❘❖❚❊❆▼❊◆❚❖ ❇❆❙❊❆❉❖ ❊▼ ❈❊◆❚❘❆▲■❉❆❉❊
P❆❘❆
❊❉❯❆❘❉❖ ▼❯❈❊▲▲■ ❘❊❩❊◆❉❊ ❖▲■❱❊■❘❆
❘❖❚❊❆▼❊◆❚❖ ❇❆❙❊❆❉❖ ❊▼ ❈❊◆❚❘❆▲■❉❆❉❊
P❆❘❆
❘❊❉❊❙ ❉❊ ❙❊◆❙❖❘❊❙ ❙❊▼ ❋■❖
❉✐ss❡rt❛çã♦ ❛♣r❡s❡♥t❛❞❛ ❛♦ Pr♦❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❞❛ ❯♥✐✈❡r✲ s✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s ❝♦♠♦ r❡✲ q✉✐s✐t♦ ♣❛r❝✐❛❧ ♣❛r❛ ❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❈✐ê♥❝✐❛ ❞❛ ❈♦♠♣✉t❛çã♦✳
❖r✐❡♥t❛❞♦r✿ ❆♥tô♥✐♦ ❆❧❢r❡❞♦ ❋❡rr❡✐r❛ ▲♦✉r❡✐r♦
❈♦♦r✐❡♥t❛❞♦r✿ ❍❡✐t♦r ❙♦❛r❡s ❘❛♠♦s ❋✐❧❤♦
❝
✷✵✶✶✱ ❊❞✉❛r❞♦ ▼✉❝❡❧❧✐ ❘❡③❡♥❞❡ ❖❧✐✈❡✐r❛✳ ❚♦❞♦s ♦s ❞✐r❡✐t♦s r❡s❡r✈❛❞♦s✳
❖❧✐✈❡✐r❛✱ ❊❞✉❛r❞♦ ▼✉❝❡❧❧✐ ❘❡③❡♥❞❡
❖✹✽r ❘♦t❡❛♠❡♥t♦ ❇❛s❡❛❞♦ ❡♠ ❈❡♥tr❛❧✐❞❛❞❡ ♣❛r❛ ❘❡❞❡s ❞❡ ❙❡♥s♦r❡s s❡♠ ❋✐♦ ✴ ❊❞✉❛r❞♦ ▼✉❝❡❧❧✐ ❘❡③❡♥❞❡ ❖❧✐✈❡✐r❛✳ ✖ ❇❡❧♦ ❍♦r✐③♦♥t❡✱ ✷✵✶✶✳
①①✱ ✺✽ ❢✳ ✿ ✐❧✳ ❀ ✷✾❝♠
❉✐ss❡rt❛çã♦ ✭♠❡str❛❞♦✮ ✖ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ▼✐♥❛s ●❡r❛✐s
❖r✐❡♥t❛❞♦r✿ ❆♥tô♥✐♦ ❆❧❢r❡❞♦ ❋❡rr❡✐r❛ ▲♦✉r❡✐r♦ ❈♦♦r✐❡♥t❛❞♦r✿ ❍❡✐t♦r ❙♦❛r❡s ❘❛♠♦s ❋✐❧❤♦
✶✳ ❈♦♠♣✉t❛çã♦ ✲ ❚❡s❡s✳ ✷✳ ❘❡❞❡s ❞❡ s❡♥s♦r❡s s❡♠ ✜♦ ✲ ❚❡s❡s✳ ✸✳ ▼❡❞✐❞❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡✳ ✹✳ ❘♦t❡❛♠❡♥t♦✳ ■✳ ❖r✐❡♥t❛❞♦r✳ ■■✳ ❈♦♦r✐❡♥t❛❞♦r✳ ■■■✳ ❚ít✉❧♦✳
❆❣r❛❞❡❝✐♠❡♥t♦s
❙ó t❡♥❤♦ ❛ ❛❣r❛❞❡❝❡r✳
❆❧❧ t❤❛t ■ ❛♠✱ ♦r ❤♦♣❡ t♦ ❜❡✱ ■ ♦✇❡ t♦ ♠② ❛♥❣❡❧ ♠♦t❤❡r
❆❜r❛❤❛♠ ▲✐♥❝♦❧♥
❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ♠ã❡ ♣♦r t✉❞♦ ❡ ♣♦r s❡r ❛ ♣❡ss♦❛ ♠❛✐s ✐♠♣♦rt❛♥t❡ ♥❛ ♠✐♥❤❛ ✈✐❞❛✳
❆ ❤❛♣♣② ❢❛♠✐❧② ✐s ❜✉t ❛♥ ❡❛r❧✐❡r ❤❡❛✈❡♥✳
●❡♦r❣❡ ❇❡r♥❛r❞ ❙❤❛✇
➚ ♠✐♥❤❛ ❢❛♠í❧✐❛ ♣♦r t❡r ❞❛❞♦ ♦ ❛♣♦✐♦ ❢✉♥❞❛♠❡♥t❛❧ ❡ ♥❡❝❡ssár✐♦ ♣❛r❛ q✉❡ ❤♦❥❡ ❡✉ ♣♦ss❛ ❝♦♥❝❧✉✐r ❡st❡ tr❛❜❛❧❤♦✳ ❆❣r❛❞❡ç♦ ❛ ♠✐♥❤❛ ✐r♠ã ♣❡❧♦s ♠♦♠❡♥t♦s ❞✐✈❡rt✐❞♦s q✉❡ ♣❛ss❛♠♦s ❥✉♥t♦s✱ ✈❛❧❡✉✱ ■s❛❜❡❧❡ ✧❇✐❜✐❧③✧ ▼✉❝❡❧❧✐ ❘✳ ❞❡ ❖❧✐✈❡✐r❛✳ ❆♦ ♠❡✉ ♣❛✐✱ ♣♦r s❡♠♣r❡ ♠❡ ♠♦t✐✈❛r ❝♦♠ s✉❛ s❛❜❡❞♦r✐❛ ❡ ❥♦✈✐❛❧✐❞❛❞❡✱ ✈❛❧❡✉✱ ❏♦sé ✧●♦r❞♦♥✧ ❞❡ ❖❧✐✈❡✐r❛✳
❚r✉❧② ❣r❡❛t ❢r✐❡♥❞s ❛r❡ ❤❛r❞ t♦ ✜♥❞✱ ❞✐✣❝✉❧t t♦ ❧❡❛✈❡✱ ❛♥❞ ✐♠♣♦ss✐❜❧❡ t♦ ❢♦r❣❡t✳
●✳ ❘❛♥❞♦❧❢
▲❛❜♦r❛tór✐♦ ✸✵✷✼✱ ♠✐♥❤❛ s❡❣✉♥❞❛ ❝❛s❛✱ ♦✉ ❛s ✈❡③❡s ❛té ❛ ♣r✐♠❡✐r❛✱ ❧✉❣❛r ❞❡ ❣r❛♥✲ ❞❡s ❛♠✐❣♦s✱ ❞❡ ♠✉✐t♦s ♠♦♠❡♥t♦s ♠❡♠♦rá✈❡✐s✳ ❆♥tô♥✐♦ ✧▲♦✉r❡✐r♦✧ ❆❧❢r❡❞♦ ❋❡rr❡✐r❛ ▲♦✉r❡✐r♦✱ ❉❛♥✐❡❧ ✧●✉✐❞♦♥✐✧ ●✉✐❞♦♥✐✱ ❊♠❛♥✉❡❧ ✧▼❛♥♦✧ ❱✐❛♥♥❛✱ ❋❡❧✐♣❡ ✧❇✐❣ ❍❡❛❞✧ ❉♦✲ ♠✐♥❣♦s ❈✉♥❤❛✱ ❋❡r♥❛♥❞♦ ❆❢♦♥s♦ ❙❛♥t♦s✱ ●✉✐❧❤❡r♠❡ ✧●✉✐❣✉✐✧ ▼❛✐❛✱ ❍❡✐t♦r ✧❍❡❝t♦r✧
❙♦❛r❡s ❘❛♠♦s ❋✐❧❤♦✱ ▲❡❛♥❞r♦ ✧❏♦s❡❧✐t♦✧ ❱✐❧❧❛s✱ ▼❛r❝❡❧♦ ●✳ ❆❧♠✐r♦♥✱ P❡❞r♦ ✧P❡❞rã♦✧ ❖❧♠♦✱ ❘❛❢❛❡❧ ✧❈♦❧❛r❡s✧ ❈♦❧❛r❡s✱ ❘❛❢❛❡❧ ✧❖❞♦♥✧ ❖❞♦♥ ❞❡ ❆❧❡♥❝❛r✱ ❘❛❢❛❡❧ ✧❙❛♥t✐♥✧ ❙❛♥t✐♥✱ ❚❤✐❛❣♦ ✧P❡❞♣❛♥♦✧ ❍❡♥r✐q✉❡ ❙✐❧✈❛✳
❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛q✉❡❧❡s q✉❡ ♥ã♦ ❡st❛✈❛♠ ♥♦ ❞✐❛✲❛✲❞✐❛ ❞♦ ❧❛❜♦r❛tór✐♦✱ ♠❛s q✉❡ ❡st❛✈❛♠ ❝♦♠✐❣♦✳ ❆♥❞r❡ ✧❏❡s✉s✧ ▲✉✐③ ❉✉rã♦✱ ❉✐♥❛❧❞♦✱ ❊♠❡rs♦♥ ✧▼❡rsã♦✧ ▼❡❧♦ ❆❧♠❡✐❞❛✱ ●✐❧❜❡rt♦ ▼❡❧♦ ❆❧♠❡✐❞❛✱ ❍✉❡r❧✐❡✱ ▼ár✐♦ ❍❡♥r✐q✉❡✱ ▼❛① ✧◆✐❤✐❧✐st❛✧ ▼❡♥❞❡❧✳
❆❣r❡❞❡ç♦ ❛q✉✐❧♦ q✉❡ ✈✐✈✐ ❡ ❛♣r❡♥❞✐ ❡✱ ❛❝r❡❞✐t♦ q✉❡ ♦ ♠❛✐♦r r❡s✉❧t❛❞♦ ❞❡st❡ ❝✉rs♦ ♥ã♦ sã♦ ❛s ♣á❣✐♥❛s q✉❡ ✈✐rã♦ ❛ s❡❣✉✐r ❝♦♠ ❢ór♠✉❧❛s ❡ ❣rá✜❝♦s✱ ♠❛s s❡r ✉♠❛ ♣❡ss♦❛ ♠❡❧❤♦r ♣♦r t❡r ❝♦♠♣❛rt✐❧❤❛❞♦ ✉♠ t❡♠♣♦ ❞❡ ✈✐❞❛ ❝♦♠ ✈♦❝ês✳
✏❚❤❡r❡ ✐s ♥♦ s✉❜st✐t✉t❡ ❢♦r ❤❛r❞ ✇♦r❦✳✑ ✭❚❤♦♠❛s ❊❞✐s♦♥✮
❘❡s✉♠♦
❖ ✉s♦ ❞❡ ❝❛r❛❝t❡ríst✐❝❛s t♦♣♦❧ó❣✐❝❛s✱ ♠❛✐s ❡s♣❡❝✐✜❝❛♠❡♥t❡✱ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ ✉♠ ❡❧❡✲ ♠❡♥t♦ r❡❧❛❝✐♦♥❛❞♦ ❝♦♠ s✉❛ ♣♦s✐çã♦ é ✉♠ ❛ss✉♥t♦ ❛♠♣❧❛♠❡♥t❡ ❡st✉❞❛❞♦✳ P♦r s✉❛ ✈❡③✱ ❛ t❡♦r✐❛ ❞❛s r❡❞❡s ❝♦♠♣❧❡①❛s ♣r♦✈ê ❛❧❣✉♠❛s ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❞❡ ✉s♦ ❣❡r❛❧ q✉❡ ❢♦✲ r❛♠ ❛♣❧✐❝❛❞❛s ❛ ✉♠❛ ✐♠❡♥s❛ ✈❛r✐❡❞❛❞❡ ❞❡ ❝❛♠♣♦s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ ❊st❡ tr❛❜❛❧❤♦ t❡♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ✉s❛r ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ♥♦ ♣r♦❥❡t♦ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ♣❛r❛ ❘❡❞❡s ❞❡ ❙❡♥s♦r❡s s❡♠ ❋✐♦ ✭❘❙❙❋s✮✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ❢♦r❛♠ ♣r♦♣♦st❛s ❞✉❛s ♥♦✈❛s ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡✱ ♦ ❙✐♥❦ ❙tr❡ss ❡ ♦ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss✱ ❛❧❣♦r✐t♠♦s ❞✐str✐❜✉í❞♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡ ❛♠❜❛s ❡ ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ár✈♦r❡ q✉❡ t✐r❛♠ ♣r♦✈❡✐t♦ ❞❛s ♠❡s♠❛s✳ ❙✐♠✉❧❛çõ❡s ❝♦♠♣❛r❛♥❞♦ ❛ ❛❜♦r❞❛❣❡♠ ♣r♦♣♦st❛ ❝♦♠ ❛❧❣✉♥s ❞♦s ❛❧❣♦r✐t♠♦s ❞❡ ❢✉sã♦ ❞❡ ❞❛❞♦s ♠❛✐s ❡✜❝✐❡♥t❡s ❞❛ ❧✐t❡r❛t✉r❛ ♠♦str❛♠ q✉❡ ♦s ❛❧❣♦r✐t♠♦s ♣r♦♣♦st♦s ❣❡r❛♠ ár✈♦r❡s ❞❡ q✉❛❧✐❞❛❞❡ ❝♦♠♣❛tí✈❡❧✱ ✉t✐❧✐③❛♥❞♦✲s❡ ❞❡ ✉♠ ♥ú♠❡r♦ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡ ♠❡♥♦r ❞❡ ♠❡♥s❛❣❡♥s ♥❛ ❝♦♥str✉çã♦ ❞❛ ár✈♦r❡✳
❆❜str❛❝t
❚❤❡ ✉s❡ ♦❢ t♦♣♦❧♦❣✐❝❛❧ ❢❡❛t✉r❡s✱ ♠♦r❡ s♣❡❝✐✜❝❛❧❧②✱ t❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ ❛♥ ❡❧❡♠❡♥t r❡❧❛t❡❞ t♦ ✐ts str✉❝t✉r❛❧ ♣♦s✐t✐♦♥ ✐s ❛ s✉❜❥❡❝t ✇✐❞❡❧② st✉❞✐❡❞✳ ❋♦r ✐♥st❛♥❝❡✱ ❝♦♠♣❧❡① ♥❡t✇♦r❦s t❤❡♦r② ♣r♦✈✐❞❡s s♦♠❡ ❣❡♥❡r❛❧ ✉s❡ ❝❡♥tr❛❧✐t② ♠❡tr✐❝s t❤❛t ❤❛✈❡ ❜❡❡♥ ❛♣♣❧✐❡❞ ✐♥ ❛ ❧❛r❣❡ ✈❛r✐❡t② ♦❢ ❦♥♦✇❧❡❞❣❡ ✜❡❧❞s✳ ❚❤✐s ✇♦r❦ ❛✐♠s t♦ ✉s❡ ❝❡♥tr❛❧✐t② ✐♥❢♦r♠❛t✐♦♥ ✐♥ t❤❡ ❞❡✲ s✐❣♥ ♦❢ r♦✉t✐♥❣ ❛❧❣♦r✐t❤♠s ❢♦r ❲✐r❡❧❡ss ❙❡♥s♦r ◆❡t✇♦r❦s ✭❲❙◆✮✳ ■♥ t❤✐s ❝♦♥t❡①t✱ ✇❡ ♣r♦♣♦s❡ t✇♦ ♥❡✇ t♦♣♦❧♦❣✐❝❛❧ ♠❡tr✐❝s✱ t❤❡ ❙✐♥❦ ❙tr❡ss✱ ❛♥❞ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss✱ ❞✐str✐❜✉✲ t❡❞ ❛❧❣♦r✐t❤♠s t♦ ❝❛❧❝✉❧❛t❡ t❤❡♠✱ ❛♥❞ ❞❡✈✐s❡ tr❡❡✲❜❛s❡❞ r♦✉t✐♥❣ ❛❧❣♦r✐t❤♠s t❤❛t t❛❦❡ ❛❞✈❛♥t❛❣❡ ♦❢ t❤❡♠✳ ❙✐♠✉❧❛t✐♦♥s ❝♦♠♣❛r✐♥❣ t❤❡ ♣r♦♣♦s❡❞ ❛♣♣r♦❛❝❤ ✇✐t❤ s♦♠❡ ♦❢ t❤❡ ♠♦st ❡✣❝✐❡♥t ❞❛t❛ ❢✉s✐♦♥ ❛❧❣♦r✐t❤♠s ❢r♦♠ t❤❡ ❧✐t❡r❛t✉r❡✱ s❤♦✇ t❤❛t t❤❡ ♣r♦♣♦s❡❞ tr❡❡ ❛❧❣♦r✐t❤♠s ❣❡♥❡r❛t❡ ❝♦♥s✐st❡♥t q✉❛❧✐t② tr❡❡s✱ ✉s✐♥❣ ❛ s✐❣♥✐✜❝❛♥t❧② s♠❛❧❧❡r ♥✉♠❜❡r ♦❢ ♠❡ss❛❣❡s ✐♥ t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ t❤❡ tr❡❡✳
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✸✳✶ ❊str✉t✉r❛ ❞♦ ♣❛❝♦t❡ ❍❡❧❧♦ ✉s❛❞♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❙tr❡ss✳ ❖s ❝❛♠♣♦s ❢♦r❛♠ ❛r♠❛③❡♥❛❞♦s ❝♦♠♦ ✈❛❧♦r❡s ✐♥t❡✐r♦s ❞❡ ✸✷ ❜✐ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✸✳✷ ❊str✉t✉r❛ ❞♦ ♣❛❝♦t❡ ❍❡❧❧♦ ✉s❛❞♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss✳ ❖s
❝❛♠♣♦s ❢♦r❛♠ ❛r♠❛③❡♥❛❞♦s ❝♦♠♦ ✈❛❧♦r❡s ✐♥t❡✐r♦s ❞❡ ✸✷ ❜✐ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✸✳✸ ❊str✉t✉r❛ ❞♦ ♣❛❝♦t❡ ❇♦r❞❡r ✉s❛❞♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss✳ ❖s
❝❛♠♣♦s ❢♦r❛♠ ❛r♠❛③❡♥❛❞♦s ❝♦♠♦ ✈❛❧♦r❡s ✐♥t❡✐r♦s ❞❡ ✸✷ ❜✐ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✸✳✹ ❯♠❛ r❡❞❡ ✐❧✉str❛t✐✈❛ ❝♦♠ ♦ s✐♥❦ ✭♣❡♥tá❣♦♥♦✮ ❡ ♥ós s❡♥s♦r❡s ✭❝ír❝✉❧♦s ❡
❧♦s❛♥❣♦s✮✳ P❛r❛ ❝❛❞❛ ♥ó✱ ♦ ✈❛❧♦r ❞♦ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss é ♠♦str❛❞♦ ❡♥tr❡ ♣❛rê♥t❡s❡s✱ ❡ ♦ ♥ú♠❡r♦ ❞❡ ❝❛♠✐♥❤♦s ♠í♥✐♠♦s✱ ❝♦♠ ♦r✐❣❡♠ ♥♦ s✐♥❦✱ ❡♥tr❡ ❝♦❧❝❤❡t❡s✳ ❖s ♥ós s❡♥s♦r❡s ❡♠ ❢♦r♠❛t♦ ❝✐r❝✉❧❛r t❡♠ ♦ ♣❛♣❡❧ ❞❡ ❘❡❧❛② ❡ ♦s ❧♦s❛♥❣♦s sã♦ ❇♦r❞❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✹✳✶ ❊rr♦ ❛❜s♦❧✉t♦✱ ♣♦r ♥í✈❡❧ ❞❡ r♦t❡❛♠❡♥t♦✱ ❞♦ ❛❧❣♦r✐t♠♦ ❞✐str✐❜✉í❞♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✹✳✷ ❚❛♠❛♥❤♦ ❞♦ ♣❛❝♦t❡ ❇♦r❞❡r ❡♠ ❞✐✈❡rs♦s ♥í✈❡✐s ❞❡ r♦t❡❛♠❡♥t♦ ✈❛r✐❛♥❞♦✲s❡ ❛
❞❡♥s✐❞❛❞❡ ❞❛ r❡❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✹✳✸ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♣❛❝♦t❡s ❞❡ ♦✈❡r❤❡❛❞ ❡♠ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛ ✈❛r✐❛çã♦ ❞♦ ♥ú♠❡r♦
❞❡ ♥ós ❣❡r❛♥❞♦ ❡✈❡♥t♦s ❡ ❞❛ ❞❡♥s✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✹✳✹ ◆ú♠❡r♦ ❞❡ ♥ós ❙t❡✐♥❡r ❡♠ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛ ✈❛r✐❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♥ós
❣❡r❛♥❞♦ ❡✈❡♥t♦s ❡ ❞❛ ❞❡♥s✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✺ ❚❛①❛ ❞❡ ❛❣r❡❣❛çã♦ ❡♠ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛ ✈❛r✐❛çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ♥ós ❣❡r❛♥❞♦
