡ss♦r ❞♦ ❡st❛❞♦ ❝♦rr❡♥t❡ t❡♠ ✈❛❧♦r ❤❡✉ríst✐❝♦ ♠❡❧❤♦r ❞♦ q✉❡ ♦ s❡✉✱ ♦✉ s❡❥❛✱ ❛♦ ❡♥tr❛r ❡♠ ✉♠ ♠á①✐♠♦✴♠í♥✐♠♦ ❧♦❝❛❧✳
❉✉r❛♥t❡ ❛ ❢❛s❡ ❞❡ ❡①♣❛♥sã♦ ❞♦ ❍❈ ♣❛❞rã♦✱ ♦ ♣r✐♠❡✐r♦ s✉❝❡ss♦r✱ ❝✉❥♦ ✈❛❧♦r ❤❡✉ríst✐❝♦ é ♠❡❧❤♦r ❞♦ q✉❡ ♦ ❞♦ ❡st❛❞♦ ❝♦rr❡♥t❡✱ é ❡s❝♦❧❤✐❞♦ ♣❛r❛ ❝♦♥t✐♥✉❛r ❛ ❜✉s❝❛✳ ❆♦ ✐♥✈és ❞✐ss♦✱ ❡♠ ✉♠❛ ❛❞❛♣t❛çã♦ ❞♦ ❍❈ ❝♦♥❤❡❝✐❞♦ ❝♦♠♦ ❙t❡❡♣❡st ❆s❝❡♥t ❍✐❧❧ ❈❧✐♠❜✐♥❣ ❬❈♦♣♣✐♥ ✷✵✵✹❪✱ t♦❞♦s ♦s s✉❝❡ss♦r❡s sã♦ ❛✈❛❧✐❛❞♦s✱ ❡ só ❞❡♣♦✐s ♦ ♠❡❧❤♦r ❞❡❧❡s é ❡s❝♦❧❤✐❞♦✳ ❊st❡ ♠ét♦❞♦ ❢✉♥❝✐♦♥❛ ❝♦♠♦ ✉♠❛ ❜✉s❝❛ ❡♠ ♣r♦❢✉♥❞✐❞❛❞❡ ♦r❞❡♥❛❞❛ ♣❡❧❛ ❤❡✉ríst✐❝❛✳ ▼❡s♠♦ ❝♦♠ ❡ss❛ ♠♦❞✐✜❝❛çã♦✱ ♦ ❛❧❣♦r✐t♠♦ ❛✐♥❞❛ ♣♦❞❡ ❡♥tr❛r ❡♠ ✉♠ ♠á①✐♠♦✴♠í♥✐♠♦ ❧♦❝❛❧ ♦♥❞❡ ❛ s♦❧✉çã♦ ❞❡s❡❥❛❞❛ ♣♦❞❡ ♥ã♦ s❡r ❡♥❝♦♥tr❛❞❛✱ s❡♥❞♦ ❛ss✐♠ ♥ã♦ ❝♦♠♣❧❡t♦✳
❯♠❛ ❢♦r♠❛ ❞❡ r❡s♦❧✈❡r ♦ ♣r♦❜❧❡♠❛ ❞❡ ♠á①✐♠♦s✴♠í♥✐♠♦s ❧♦❝❛✐s é ❛ s✉❝❡ss✐✈❛ ❡①♣❧♦r❛çã♦ ❞♦ ❡s♣❛ç♦ ❞❡ ❡st❛❞♦s✱ ❛ss✐♠ ❝♦♠♦ é ❢❡✐t♦ ♥♦ ❘❛♥❞♦♠✲❘❡st❛rt ❍✐❧❧ ❈❧✐♠❜✐♥❣✳ ❊❧❡ ❡①❡❝✉t❛ ✉♠❛ sér✐❡ ❞❡ ❜✉s❝❛s ❝♦♠ ♦ ❍❈✱ ♦♥❞❡ ♦s ❡st❛❞♦s ✐♥✐❝✐❛✐s sã♦ ❣❡r❛❞♦s ❛❧❡❛t♦r✐❛♠❡♥t❡ q✉❛♥❞♦ ❛ ❜✉s❝❛ ❡♥tr❛ ❡♠ ♠á①✐♠♦s✴♠í♥✐♠♦s ❧♦❝❛✐s✳
❏á ♦ ❊♥❢♦r❝❡❞ ❍✐❧❧ ❈❧✐♠❜✐♥❣ ✭❊❍❈✮✱ é ✉♠ ♠ét♦❞♦ ❣✉✐❛❞♦ ♣♦r ❤❡✉ríst✐❝❛ q✉❡ ❝♦♠❜✐♥❛ ♦s ❛❧❣♦r✐t♠♦s ❍❈ ❝♦♠ ❜✉s❝❛ ❡♠ ❧❛r❣✉r❛ ❛ ✜♠ ❡s❝❛♣❛r ❞❡ ♠á①✐♠♦s✴♠í♥✐♠♦s ❧♦❝❛✐s✳ ❊❧❡ ❢♦✐ ✐♥tr♦❞✉③✐❞♦ ♣❡❧♦ ♣❧❛♥❡❥❛❞♦r ❋❛st ❋♦r✇❛r❞ ✭❋❋✮ ❬❍♦✛♠❛♥♥ ❡ ◆❡❜❡❧ ✷✵✵✶❪ ❝♦♠♦ ♣❛rt❡ ❞❡ s✉❛ ❡str❛té❣✐❛ ❞❡ ❜✉s❝❛✱ ❡ é ✉♠ ❛❧❣♦r✐t♠♦ ♠✉✐t♦ ✉s❛❞♦ ♥♦s ♣❧❛♥❡❥❛❞♦r❡s ❛t✉❛✐s ♣♦r s❡r ❡①tr❡♠❛♠❡♥t❡ á❣✐❧ ❡ t❡♥t❛r r❡s♦❧✈❡r ♣r♦❜❧❡♠❛s ♦ ♠❛✐s rá♣✐❞♦ ♣♦ssí✈❡❧✳ ❆♣❡s❛r ❞❡ ❝♦♥s❡✲ ❣✉✐r ❡s❝❛♣❛r ❞❡ ♠á①✐♠♦s✴♠í♥✐♠♦s ❧♦❝❛✐s ❝♦♠ ❢r❡q✉ê♥❝✐❛✱ ❡❧❡ ❛✐♥❞❛ ♣♦❞❡ ♥ã♦ ❡♥❝♦♥tr❛r ❛ s♦❧✉çã♦ ❞❡♣❡♥❞❡♥❞♦ ❞♦ ❝❛♠✐♥❤♦ q✉❡ ❛ ❜✉s❝❛ ♣r♦ss❡❣✉✐✉✱ ✜❝❛♥❞♦ ♣r❡s♦ ❡♠ ✉♠ ✏❜❡❝♦ s❡♠ s❛í❞❛✑ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ❡❧❡ ❢❛❧❤❡✳ ❉❡✈✐❞♦ ❛♦ ❢❛t♦ ❞❡❧❡ ❢❛③❡r ♣❛rt❡ ❞♦ ♣❧❛♥❡❥❛❞♦r ❞❡s❡♥✲ ✈♦❧✈✐❞♦ ♥❡st❡ tr❛❜❛❧❤♦✱ ♣♦ré♠ ❝♦♠ ❛❧❣✉♠❛s ♦t✐♠✐③❛çõ❡s✱ ♦ ❊❍❈ é ❞❡s❝r✐t♦ ❞❡ ❢♦r♠❛ ♠❛✐s ❞❡t❛❧❤❛❞❛ ❛ s❡❣✉✐r✱ ❥✉♥t❛♠❡♥t❡ ❝♦♠ s❡✉ ♣s❡✉❞♦✲❝ó❞✐❣♦ ✭❆❧❣♦r✐t♠♦ ✶✮✳
❖ ❛❧❣♦r✐t♠♦ ✉s❛ ❞✉❛s ❧✐st❛s✿ aberta ❡ f echada✳ ❚♦❞♦s ♦s ❡st❛❞♦s q✉❡ s❡rã♦ ❛✈❛❧✐❛❞♦s
sã♦ ❛r♠❛③❡♥❛❞♦s ♥❛ ❧✐st❛aberta✳ ❖s ❡st❛❞♦s ❥á ❛✈❛❧✐❛❞♦s sã♦ ♠❛♥t✐❞♦s ♥❛ ❧✐st❛ f echada✳
❖ ❊❍❈ ✐♥✐❝✐❛ ✐♥st❛♥❝✐❛♥❞♦ ♦ scorrente ✭❡st❛❞♦ ❝♦rr❡♥t❡✮ ❝♦♠♦ s❡♥❞♦ ♦ ❡st❛❞♦ ✐♥✐❝✐❛❧ ✭❧✐♥❤❛ ✶✮✱ ❡ ✈❡r✐✜❝❛ s❡ scorrente é ❛ ♠❡t❛ ✭❧✐♥❤❛s ✷✲✹✮✳ ❆ ✈❛r✐á✈❡❧ melhorV alor s❡♠♣r❡ ❣✉❛r❞❛ ♦ ♠❡❧❤♦r ✈❛❧♦r ❤❡✉ríst✐❝♦ ❡♥❝♦♥tr❛❞♦ ❞✉r❛♥t❡ ❛ ❜✉s❝❛✱ ❡ é ✐♥✐❝✐❛❧✐③❛❞❛ ❝♦♠ ♦ ✈❛❧♦r ❞♦ ❡st❛❞♦ ❝♦rr❡♥t❡ h(scorrente) ❛✐♥❞❛ ♥♦ ✐♥í❝✐♦ ❞♦ ❛❧❣♦r✐t♠♦ ✭❧✐♥❤❛ ✺✮✳ ❉❡♣♦✐s✱ ♦ ❡st❛❞♦