❡✈❡♥t♦s ❡ ❞❛ ❞❡♥s✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✹✳✻ ◗✉❛♥t✐❞❛❞❡ ❞❡ ♣❛❝♦t❡s ♣♦r ❞❛❞♦ r❡♣♦rt❛❞♦ ❡♠ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛ ✈❛r✐❛çã♦ ❞♦
♥ú♠❡r♦ ❞❡ ♥ós ❣❡r❛♥❞♦ ❡✈❡♥t♦s ❡ ❞❛ ❞❡♥s✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✵
❆✳✶ ❊rr♦ ♣❡r❝❡♥t✉❛❧ r❡❧❛t✐✈♦ q✉❛♥❞♦ s❡ ❧✐♠✐t❛ ❡♠ ✺ ❡❧❡♠❡♥t♦s ♦ t❛♠❛♥❤♦ ❞♦ ❛rr❛② sonsP aths ❝♦♥t✐❞♦ ♥♦ ♣❛❝♦t❡ ❇♦r❞❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻
❆✳✷ ❊rr♦ ♣❡r❝❡♥t✉❛❧ r❡❧❛t✐✈♦ q✉❛♥❞♦ s❡ ❧✐♠✐t❛ ❡♠ ✸✵ ❡❧❡♠❡♥t♦s ♦ t❛♠❛♥❤♦ ❞♦ ❛rr❛② sonsP aths ❝♦♥t✐❞♦ ♥♦ ♣❛❝♦t❡ ❇♦r❞❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼
❆✳✸ ◆ú♠❡r♦ ❞❡ ♥ós ❙t❡✐♥❡r ♣r❡s❡♥t❡s ♥❛ ár✈♦r❡ ❝r✐❛❞❛ ♣❡❧♦ ❈❚ ❝♦♠ ❧✐♠✐t❡s ✐♠♣♦st♦s ❛♦ ❛rr❛② sonsP aths ❝♦♥t✐❞♦ ♥♦ ♣❛❝♦t❡ ❇♦r❞❡r ❡♠ ✺ ❡ ✸✵ ❡❧❡♠❡♥t♦s ✺✽
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❉❡s❝r✐çã♦ ❞❛s ✈❛r✐á✈❡✐s ♥♦ ❛❧❣♦r✐t♠♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❙tr❡ss ✳ ✳ ✳ ✳ ✳ ✶✼ ✸✳✷ ❉❡s❝r✐çã♦ ❞❛s ✈❛r✐á✈❡✐s ❛❞✐❝✐♦♥❛✐s ❛♦ ❛❧❣♦r✐t♠♦ ❞♦ ❝á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❙tr❡ss
♣❛r❛ ❛ ❝r✐❛çã♦ ❞❛ ❡str✉t✉r❛ ❡♠ ár✈♦r❡ ❙tr❡ss ❚r❡❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✸✳✸ ❉❡s❝r✐çã♦ ❞❛s ✈❛r✐á✈❡✐s ♥♦ ❛❧❣♦r✐t♠♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss ✳ ✷✵ ✸✳✹ ❖ ❝♦♥t❡ú❞♦ ❞♦ ❛rr❛② sonsP aths ♥♦ ♣❛❝♦t❡ ❇♦r❞❡r✱ ❡ ♦ ❝♦♥❥✉♥t♦ ψ ♣❛r❛
❝❛❞❛ ♥ó ❞❛ r❡❞❡ ✐❧✉str❛❞❛ ♥❛ ✜❣✉r❛ ✸✳✹✳ ❈❛❞❛ ♣♦s✐çã♦ ❞♦ ❛rr❛② é ❢♦r♠❛t❛❞❛ ❝♦♠♦ ✭❝❤❛✈❡✱ ✈❛❧♦r✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✸✳✺ ❉❡s❝r✐çã♦ ❞❛s ✈❛r✐á✈❡✐s ❛❞✐❝✐♦♥❛✐s ❛♦ ❛❧❣♦r✐t♠♦ ❞♦ ❝á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❇❡t✇❡✲
❡♥♥❡ss ♣❛r❛ ❛ ❝r✐❛çã♦ ❞❛ ❡str✉t✉r❛ ❡♠ ár✈♦r❡ ❈❡♥tr❛❧✐t② ❚r❡❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✹✳✶ P❛râ♠❡tr♦s ❡ ✈❛❧♦r❡s ✉t✐❧✐③❛❞♦s ♥❛s s✐♠✉❧❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽
▲✐st❛ ❞❡ ❆❧❣♦r✐t♠♦s
✶ ❆❧❣♦r✐t♠♦ ❉✐str✐❜✉í❞♦ ♣❛r❛ ♦ ❙✐♥❦ ❙tr❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷ ❖ ❆❧❣♦r✐t♠♦ ❞❡ ❘♦t❡❛♠❡♥t♦ ❡♠ ➪r✈♦r❡✿ ❙tr❡ss ❚r❡❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✸ ❆❧❣♦r✐t♠♦ ❉✐str✐❜✉í❞♦ ♣❛r❛ ♦ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✹ ❖ ❆❧❣♦r✐t♠♦ ❞❡ ❘♦t❡❛♠❡♥t♦ ❡♠ ➪r✈♦r❡✿ ❈❡♥tr❛❧✐t② ❚r❡❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
❙✉♠ár✐♦
❆❣r❛❞❡❝✐♠❡♥t♦s ✈
❘❡s✉♠♦ ✐①
❆❜str❛❝t ①✐
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐✐✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✈
✶ ■♥tr♦❞✉çã♦ ✶
✶✳✶ ▼♦t✐✈❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ✶✳✷ ❖❜❥❡t✐✈♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✷ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s ✺
✷✳✶ ❈❡♥tr❛❧✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✶✳✶ ❉❡s❛✜♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✶✳✷ ▼étr✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✷✳✶✳✸ ❘♦t❡❛♠❡♥t♦ ❡♠ r❡❞❡s ❛❞✲❤♦❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✷✳✷ ❆❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ❘❙❙❋s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✶ ❉❡s❛✜♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵ ✷✳✷✳✷ ❆❧❣♦r✐t♠♦s ❤✐❡rárq✉✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✷✳✷✳✸ ❆❧❣♦r✐t♠♦s ♥ã♦✲❡str✉t✉r❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✷✳✷✳✹ ❆❧❣♦r✐t♠♦s ❜❛s❡❛❞♦s ❡♠ ár✈♦r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸
✸ Pr♦♣♦st❛ ✶✺
✸✳✶ ❙✐♥❦ ❙tr❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✸✳✶✳✶ ❆ ▼étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✸✳✶✳✷ ❖ ❆❧❣♦r✐t♠♦ ❉✐str✐❜✉í❞♦ ✲ ❈á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❙tr❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✸✳✶✳✸ ❖ ❆❧❣♦r✐t♠♦ ❞❡ ❘♦t❡❛♠❡♥t♦ ❡♠ ➪r✈♦r❡✿ ❙tr❡ss ❚r❡❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✸✳✷ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✸✳✷✳✶ ❆ ▼étr✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✸✳✷✳✷ ❖ ❆❧❣♦r✐t♠♦ ❉✐str✐❜✉í❞♦ ✲ ❈á❧❝✉❧♦ ❞♦ ❙✐♥❦ ❇❡t✇❡❡♥♥❡ss ✳ ✳ ✳ ✳ ✷✵ ✸✳✷✳✸ ❖ ❆❧❣♦r✐t♠♦ ❞❡ ❘♦t❡❛♠❡♥t♦ ❡♠ ➪r✈♦r❡✿ ❈❡♥tr❛❧✐t② ❚r❡❡ ✳ ✳ ✳ ✳ ✷✸
✹ ❘❡s✉❧t❛❞♦s ✷✼
✹✳✶ ❆❧❣♦r✐t♠♦s ❉✐str✐❜✉í❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✹✳✷ ❆❧❣♦r✐t♠♦s ❞❡ ❘♦t❡❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✹✳✸ ❈♦♥❝❧✉sõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶
✺ ❈♦♥❝❧✉sõ❡s ✹✸
✻ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✹✺
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✹✼
❆ ❯♠❛ s♦❧✉çã♦ ♣❛r❛ ♦ ♣r♦❜❧❡♠❛ ❞♦ ❝r❡s❝✐♠❡♥t♦ ❞♦ ♣❛❝♦t❡ ❇♦r❞❡r ✺✺
❚♦❞❛ ❣r❛♥❞❡ ❝❛♠✐♥❤❛❞❛ ❝♦♠❡ç❛ ♣❡❧♦ ♣r✐♠❡✐r♦ ♣❛ss♦✳
▼❛♦ ❚sé✲❚✉♥❣
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
✶✳✶ ▼♦t✐✈❛çã♦
❉❡s❞❡ ♦ ❝♦♠❡ç♦ ❞❛ ❞é❝❛❞❛ ♣❛ss❛❞❛✱ ❛s ❘❡❞❡s ❞❡ ❙❡♥s♦r❡s s❡♠ ❋✐♦ ✭❘❙❙❋s✮ ❬❆❦②✐❧❞✐③ ❡t ❛❧✳✱✷✵✵✷❀P♦tt✐❡ ❛♥❞ ❑❛✐s❡r✱✷✵✵✵❀❨✐❝❦ ❡t ❛❧✳✱✷✵✵✽❪ tê♠ r❡❝❡❜✐❞♦ ❜❛st❛♥t❡ ❛t❡♥çã♦ ❞❛ ❝♦♠✉♥✐❞❛❞❡ ❝✐❡♥tí✜❝❛ ❞❡✈✐❞♦ à s✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ r❡❛❧✐③❛r ♠♦♥✐t♦r❛♠❡♥t♦ ❞❡ ❛♠❜✐❡♥t❡s ❡ ❝♦❧❡t❛ ❞❡ ❞✐✈❡rs♦s t✐♣♦s ❞❡ ✐♥❢♦r♠❛çã♦ ❬▲♦✉r❡✐r♦ ❡t ❛❧✳✱✷✵✵✸❪✳ ❆ ♣r✐♥❝✐♣❛❧ ❝❛r❛❝t❡ríst✐❝❛ q✉❡ ❞✐st✐♥❣✉❡ ♦ ♣r♦❥❡t♦ ❞❡ ❘❙❙❋s ❞❛s ❞❡♠❛✐s r❡❞❡s é q✉❡ ♦s ♥ós s❡♥s♦r❡s ♣♦ss✉❡♠ r❡❝✉rs♦s ❜❛st❛♥t❡ r❡str✐t♦s✱ t❛✐s ❝♦♠♦ ❝❛♣❛❝✐❞❛❞❡ ❧✐♠✐t❛❞❛ ❞❡ ♠❡♠ór✐❛✱ ❞❡ ❧❛r❣✉r❛ ❞❡ ❜❛♥❞❛ ❬❈❤♦♥❣ ❛♥❞ ❑✉♠❛r✱ ✷✵✵✸❪✱ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡ ❞❡ ❡♥❡r❣✐❛ ❬▼❛r✐♥ ❡t ❛❧✳✱ ✷✵✵✺❪✳
❖ ♥ó s❡♥s♦r é t✐♣✐❝❛♠❡♥t❡ ♣❡q✉❡♥♦✱ ♦ q✉❡ t❡♥❞❡ ❛ ❧✐♠✐t❛r ❛ s✉❛ ❝❛♣❛❝✐❞❛❞❡ ❞❡ r❡✲ ❝✉rs♦s✱ s❡ ❝♦♠♣❛r❛❞♦ ❛ ✉♠ s❡♥s♦r tr❛❞✐❝✐♦♥❛❧ ✉s❛❞♦ ❛♣❡♥❛s ♣❛r❛ ❝♦❧❡t❛ ❞❡ ❞❛❞♦s ❬❨✐❝❦ ❡t ❛❧✳✱ ✷✵✵✽❪✳ ❆❧é♠ ❞✐ss♦✱ ❛ s✉❛ ❡♥❡r❣✐❛ é ♣r♦✈✐❞❛ ♣♦r ✉♠❛ ❜❛t❡r✐❛ ✐♥t❡❣r❛❞❛ ❡✱ ❡♠ ♠✉✐t❛s ❛♣❧✐❝❛çõ❡s✱ ❡ss❡ ♥ó é ❞❡♣♦s✐t❛❞♦ ❡♠ ár❡❛s r❡♠♦t❛s✱ ❞✐✜❝✉❧t❛♥❞♦ ♦✉ ♠❡s♠♦ ✐♠✲ ♣♦ss✐❜✐❧✐t❛♥❞♦ ♦ ❛❝❡ss♦ ❛ ❡ss❡ ❡❧❡♠❡♥t♦ ♣❛r❛ s✉❛ ♠❛♥✉t❡♥çã♦ ❬▲♦✉r❡✐r♦ ❡t ❛❧✳✱ ✷✵✵✸❪✳ ◆❡ss❡ ❝❡♥ár✐♦✱ ♦ t❡♠♣♦ ❞❡ ✈✐❞❛ ❞❛ r❡❞❡ ❞❡♣❡♥❞❡ ❞❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❡♥❡r❣✐❛ ❞✐s♣♦♥í✈❡❧ ♥♦s ♥ós s❡♥s♦r❡s ❡✱ ♣♦r ✐ss♦✱ ❡ss❡s ♥ós ❞❡✈❡♠ ❜❛❧❛♥❝❡❛r s❡✉s r❡❝✉rs♦s ❧✐♠✐t❛❞♦s ❝♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❛✉♠❡♥t❛r ♦ t❡♠♣♦ ❞❡ ✈✐❞❛ ❞❛ r❡❞❡✳ P♦rt❛♥t♦✱ ❛ ❝♦♥s❡r✈❛çã♦ ❞❡ ❡♥❡r❣✐❛ é ✉♠ ❞♦s ❛s♣❡❝t♦s ♠❛✐s ✐♠♣♦rt❛♥t❡s ❛ s❡r❡♠ ❝♦♥s✐❞❡r❛❞♦s ♥♦ ♣r♦❥❡t♦ ❞❛s ❘❙❙❋s ❬❆♥❛st❛s✐ ❡t ❛❧✳✱ ✷✵✵✾❪✳
◆✉♠❛ ❘❙❙❋✱ ♦s ♥ós s❡♥s♦r❡s ❝♦❧❡t❛♠ ♦s ❞❛❞♦s ❞❡ ✐♥t❡r❡ss❡✱ ♣r♦❝❡ss❛♠ ❧♦❝❛❧♠❡♥t❡ ♦✉ ❝♦♦r❞❡♥❛❞❛♠❡♥t❡ ❡♥tr❡ ♦s ♥ós ✈✐③✐♥❤♦s ❡ ❡♥✈✐❛♠ ❡ss❛ ✐♥❢♦r♠❛çã♦ r❡s✉❧t❛♥t❡ ♣❛r❛ ✉♠ ♥ó ❡s♣❡❝✐❛❧✱ ❝❤❛♠❛❞♦ ❞❡ ❡st❛çã♦ ❜❛s❡ ✭s✐♥❦✮✳ ❖ ♣r♦❥❡t♦ ❞♦ ❛❧❣♦r✐t♠♦ ❞✐str✐❜✉í❞♦ ♣❛r❛ ❡st❛❜❡❧❡❝❡r ❡ ♠❛♥t❡r r♦t❛s ♥✉♠❛ ❘❙❙❋ ❞❡♣❡♥❞❡ ❞❡ ✈ár✐♦s ❢❛t♦r❡s✱ ❞❡♥tr❡ ❡❧❡s✱ ❛
✷ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉çã♦
❢r❡q✉ê♥❝✐❛ ❝♦♠ q✉❡ ♦s ❞❛❞♦s ❞❡✈❡♠ s❡r ❡♥✈✐❛❞♦s ♣❛r❛ ❛ ❡st❛çã♦ ❜❛s❡✱ q✉❛❧✐❞❛❞❡ ❞❡ s❡r✲ ✈✐ç♦ ❡s♣❡r❛❞❛ ♥❡ss❛ ❝♦♠✉♥✐❝❛çã♦ ✭❡✳❣✳✱ r♦t❛s ❝♦♠ ♠❡♥♦r ❧❛tê♥❝✐❛ ♦✉ ♠❡♥♦r ❝♦♥s✉♠♦ ❞❡ ❡♥❡r❣✐❛✮ ❡ ♦✉tr❛s ❢✉♥çõ❡s q✉❡ ♣♦❞❡♠ s❡r ❡①❡❝✉t❛❞❛s ❝♦♥❥✉♥t❛♠❡♥t❡ ❝♦♠ ♦ r♦t❡❛♠❡♥t♦ ❝♦♠♦ ❛ ❛❣r❡❣❛çã♦ ❞❡ ❞❛❞♦s✳
●❡r❛❧♠❡♥t❡✱ ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ♣❛r❛ ❘❙❙❋s tê♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❧❡✈❛r ♦s ❞❛❞♦s ♣♦r r♦t❛s q✉❡ ♠✐♥✐♠✐③❛♠ ♦ ♥ú♠❡r♦ ❞❡ r❡tr❛♥s♠✐ssõ❡s ❡✱ ♣♦t❡♥❝✐❛❧♠❡♥t❡✱ ♦ ❣❛st♦ ❞❡ ❡♥❡r❣✐❛ ❞❛ r❡❞❡✳ P❛r❛ t❛♥t♦✱ ❛ ❡str✉t✉r❛ ❞❡ r♦t❡❛♠❡♥t♦ ♣r❡❝✐s❛ s❡r ❝♦♥❝❡❜✐❞❛ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ t♦❞♦s ♦s ♥ós ❢♦♥t❡✱ ❡✳❣✳✱ ♥ós q✉❡ ❞❡t❡❝t❛r❛♠ ✉♠ ❡✈❡♥t♦✱ ♣♦ss❛♠ ❡s❝♦❛r s✉❛s ❧❡✐t✉r❛s ❛té ♦ s✐♥❦ ❞❛ ♠❛♥❡✐r❛ ♠❛✐s ❡✜❝✐❡♥t❡✱ ♦✉ s❡❥❛✱ r❡q✉✐s✐t❛♥❞♦ ♦ ♠❡♥♦r ♥ú♠❡r♦ ❞❡ r❡tr❛♥s♠✐ssõ❡s ♣♦ssí✈❡❧✳ ❆❧é♠ ❞✐st♦✱ ❛♦ r♦t❡❛r ♣❛❝♦t❡s✱ ♦ ❛❧❣♦r✐t♠♦ ♣♦❞❡ ✉t✐❧✐③❛r té❝♥✐❝❛s ❝♦♠♦ ❛❣r❡❣❛çã♦ ❞❡ ❞❛❞♦s ❬◆❛❦❛♠✉r❛ ❡t ❛❧✳✱✷✵✵✾❪✱ q✉❡ ❡①♣❧♦r❛ ❛ ❝♦rr❡❧❛çã♦ ❞♦s ❞❛❞♦s ❡ r❡❛❧✐③❛ ❛ ❛❣r❡❣❛çã♦ ❡♠ ♥ós ✐♥t❡r♠❡❞✐ár✐♦s r❡❞✉③✐♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ ♠❡♥s❛❣❡♥s tr♦❝❛❞❛s ♥❛ r❡❞❡✳