scorrente é ✐♥s❡r✐❞♦ ❡♠ ❛♠❜❛s ❛s ❧✐st❛s✱ aberta ✭❧✐♥❤❛ ✻✮ ❡f echada ✭❧✐♥❤❛ ✼✮✳
❖ ❧❛ç♦ ♣r✐♥❝✐♣❛❧ ✭❧✐♥❤❛s ✽✲✷✼✮ ✈❛rr❡ t♦❞♦s ♦s ❡st❛❞♦s ♥❛ ❧✐st❛ aberta✳ ❙❡ ❡st❛ ❧✐st❛ s❡
✷✳✶✳ ❇✉s❝❛ ✸✸
❆❧❣♦r✐t♠♦ ✶ ❊❍❈✭sinicial, smeta✮ ✶✿ scorrente←sinicial
✷✿ s❡scorrente=smeta❡♥tã♦ ✸✿ r❡t♦r♥❛ s✉❝❡ss♦ ✹✿ ✜♠ s❡
✺✿ melhorV alor←h(scorrente) ✻✿ f echada.insere(scorrente) ✼✿ aberta.insere(scorrente) ✽✿ ❡♥q✉❛♥t♦aberta6=vazia❢❛ç❛ ✾✿ scorrente←aberta.remove() ✶✵✿ ❡♥q✉❛♥t♦s′∈suc(s
corrente)❢❛ç❛ ✶✶✿ s❡s′
/
∈f echada❡♥tã♦ ✶✷✿ f echada.insere(s′
) ✶✸✿ s❡s′
=smeta ❡♥tã♦ ✶✹✿ r❡t♦r♥❛ s✉❝❡ss♦ ✶✺✿ s❡♥ã♦
✶✻✿ s❡h(s′
)< melhorV alor❡♥tã♦ ✶✼✿ melhorV alor←h(s′
) ✶✽✿ aberta← {}
✶✾✿ aberta.insere(s′)
✷✵✿ ♣❛r❛ ❧❛ç♦✱ ✐♥t❡rr♦♠♣❡ ❛ ❡①♣❛♥sã♦
✷✶✿ s❡♥ã♦
✷✷✿ aberta.insere(s′
)
✷✸✿ ✜♠ s❡
✷✹✿ ✜♠ s❡ ✷✺✿ ✜♠ s❡ ✷✻✿ ✜♠ ❡♥q✉❛♥t♦ ✷✼✿ ✜♠ ❡♥q✉❛♥t♦ ✷✽✿ r❡t♦r♥❛ ❢❛❧❤❛
■♥t❡r♥❛♠❡♥t❡ é ❢❡✐t❛ ❛ ❡①♣❛♥sã♦ ❞♦ ❡st❛❞♦ ❝♦rr❡♥t❡scorrente✭❧✐♥❤❛s ✶✵✲✷✻✮✱ q✉❡ é ♦❜t✐❞♦ r❡♠♦✈❡♥❞♦ ♦ ♣r✐♠❡✐r♦ ❡st❛❞♦ ❞❛ ❧✐st❛ aberta✭❧✐♥❤❛ ✾✮✳ ❉✉r❛♥t❡ ❡ss❛ ❡①♣❛♥sã♦ sã♦ ❝♦♥s✐✲
❞❡r❛❞♦s ❛♣❡♥❛s ❡st❛❞♦s q✉❡ ♥ã♦ ❢♦r❛♠ ✈✐s✐t❛❞♦s ✭❧✐♥❤❛ ✶✶✮✳ ❊♥tã♦✱ ♣❛r❛ ❝❛❞❛ s✉❝❡ss♦rs′
♦❜t✐❞♦✱ ❡❧❡ é ✐♥s❡r✐❞♦ ♥❛ ❧✐st❛f echada ✭❧✐♥❤❛ ✶✷✮✱ ❡ ✉♠ t❡st❡ é ❡①❡❝✉t❛❞♦ ♣❛r❛ ✈❡r✐✜❝❛r s❡