❆ ❛❣r❡❣❛çã♦ ❞❡ ❞❛❞♦s ✈✐s❛ ❝♦♠❜✐♥❛r ✐♥❢♦r♠❛çõ❡s ❞❡ ❢♦♥t❡s ❞✐❢❡r❡♥t❡s ❡✱ ❛tr❛✈és ❞❡ ✉♠❛ ❡str✉t✉r❛ ❞❡ r♦t❡❛♠❡♥t♦✱ ❣❡r❛❧♠❡♥t❡ ❡♠ ár✈♦r❡ ❬◆❛❦❛♠✉r❛ ❡t ❛❧✳✱ ✷✵✵✾❪✱ ❡st❛ ✐♥❢♦r♠❛çã♦ ❝♦♠❜✐♥❛❞❛ é ❡♥✈✐❛❞❛ ❡♠ ❞✐r❡çã♦ ❛♦ s✐♥❦✳ ❆ ❢✉sã♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❝♦♥t✐❞❛s ♥♦s ♣❛❝♦t❡s é ❢❡✐t❛ ♣♦r ❝❡rt♦s ♥ós ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ❛❣r❡❣❛❞♦r❡s✱ ♣r❡s❡♥t❡s ❡♠ ♣♦♥t♦s ❞❡ ❥✉♥çã♦ ❞❡ ❞✉❛s✱ ♦✉ ♠❛✐s r♦t❛s ❡♠ ❞✐r❡çã♦ ❛♦ s✐♥❦✳ ❉❡st❛ ❢♦r♠❛✱ q✉❛♥t♦ ♠❛✐s r♦t❛s ♣❛ss❛♠ ♣♦r ✉♠ ♥ó✱ ♠❛✐♦r s✉❛ ✐♠♣♦rtâ♥❝✐❛ s♦❜r❡ ❛ ❛❣r❡❣❛çã♦ ❡ tr❛♥s♠✐ssã♦ ❞♦s ❞❛❞♦s✳ ❆ ✐♠♣♦rtâ♥❝✐❛ ❞❡ ✉♠ ♥ó ♥❛ ❡str✉t✉r❛ ❞❡ ✉♠ ❣r❛❢♦ ♣♦❞❡ s❡r ♠❡♥s✉r❛❞❛ ❛tr❛✈és ❞❡ ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡✱ ♦✉ í♥❞✐❝❡s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❞❡s❞❡ ❛ ♠❡t❛❞❡ ❞♦ sé❝✉❧♦ ♣❛s✲ s❛❞♦ ❬❇❛✈❡❧❛s✱ ✶✾✹✽❪✳ ❖ ♦❜❥❡t✐✈♦ ❞❡st❛s ♠étr✐❝❛s é ❝❧❛ss✐✜❝❛r ♦s ✈ért✐❝❡s s❡❣✉♥❞♦ s✉❛ ✐♠♣♦rtâ♥❝✐❛ ♥❛ r❡❞❡ ✉t✐❧✐③❛♥❞♦✲s❡✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ ♣r♦①✐♠✐❞❛❞❡ ❞♦ ♠❡s♠♦ ❡♠ r❡❧❛çã♦ ❛♦s ❞❡♠❛✐s✱ ♦✉ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❝❛♠✐♥❤♦s q✉❡ ♣❛ss❛♠ ♣♦r ❡❧❡✳ ❱ért✐❝❡s ♣♦s✐❝✐♦♥❛❞♦s ❡♠ ár❡❛s ❝❡♥tr❛✐s ❝♦st✉♠❛♠ t❡r ♠❛✐♦r ✐♠♣♦rtâ♥❝✐❛ ❡str✉t✉r❛❧ ❞♦ q✉❡ ❛q✉❡❧❡s ❧♦❝❛❧✐③❛✲ ❞♦s ♥❛s ♠❛r❣❡♥s ❞❛ r❡❞❡✱ ❡✱ ♥♦s ❝❛s♦s ❡♠ q✉❡ ❤á ✢✉①♦ ❞❡ ❞❛❞♦s✱ ♥ós ❝❡♥tr❛✐s sã♦ ♦s ❞✐❢✉s♦r❡s ♥❛t✉r❛✐s ❞❡ ✐♥❢♦r♠❛çã♦✳ ❉❡ ♠❛♥❡✐r❛ ❣❡r❛❧✱ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦ ✈ért✐❝❡ ❝r❡s❝❡ ❞✐r❡t❛♠❡♥t❡ ♣r♦♣♦r❝✐♦♥❛❧ à s✉❛ ♣❛rt✐❝✐♣❛çã♦ ♥♦s ❝❛♠✐♥❤♦s ❬❞❛ ❋✳ ❈♦st❛ ❡t ❛❧✳✱ ✷✵✵✼❪✳ ❈♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ ✉♠ ❡❧❡♠❡♥t♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡♠ ✉♠❛ r❡❞❡ ♣♦❞❡ s❡r ❝❛❧❝✉❧❛❞❛ ❝♦♠ ❜❛s❡ ♥❛ s✉❛ ❝❡♥tr❛❧✐❞❛❞❡ t♦♣♦❧ó❣✐❝❛✳
✶✳✷✳ ❖❜❥❡t✐✈♦s ✸
t❡①t♦ ❞❛s ❘❙❙❋s ❡ ❛❧❣♦r✐t♠♦s ❞✐str✐❜✉í❞♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛s ♠❡s♠❛s✳ ❆❧é♠ ❞✐st♦✱ ❢♦r❛♠ ♣r♦♣♦st♦s ❞♦✐s ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ár✈♦r❡ q✉❡ ❢❛③❡♠ ♣r♦✈❡✐t♦ ❞❡st❛s ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❛ ✜♠ ❞❡ ❛✉♠❡♥t❛r ❛ ♦❝♦rrê♥❝✐❛ ❞❡ s♦❜r❡♣♦s✐çã♦ ❞❡ r♦t❛s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♠❡❧❤♦r❛r ❛ ❢✉sã♦ ❞❡ ❞❛❞♦s✳
✶✳✷ ❖❜❥❡t✐✈♦s
❖ ♦❜❥❡t✐✈♦ ❞❡st❡ tr❛❜❛❧❤♦ é ✐♥✈❡st✐❣❛r ❛ ❝❡♥tr❛❧✐❞❛❞❡ ❞♦s ♥ós ❝♦♠♦ ❡❧❡♠❡♥t♦ ❜❛s❡ ♥♦ ♣r♦❥❡t♦ ❞❡ ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ár✈♦r❡ ♣❛r❛ ❘❙❙❋s✳ ◆❡st❡ ❝♦♥t❡①t♦✱ é ♥❡❝❡s✲ sár✐♦ ❛ ❝r✐❛çã♦ ❞❡ ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ q✉❡ ❧❡✈❡♠ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ❝❛r❛❝t❡ríst✐❝❛s ❞❛s ❘❙❙❋s ❡✱ ❛❧é♠ ❞✐st♦✱ ❛❧❣♦r✐t♠♦s ❞✐str✐❜✉í❞♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡st❛s ♠étr✐❝❛s✳ P♦r ✜♠✱ ❝r✐❛r ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ q✉❡ s❡❧❡❝✐♦♥❡♠ ♦s ♥ós r❡tr❛♥s♠✐ss♦r❡s s❡❣✉♥❞♦ s✉❛ ❝❡♥tr❛❧✐❞❛❞❡ ❞❡ ♠❛♥❡✐r❛ ❛ ♠❛①✐♠✐③❛r ❛ s♦❜r❡♣♦s✐çã♦ ❞❡ r♦t❛s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♠❛①✐♠✐③❛r ❛ ❢✉sã♦ ❞❡ ❞❛❞♦s✳
❉❡st❛ ❢♦r♠❛✱ ♦s ♦❜❥❡t✐✈♦s ❡s♣❡❝í✜❝♦s ❞❡st❡ tr❛❜❛❧❤♦ sã♦✿
✶✳ Pr♦♣♦r ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❝♦♠♣❛tí✈❡✐s ❝♦♠ ❛s ❘❙❙❋s❀
✷✳ Pr♦♣♦r ❛❧❣♦r✐t♠♦s ❞✐str✐❜✉í❞♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡st❛s ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡❀
✸✳ Pr♦♣♦r ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ár✈♦r❡ q✉❡ ❢❛ç❛♠ ✉s♦ ❞♦s ✈❛❧♦r❡s ❞❡ ❝❡♥tr❛✲ ❧✐❞❛❞❡ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♠❛①✐♠✐③❛r ❛ ❢✉sã♦ ❞❡ ❞❛❞♦s✳
✶✳✸ ❖r❣❛♥✐③❛çã♦ ❞♦ ❚r❛❜❛❧❤♦
❊✈❡r② ♥❡✇ ❜❡❣✐♥♥✐♥❣ ❝♦♠❡s ❢r♦♠ s♦♠❡ ♦t❤❡r ❜❡❣✐♥♥✐♥❣✬s ❡♥❞✳
❙❡♥❡❝❛
❈❛♣ít✉❧♦ ✷
❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s
❊st❡ tr❛❜❛❧❤♦ ♣r♦♣õ❡ ♦ ✉s♦ ❞♦ ❝♦♥❝❡✐t♦ ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❡♠ ❘❙❙❋s ❡✱ ♣❛r❛ t❛❧✱ sã♦ ♣r♦✲ ♣♦st❛s ❞✉❛s ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡✱ ❢♦r♠❛s ❞❡ ❝❛❧❝✉❧á✲❧❛s ❞❡ ♠❛♥❡✐r❛ ❞✐str✐❜✉í❞❛ ❡ ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ár✈♦r❡ q✉❡ ❢❛③❡♠ ✉s♦ ❞❛s ♠❡s♠❛s ❝♦♠ ✐♥t✉✐t♦ ❞❡ ♠❛①✐✲ ♠✐③❛r ❛ ❢✉sã♦ ❞❡ ❞❛❞♦s✳
❊st❡ ❝❛♣ít✉❧♦ ❞✐s❝✉t❡ ❛❧❣✉♠❛s ♣r♦♣♦st❛s ❡♥❝♦♥tr❛❞❛s ♥❛ ❧✐t❡r❛t✉r❛ q✉❡ ❛❜♦r❞❛♠ ♦s ♣r✐♥❝✐♣❛✐s ❝♦♥❝❡✐t♦s ❞❡st❡ tr❛❜❛❧❤♦✱ ❝❡♥tr❛❧✐❞❛❞❡ ❡ ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ❘❙❙❋s✳ ❆ s❡çã♦ ✷✳✶ ❛♣r❡s❡♥t❛ ♦s ❞❡s❛✜♦s ❞❡ s❡ ❛♣❧✐❝❛r ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ♥✉♠ ❝♦♥t❡①t♦ ❞❡ ❘❙❙❋s✱ ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❝❧áss✐❝❛s✱ ♠étr✐❝❛s ♣r♦♣♦st❛s ♣❛r❛ ❝♦♥t❡①t♦s ❡s♣❡❝í✜❝♦s ❡ s✉❛s ❛♣❧✐❝❛çõ❡s ❡♠ ❞✐✈❡rs❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ P♦st❡r✐♦r♠❡♥t❡✱ ♥❛ s❡çã♦ ✷✳✷ s❡rã♦ ❛❜♦r❞❛❞♦s ♦s ❞❡s❛✜♦s ❡ ❞✐✈❡rs♦s tr❛❜❛❧❤♦s ♥♦ ❝❛♠♣♦ ❞♦s ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ❘❙❙❋s✳
✷✳✶ ❈❡♥tr❛❧✐❞❛❞❡
✷✳✶✳✶ ❉❡s❛✜♦s
❆♣❡s❛r ❞♦s ❞✐✈❡rs♦s ❝♦♥t❡①t♦s ♥♦s q✉❛✐s ♦ ❝♦♥❝❡✐t♦ ❝❡♥tr❛❧✐❞❛❞❡ ❢♦✐ ❛♠♣❧❛♠❡♥t❡ ❡s✲ t✉❞❛❞♦ ❑♦s❝❤üt③❦✐ ❡t ❛❧✳ ❬✷✵✵✺❪✱ ❡①✐st❡♠ ♣♦✉❝♦s tr❛❜❛❧❤♦s ♥❛ ❧✐t❡r❛t✉r❛ q✉❡ ❛❜♦r❞❛♠ r♦t❡❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❡♠ ❘❙❙❋s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦rq✉❡ ❡st❡ é ✉♠ ❛♠❜✐❡♥t❡ ❝♦♠♣✉t❛❝✐✲ ♦♥❛❧♠❡♥t❡ r❡str✐t♦ ❡✱ ♣♦rt❛♥t♦✱ ✐♠♣r❛t✐❝á✈❡❧ ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❡ ♠✉✐t❛s ♠étr✐❝❛s ❝❧áss✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡✳ ❖ ❝✉st♦ ♣❛r❛ ❝♦♠♣✉t❛r✱ ❞❡ ♠❛♥❡✐r❛ ❝❡♥tr❛❧✐③❛❞❛✱ ✉♠❛ ♠étr✐❝❛ ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❝❧áss✐❝❛ ❝♦♥❤❡❝✐❞❛ ❝♦♠♦ ❇❡t✇❡❡♥❡ss ❬❆♥t❤♦♥✐ss❡✱ ✶✾✼✶❀ ❋r❡❡♠❛♥✱ ✶✾✼✼✱
✶✾✼✾❪ é O(nm+n2logn) ♣❛r❛ ❣r❛❢♦s ♣♦♥❞❡r❛❞♦s ❡ O(nm) ♣❛r❛ ❣r❛❢♦s ♥ã♦ ♣♦♥❞❡r❛✲
❞♦s ❬❇r❛♥❞❡s✱✷✵✵✶❪✱ ♦♥❞❡n é ♦ ♥ú♠❡r♦ ❞❡ ♥ós ❡m é ♦ ♥ú♠❡r♦ ❞❡ ❛r❡st❛s✳ ❖❜s❡r✈❡ q✉❡
✻ ❈❛♣ít✉❧♦ ✷✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s
❡st❛ ❝♦♠♣✉t❛çã♦ r❡q✉❡r ♦ ❝á❧❝✉❧♦ ❞❡ t♦❞♦s ♦s ❝❛♠✐♥❤♦s ♠í♥✐♠♦s q✉❡ ♣❛ss❛♠ ♣❡❧♦s ✈ér✲ t✐❝❡s✳ ❖ ❝✉st♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ❝❛❧❝✉❧❛r ❛❧❣✉♠❛s ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❡♠ r❡❞❡s ❝♦♠ ♠✐❧❤❛r❡s ❞❡ ♥ós ♣♦❞❡ s❡r ✐♠♣r❛t✐❝á✈❡❧ ❬❇r❛♥❞❡s ❛♥❞ P✐❝❤✱ ✷✵✵✼❪✳ ❙❡♥❞♦ ♣♦ssí✈❡❧ ❛❞❡q✉❛r ♠étr✐❝❛s ♣❛r❛ ♦ ❝♦♥t❡①t♦ ❞❛s ❘❙❙❋s ❡ ❝❛❧❝✉❧❛r ❛ ❝❡♥tr❛❧✐❞❛❞❡ ❞❡ ❝❛❞❛ ♥ó ❞❛ r❡❞❡ ❞❡ ♠❛♥❡✐r❛ ❞✐str✐❜✉í❞❛✱ ♣♦❞❡✲s❡ ❛♣r♦✈❡✐t❛r t❛❧ ❝❛r❛❝t❡ríst✐❝❛ ❡♠ ❢✉♥çõ❡s ❞❛ r❡❞❡ ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♥♦ r♦t❡❛♠❡♥t♦✳ ❆ ♣ró①✐♠❛ s❡çã♦ ❛♣r❡s❡♥t❛ ❞✐✈❡rs❛s ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❡ s✉❛s ❛♣❧✐❝❛çõ❡s ♥♦s ♠❛✐s ✈❛r✐❛❞♦s ❝♦♥t❡①t♦s✳
✷✳✶✳✷ ▼étr✐❝❛s
◆❛ t❡♦r✐❛ ❞♦s ❣r❛❢♦s✱ ❛ ✐❞é✐❛ ❞❡ ❝❧❛ss✐✜❝❛r ✉♠ ✈ért✐❝❡ ♣♦r s✉❛ ✐♠♣♦rtâ♥❝✐❛ ❢♦✐ ✐♥tr♦❞✉③✐❞❛ ♣♦r ❬❇❛✈❡❧❛s✱✶✾✹✽❪ ❡ ❬▲❡❛✈✐tt✱ ✶✾✺✶❪✱ q✉❡ r❡s✉❧t♦✉ ♥❛ ♣r♦♣♦s✐çã♦ ❞♦ ♣r✐♠❡✐r♦ í♥❞✐❝❡ ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ♣❛r❛ r❡❞❡s ❝♦♥❡❝t❛❞❛s✱ ♦ í♥❞✐❝❡ ❞❡ ❇❛✈❡❧❛✳
▼❡❞✐❞❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❬❑♦s❝❤üt③❦✐ ❡t ❛❧✳✱ ✷✵✵✺❀ ❞❛ ❋✳ ❈♦st❛ ❡t ❛❧✳✱ ✷✵✵✼❪ tê♠ ♦ ✐♥t✉✐t♦ ❞❡ ❡st✐♠❛r ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ ✉♠ ❞❛❞♦ ✈ért✐❝❡ ❬❨✐✇❡✐ ❡t ❛❧✳✱ ✷✵✵✻❪✱ ♦✉ s❡❥❛✱ r❛♥q✉❡á✲❧♦ s❡❣✉♥❞♦ s✉❛ ✐♠♣♦rtâ♥❝✐❛ t♦♣♦❧ó❣✐❝❛ ❬❲❛ss❡r♠❛♥ ❛♥❞ ❋❛✉st✱✶✾✾✹❪✳ ◆ós ❡♠ ♣♦s✐çõ❡s ❝❡♥tr❛✐s ❣❡r❛❧♠❡♥t❡ tê♠ ❣r❛♥❞❡ ✐♠♣♦rtâ♥❝✐❛ ❡str✉t✉r❛❧ ❡✱ ❡♠ ❝❛s♦s ♦♥❞❡ ❤á ✢✉①♦ ❞❡ ❞❛❞♦s✱ sã♦ ❛❣❡♥t❡s ❞❡ ❡s❝♦❛♠❡♥t♦ ✈✐t❛✐s✳ ●❡r❛❧♠❡♥t❡✱ q✉❛♥t♦ ♠❛✐♦r ❢♦r ❛ ♣❛rt✐❝✐♣❛çã♦ ❞❡ ✉♠ ✈ért✐❝❡ ♦✉ ❞❡ ✉♠❛ ❛r❡st❛ ❡♠ ❝❛♠✐♥❤♦s ♥♦ ❣r❛❢♦✱ ♠❛✐♦r s❡rá s✉❛ ✐♠♣♦rtâ♥❝✐❛ ❬❞❛ ❋✳ ❈♦st❛ ❡t ❛❧✳✱ ✷✵✵✼❪✳ ❉❡st❛ ❢♦r♠❛✱ ♣♦❞❡✲s❡ s❛❜❡r ♦ q✉ã♦ ✐♠♣♦rt❛♥t❡ é✱ ♣♦r ❡①❡♠♣❧♦✱ ✉♠ ❡❧❡♠❡♥t♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ♣❛r❛ ✉♠❛ r❡❞❡✱ ♦✉ ✉♠❛ ♣❡ss♦❛ ❡♠ ✉♠❛ r❡❞❡ s♦❝✐❛❧✱ ✐♥❢❡r✐♥❞♦✲s❡ ❡st❛ ✐♠♣♦rtâ♥❝✐❛ ❛ ♣❛rt✐r ❞❛ ♣♦s✐çã♦ ❞❡st❛ ❡♥t✐❞❛❞❡ ❢r❡♥t❡ às ❞❡♠❛✐s✳
❊①✐st❡♠ ❞✐✈❡rs❛s ♠étr✐❝❛s ❝❧áss✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❜❛s❡❛❞❛s ❡♠ ❞✐❢❡r❡♥t❡s ❝❛✲ r❛❝t❡ríst✐❝❛s ❞♦ ❣r❛❢♦ ❝♦♥s✐❞❡r❛♥❞♦✱ t❛♥t♦ ❛s♣❡❝t♦s s✐♠♣❧❡s ❝♦♠♦ ♦ ❣r❛✉ ❞♦ ♥ó✱ q✉❛♥t♦ ❝♦♥❝❡✐t♦s ♠❛✐s ❡❧❛❜♦r❛❞♦s ❝♦♠♦ ❛ r❡❧❛çã♦ ♠út✉❛ ❞❡ ✐♠♣♦rtâ♥❝✐❛ ❡♥tr❡ ♦s ♥ós ✈✐③✐♥❤♦s✳ ❆ ♠étr✐❝❛ ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ♠❛✐s s✐♠♣❧❡s é ♦ ❉❡❣r❡❡ ❈❡♥tr❛❧✐t② ❬❑♦s❝❤üt③❦✐ ❡t ❛❧✳✱ ✷✵✵✺❪✱ s❡♥❞♦✱ ♣❛r❛ ❣r❛❢♦s ♥ã♦ ❞✐r❡❝✐♦♥❛❞♦sCD(v) =g(v) ♦♥❞❡v é ✉♠ ♥ó q✉❛❧q✉❡r ❞♦ ❣r❛❢♦ ❡ g é s❡✉ ❣r❛✉✳ ◆♦ ❝❛s♦ ❞❡ ❣r❛❢♦s ❞✐r❡❝✐♦♥❛❞♦s✱ ❞✉❛s ✈❛r✐❛çõ❡s sã♦ ❛❞❡q✉❛❞❛s✿ ■♥✲❉❡❣r❡❡
❈❡♥tr❛❧✐t②✱ CIn−Degree(v) = g−(v)✱ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ❣r❛✉ ❞❡ ❡♥tr❛❞❛ ❞♦ ♥ó v ❡ ♦ ❖✉t✲❉❡❣r❡❡ ❈❡♥tr❛❧✐t②✱ COut−Degree(v) = g+(v)✱ q✉❡ ❝♦rr❡s♣♦♥❞❡ ❛♦ ❣r❛✉ ❞❡ s❛í❞❛ ❞♦ ♥óv✳ ❊♠ ❬❍❛❣❡ ❛♥❞ ❍❛r❛r②✱ ✶✾✾✺❪ é ♣r♦♣♦st❛ ❛ ♠étr✐❝❛ ❊❝❝❡♥tr✐❝✐t② ❈❡♥tr❛❧✐t② ❞❡✜✲
♥✐❞❛✱ ♣❛r❛ ✉♠ ♥ó v q✉❛❧q✉❡r✱ ❝♦♠♦ CEccentricity(v) = max{d(u,v1 ):v∈V}✱ ♦✉ s❡❥❛✱ v s❡rá ♦ ♥ó ♠❛✐s ❝❡♥tr❛❧ s❡ ♣♦ss✉✐r ❛ ♠❡♥♦r ❞✐stâ♥❝✐❛ ♠á①✐♠❛ ❡♥tr❡ q✉❛❧q✉❡r ✈ért✐❝❡✳
✷✳✶✳ ❈❡♥tr❛❧✐❞❛❞❡ ✼
❞❛s ❞✐stâ♥❝✐❛s ❞❡ ✉♠ ♥ó q✉❛❧q✉❡r ❛té ♦s ❞❡♠❛✐s ❡✱ ❛tr✐❜✉✐ ♦ ✐♥✈❡rs♦ ❞❡st❡ ✈❛❧♦r ❛♦s ♥ós✱ ❞❡st❛ ❢♦r♠❛✱ ♦ ♥ó ❝✉❥♦ s♦♠❛tór✐♦ ❢♦r ♦ ♠❡♥♦r✱ s❡rá ♦ ♠❛✐s ❝❡♥tr❛❧✱ ♦✉ ♦ ♥ó q✉❡ ❡stá ♠❛✐s ♣❡rt♦ ❞♦s ❞❡♠❛✐s✳ ❖✉tr❛s ♠étr✐❝❛s ♠❡♥♦s ❞✐❢✉♥❞✐❞❛s q✉❡ t❛♠❜é♠ ❢❛③❡♠ ✉s♦ ❞❛ ❝❡♥tr❛❧✐❞❛❞❡ sã♦ ■♥❢♦r♠❛t✐♦♥ ❈❡♥tr❛❧✐t② ❬❙t❡♣❤❡♥s♦♥ ❛♥❞ ❩❡❧❡♥✱ ✶✾✽✾❪ ❡ ♦ ❈❡♥✲ tr♦✐❞ ❬❑♦s❝❤üt③❦✐ ❡t ❛❧✳✱ ✷✵✵✺❪✳
❆❧é♠ ❞✐st♦✱ ♦✉tr❛ ❝❛r❛❝t❡ríst✐❝❛ ❜❛s❡ ✉s❛❞❛ ♣❡❧❛s ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ é ♦ ❝❛✲ ♠✐♥❤♦ ♠í♥✐♠♦✱ ✉t✐❧✐③❛❞♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♣❡❧♦ ❙tr❡ss ❈❡♥tr❛❧✐t② ❬❙❤✐♠❜❡❧✱✶✾✺✸❪✱ ❙❤♦rt❡st✲ ♣❛t❤ ❇❡t✇❡❡♥❡ss ❈❡♥tr❛❧✐t② q✉❡✱ ♥❡st❡ tr❛❜❛❧❤♦ s❡rá ❝❤❛♠❛❞♦ ❛♣❡♥❛s ❞❡ ❇❡t✇❡❡♥♥❡ss ❡ ❘❡❛❝❤ ❬●✉t♠❛♥✱ ✷✵✵✹❀ ●♦❧❞❜❡r❣ ❡t ❛❧✳✱ ✷✵✵✻❪✳ ❖ ❙tr❡ss ❞❡ ✉♠ ♥ó v q✉❛❧q✉❡r ♣♦❞❡
s❡r ❞❡✜♥✐❞♦ ❝♦♠♦✿
CStress(v) =
X
a6=v∈V
X
t6=v∈V
σat(v) ✭✷✳✶✮
♦♥❞❡ a ❡ t sã♦ t♦❞♦s ♦s ♣❛r❡s ❞❡ ♥ós ❞✐st✐♥t♦s ❞♦ ❣r❛❢♦ ❡ σat(v) é ♦ ♥ú♠❡r♦ ❞❡ ❝❛♠✐♥❤♦s ♠í♥✐♠♦s q✉❡ ♣❛rt❡♠ ❞❡ a❛té t q✉❡ ♣❛ss❛♠ ♣❡❧♦ ✈ért✐❝❡v✳ ❏á ♦ ❇❡t✇❡❡♥♥❡ss
❞❡ ✉♠ ♥ó v q✉❛❧q✉❡r ♣♦❞❡ s❡r ❞❡✜♥✐❞♦ ❝♦♠♦ s❡ s❡❣✉❡✿
CBetweenness(v) =
X
a6=v∈V
X
t6=v∈V
σat(v) σat
✭✷✳✷✮
♦♥❞❡a❡tsã♦ t♦❞♦s ♦s ♣❛r❡s ❞❡ ♥ós ❞✐st✐♥t♦s ❞♦ ❣r❛❢♦✱σaté ♦ ♥ú♠❡r♦ ❞❡ ❝❛♠✐♥❤♦s ♠í♥✐♠♦s q✉❡ ♣❛rt❡♠ ❞❡ a ❛té t ❡σat(v) é ♦ ♥ú♠❡r♦ ❞❡ ❝❛♠✐♥❤♦s ♠í♥✐♠♦s q✉❡ ♣❛rt❡♠ ❞❡ a ❛té t✱ ♠❛s q✉❡ ♣❛ss❛♠ ♣❡❧♦ ✈ért✐❝❡ v✳ ❊♠ ❬❋r❡❡♠❛♥✱ ✶✾✼✼❪ ❡st❛ ♠étr✐❝❛ ❢♦✐
♣r♦♣♦st❛ ❝♦♠♦ ❢♦r♠❛ ❞❡ s❡ ❝♦♥t♦r♥❛r ♦ ♣r♦❜❧❡♠❛ q✉❡ ❡①✐st❡ ❛♦ s❡ ❛♣❧✐❝❛r ♦ ❈❧♦s❡♥❡ss ❡♠ ❣r❛❢♦s ❞❡s❝♦♥❡①♦s✳ ❆ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞♦✐s ✈ért✐❝❡s ♥ã♦ ❝♦♥❡①♦s é✱ ✉s✉❛❧♠❡♥t❡✱ ❞❡✜♥✐❞❛ ❝♦♠♦ ✐♥✜♥✐t❛ ❡✱ ✉♠❛ ✈❡③ q✉❡ ♦ ❈❧♦s❡♥❡ss s♦♠❛ ♦ ✐♥✈❡rs♦ ❞❡st❛s ❞✐stâ♥❝✐❛s✱ ♥❡♥❤✉♠❛ ✐♥❢♦r♠❛çã♦ út✐❧ ♣♦❞❡r✐❛ s❡r ❡①tr❛í❞❛ ❞♦ ❝á❧❝✉❧♦✳ ❏á ♦ ❇❡t✇❡❡♥♥❡ss ♥ã♦ ♣♦ss✉✐ t❛❧ ♣r♦❜❧❡♠❛✱ ♣♦✐s ❛ ✐♥❡①✐stê♥❝✐❛ ❞❡ ✉♠ ❝❛♠✐♥❤♦ ❡♥tr❡ ❞♦✐s ♥ós ❛❞✐❝✐♦♥❛rá ③❡r♦ ♥❛ ♣❛r❝❡❧❛ ❞♦ s♦♠❛tór✐♦ ❡s♣❡❝í✜❝❛ r❡❢❡r❡♥t❡ ❛q✉❡❧❡ ♥ó✳ ❙tr❡ss ❡ ❇❡t✇❡❡♥♥❡ss sã♦ ♠étr✐❝❛s s✐♠✐❧❛r❡s✱ ♠❛s ♦ ♣r✐♠❡✐r♦ ✉s❛ ❛ ❝♦♥t❛❣❡♠ ❛❜s♦❧✉t❛ ❞♦s ❝❛♠✐♥❤♦s ♠í♥✐♠♦s ❡♥q✉❛♥t♦ ♦ s❡❣✉♥❞♦ ✉s❛ ❛ s♦♠❛ r❡❧❛t✐✈❛ ❞♦ ♥ú♠❡r♦ ❞❡ ❝❛♠✐♥❤♦s ♣❛r❛ t♦❞♦s ♦s ♣❛r❡s ❞❡ ✈ért✐❝❡s✳ ❯♠❛ ❢♦r♠❛ ❞❡ s❡ ✐♥t❡r♣r❡t❛r ♦ ❇❡t✇❡❡♥♥❡ss✱ é q✉❡ ❡st❛ ♠étr✐❝❛ ♠❡♥s✉r❛ ♦ ❝♦♥tr♦❧❡ ❞❡ ✉♠ ♥ó s♦❜r❡ ♦ ✢✉①♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❡♥tr❡ ♦s ❞❡♠❛✐s ♥ós✳
❍á ❛✐♥❞❛ ❛ ✉t✐❧✐③❛çã♦ ❞❛ ✐♠♣♦rtâ♥❝✐❛ ❞♦s ✈✐③✐♥❤♦s ♣❛r❛ ♦ ❝á❧❝✉❧♦ ❞❛ ✐♠♣♦rtâ♥❝✐❛ ♣ró♣r✐❛✱ ❝♦♠♦ é ♦ ❝❛s♦ ❞❛ ♠étr✐❝❛ ❊✐❣❡♥✈❡❝t♦r ❬❇♦♥❛❝✐❝❤✱ ✶✾✼✷❪✱ ♦✉ ❛✐♥❞❛ ❛s ♠étr✐❝❛s ❝♦rr❡❧❛t❛s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞❡ ♣á❣✐♥❛s ❲❡❜ ❍✉❜ ❙❝♦r❡✱ ❆✉t❤♦r✐t② ❬❑❧❡✐♥❜❡r❣✱ ✶✾✾✾❪ ❡ P❛❣❡❘❛♥❦ ❬❇r✐♥✱✶✾✾✽❪✳
✽ ❈❛♣ít✉❧♦ ✷✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s
s❛s ár❡❛s ❞♦ ❝♦♥❤❡❝✐♠❡♥t♦✳ ◆❛ ❜✐♦❧♦❣✐❛✱ ❛s ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❢♦r❛♠ ❛♣❧✐❝❛❞❛s ❡♠ r❡❞❡s ❜✐♦♠♦❧❡❝✉❧❛r❡s ❬▼❛s♦♥ ❛♥❞ ❱❡r✇♦❡r❞✱ ✷✵✵✼❪✱ ❝❛❞❡✐❛s ❛❧✐♠❡♥t❛r❡s ❬❏♦r❞❛♥ ❡t ❛❧✳✱
✷✵✵✼❀❏♦r❞❛♥✱✷✵✵✾❪ s❡♥❞♦ q✉❡✱ ❝♦♠♦ r❡s✉❧t❛❞♦ ❞❡st❡ ú❧t✐♠♦✱ ❢♦✐ ♣r♦♣♦st❛ ❛ ♠étr✐❝❛ ❘ ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❡s♣❡❝í✜❝❛ ♣❛r❛ t❛❧ ❝♦♥t❡①t♦✳ ➪r❡❛s ❝♦♠♦ ✉r❜❛♥✐s♠♦ ❡ s♦❝✐♦❧♦❣✐❛ t❛♠❜é♠ ❡st✉❞❛♠ ❡ ❛♣❧✐❝❛♠ ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡✳ P♦r ❡①❡♠♣❧♦✱❈r✉❝✐tt✐ ❡t ❛❧✳ ❬✷✵✵✻❪ ❢❛③❡♠ ✉♠ ❡st✉❞♦ s♦❜r❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❛ ❝❡♥tr❛❧✐❞❛❞❡ ❡♠ ❣r❛❢♦s q✉❡ r❡♣r❡s❡♥t❛♠ ❛ ♠❛❧❤❛ ✈✐ár✐❛ ❞❡ ❞✐✈❡rs❛s ❝✐❞❛❞❡s ♥♦ ♠✉♥❞♦✳ ◆❡ss❡ tr❛❜❛❧❤♦ sã♦ ❞❡s❝r✐t❛s ♣♦ssí✈❡✐s ❛♣❧✐❝❛çõ❡s ❡ ❛ ✐♥✢✉ê♥❝✐❛ ❞❡ ❡st✉❞♦s ❞❛ ❝❡♥tr❛❧✐❞❛❞❡ s♦❜r❡ ❛♠❜✐❡♥t❡s ✉r❜❛♥♦s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ♥♦ ♣❧❛♥❡❥❛♠❡♥t♦ ❞♦ ✢✉①♦ ❞❡ ❝❛rr♦s✱ ♦✉ ♣❡ss♦❛s ❬P♦rt❛ ❡t ❛❧✳✱✷✵✵✽❪✳ ❊♠ ❬❋✉ ❛♥❞ ❈❤❡♥✱
✷✵✵✽❪✱ é ❢❡✐t♦ ✉♠ ❡st✉❞♦ ❞❡ ❝❛s♦ s♦❜r❡ ♦ ❛t✐✈✐s♠♦ ✈✐rt✉❛❧ ♣❡❧❛ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❞♦ ❚✐❜❡t ❛tr❛✈és ❞❡ ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡
❆ ♣❛rt✐r ❞♦s tr❛❜❛❧❤♦s r❡❧❛t❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ✜❝♦✉ ❡✈✐❞❡♥t❡ q✉❡ ♥❡♠ t♦❞❛ ♠é✲ tr✐❝❛ ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ é ❛♣r♦♣r✐❛❞❛ ♣❛r❛ t♦❞♦ ❝♦♥t❡①t♦✳ ❈♦♠ ♦ t❡♠♣♦✱ ✈❛r✐❛çõ❡s ❢♦r❛♠ s❡♥❞♦ ♣r♦♣♦st❛s✱ s❡♥❞♦ ❛ ♠❛✐♦r✐❛ ❜❛s❡❛❞❛ ♥❛s ♠étr✐❝❛s ❞❡s❝r✐t❛s ❛♥t❡r✐♦r♠❡♥t❡✳ P♦r s❡r ✉♠❛ ♠étr✐❝❛ ❛♠♣❧❛♠❡♥t❡ ❡st✉❞❛❞❛✱ ❞✐✈❡rs❛s ✈❛r✐❛çõ❡s ❞♦ ❇❡t✇❡❡♥♥❡ss ❢♦r❛♠ ♣r♦✲ ♣♦st❛s ♥❛ ❧✐t❡r❛t✉r❛✳ P♦r ❡①❡♠♣❧♦✱ ♦ ❋❧♦✇ ❇❡t✇❡❡♥♥❡ss ❈❡♥tr❛❧✐t② ✭❋❇❈✮ ❬❋r❡❡♠❛♥ ❡t ❛❧✳✱✶✾✾✶❪ ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ t♦❞♦s ♦s ❝❛♠✐♥❤♦s✱ ❡♥tr❡ ❢♦♥t❡ ❡ ❞❡st✐♥♦✱ ♣❡❧♦s q✉❛✐s ❛s ✐♥❢♦r♠❛çõ❡s tr❛❢❡❣❛♠ q✉❛♥❞♦ ✉♠ ✢✉①♦ ♠á①✐♠♦ é ✐♥s❡r✐❞♦ ♥❛ r❡❞❡✳ ❚❛♥t♦ ❛ ♠é✲ tr✐❝❛ ♦r✐❣✐♥❛❧ q✉❛♥t♦ ♦ ❋❇❈ ❢❛③❡♠ s✉♣♦s✐çõ❡s ❞❡ ♦t✐♠❛❧✐❞❛❞❡✱ ♦✉ s❡❥❛✱ ♣❛r❛ ❛ ♣r✐♠❡✐r❛✱ ❛♣❡♥❛s ❝❛♠✐♥❤♦s ❣❡♦❞és✐❝♦s sã♦ ❝♦♠♣✉t❛❞♦s✱ ❡♥q✉❛♥t♦ ♥❛ s❡❣✉♥❞❛✱ ❛♣❡♥❛s ❝❛♠✐♥❤♦s r❡❢❡r❡♥t❡s ❛♦ ✢✉①♦ ♠á①✐♠♦✳ ❈♦♠♦ r❡s✉❧t❛❞♦✱ ◆❡✇♠❛♥ ❬✷✵✵✺❪ ♣r♦♣ôs ✉♠❛ ✈❡rsã♦ ❞♦ ❇❡t✇❡❡♥♥❡ss q✉❡ ❝♦♥s✐❞❡r❛ t♦❞♦s ♦s ❝❛♠✐♥❤♦s ❡♥tr❡ ✉♠ ♣❛r ❞❡ ♥ós✱ ✉♠❛ ✈❡③ q✉❡ ❡st❛ é ✉♠❛ s✉♣♦s✐çã♦ r❛③♦á✈❡❧ ♣❛r❛ ❛♠❜✐❡♥t❡s ❝✉❥❛ tr♦❝❛ ❞❡ ❞❛❞♦s ♥❡♠ s❡♠♣r❡ ❡stá r❡str✐t❛ ❛♦s ❝❛♠✐♥❤♦s ♠í♥✐♠♦s✳ ❊ss❛ ♠étr✐❝❛ ✐♥❞✐❝❛✱ ❡♠ ❡ssê♥❝✐❛✱ ♦ q✉ã♦ ❢r❡q✉❡♥t❡ ✉♠ ✈ért✐❝❡ ✐♥t❡r♠❡❞✐ár✐♦i s❡rá ✈✐s✐t❛❞♦ q✉❛♥❞♦ s❡ ❝❛♠✐♥❤❛ ❞❡ ✉♠ ✈ért✐❝❡j ❛té ♦✉tr♦ k✳ ❋r❡❡♠❛♥
❬✶✾✼✼❪ ♣r♦♣ôs ❛ ♠étr✐❝❛ ❈❡♥tr❛❧ P♦✐♥t ❉♦♠✐♥❛♥❝❡ q✉❡ ❢❛③ ✉s♦ ❞♦ ❇❡t✇❡❡♥♥❡ss ♠á①✐♠♦ ❡ ❛♣❧✐❝❛ ❛ ♥♦r♠❛❧✐③❛çã♦ ❞♦ ✈❛❧♦r ❞❡ ✐♠♣♦rtâ♥❝✐❛ ❞♦s ✈ért✐❝❡s ❡♥tr❡ 0✱ ♣❛r❛ ✈ért✐❝❡s ❞❡
✉♠ ❣r❛❢♦ ❝♦♠♣❧❡t♦ ❡1✱ ♣❛r❛ ♦ ✈ért✐❝❡ ❝❡♥tr❛❧ ❞❡ ✉♠ ❣r❛❢♦ ❡str❡❧❛✳ ❑r❛✉s❡ ❡t ❛❧✳ ❬✷✵✵✻❪
♣r♦♣✉s❡r❛♠ ♦ ❈✉♠✉❧❛t✐✈❡ ❇❡t✇❡❡♥❡ss q✉❡ ❛tr✐❜✉✐ ❛♦ ♥ói✉♠❛ ✐♠♣♦rtâ♥❝✐❛ ❜❛s❡❛❞❛ ♥♦s
✈❛❧♦r❡s ❞♦ ❇❡t✇❡❡♥♥❡ss ❧♦❝❛❧ ❡ ❞♦s ♥ós q✉❡ tê♠ ✉♠❛ ❛r❡st❛ ✐♥❝✐❞❡♥t❡ à i✳ ❊♠ ❬❲❛♥❣ ❡t ❛❧✳✱ ✷✵✵✽❪✱ é ♣r♦♣♦st❛ ✉♠❛ ♠étr✐❝❛ ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ q✉❡ ❝❛❧❝✉❧❛ ❛ ✐♠♣♦rtâ♥❝✐❛ ❞❡ ✉♠ ♥ó ❛tr❛✈és ❞❡ s❡✉ ✈❛❧♦r ❞❡ ❇❡t✇❡❡♥♥❡ss✱ ❣r❛✉ ♣ró♣r✐♦ ❡ ❞❡ s❡✉s ✈✐③✐♥❤♦s✳ ◆❡ss❡ tr❛❜❛❧❤♦ é ❢❡✐t♦ ✉♠ ❡st✉❞♦ ❞❡ ❝❛s♦ ❡♠ ✉♠❛ r❡❞❡ s❡①✉❛❧ ❞❡ r❡❧❛❝✐♦♥❛♠❡♥t♦s ❞❛ ❆■❉❙ ♥❛ q✉❛❧✱ s❡❣✉♥❞♦ ♦s r❡s✉❧t❛