❡❧❡ ♥ã♦ é ❛ ♠❡t❛ ✭❧✐♥❤❛s ✶✸✲✶✺✮✳
❆♣ós ✐ss♦✱ ❛✐♥❞❛ ❞❡♥tr♦ ❞❛ ❡①♣❛♥sã♦✱ é ✈❡r✐✜❝❛❞♦ s❡ ♦ ✈❛❧♦r ❤❡✉ríst✐❝♦ ❞♦ s✉❝❡ss♦r é ♠❡♥♦r ❞♦ q✉❡ ♦ ♠❡❧❤♦r ✈❛❧♦r ❤❡✉ríst✐❝♦ ❡♥❝♦♥tr❛❞♦ ❛té ♦ ♠♦♠❡♥t♦ ✭melhorV alor✮ ✭❧✐♥❤❛
✶✻✮✳ ❙❡ ❢♦r ♠❡♥♦r✱ melhorV alor s❡rá ❛t✉❛❧✐③❛❞♦ ❝♦♠ ❡ss❡ ♥♦✈♦ ✈❛❧♦r ✭❧✐♥❤❛ ✶✼✮✱ ❛ ❧✐st❛ abertaé ❡s✈❛③✐❛❞❛✱ ❡ s♦♠❡♥t❡ ♦ s✉❝❡ss♦r s❡❧❡❝✐♦♥❛❞♦ s❡rá ♠❛♥t✐❞♦ ♣❛r❛ q✉❡ ❡❧❡ ♣♦ss❛ s❡r
❡s❝♦❧❤✐❞♦ ❝♦♠♦ ❡st❛❞♦ ❝♦rr❡♥t❡ ♥❛ ♣ró①✐♠❛ ✐t❡r❛çã♦ ✭❧✐♥❤❛s ✶✽✲✶✾✮✳ ❊♥tã♦ ❛ ❡①♣❛♥sã♦ ♣❛r❛ ✭❧✐♥❤❛ ✷✵✮✱ ❡❝♦♥♦♠✐③❛♥❞♦ t❡♠♣♦✱ s❡♥❞♦ q✉❡ ♦s ♣ró①✐♠♦s s✉❝❡ss♦r❡s t❡r✐❛♠ ✈❛❧♦r❡s ❤❡✉ríst✐❝♦s s✐♠✐❧❛r❡s ❛♦s ❡♥❝♦♥tr❛❞♦s ❛té ♦ ♠♦♠❡♥t♦✳
P♦ré♠✱ s❡ ♦ ✈❛❧♦r ❤❡✉ríst✐❝♦ ❞❡ s′ ♥ã♦ é ♠❡♥♦r q✉❡ melhorV alor✱ s′ s❡rá ♠❛♥t✐❞♦ ♥❛
❧✐st❛ f echada ✭❧✐♥❤❛ ✷✷✮✳ ❊♥tã♦✱ q✉❛♥❞♦ ❛ ❜✉s❝❛ ❡♥tr❛r ❡♠ ✉♠ ♠á①✐♠♦✴♠í♥✐♠♦ ❧♦❝❛❧✱
♦♥❞❡ ♦s ✈❛❧♦r❡s ❤❡✉ríst✐❝♦s ❞♦s ❡st❛❞♦s ❣❡r❛❞♦s ♣❛r❛♠ ❞❡ ❞❡❝r❡s❝❡r✱ ♦ ❛❧❣♦r✐t♠♦ ❡①❡❝✉t❛ ✉♠❛ ❜✉s❝❛ ❡♠ ❧❛r❣✉r❛ ❛ ♣❛rt✐r ❞♦s ❡st❛❞♦s ❞❛ ❧✐st❛ f echada✳ ❉❡st❛ ❢♦r♠❛✱ ❡❧❡ ❝♦♥t✐♥✉❛
r❡❛❧✐③❛♥❞♦ ❛ ❜✉s❝❛ ❛té q✉❡ ❡❧❡ ❡♥❝♦♥tr❡ ❛ ♠❡t❛ ♦✉ ✉♠ ❡st❛❞♦ q✉❡ t❡♥❤❛ ✈❛❧♦r ❤❡✉ríst✐❝♦ ♠❡♥♦r q✉❡ melhorV alor✱ ♦ q✉❡ ❢❛③ ❝♦♠ q✉❡ ❡❧❡ ❡s❝❛♣❡ ❞♦ ♠á①✐♠♦✴♠í♥✐♠♦ ❧♦❝❛❧ ❡ ✈♦❧t❡
❛ s✉❛ ❡①❡❝✉çã♦ ♥♦r♠❛❧✳
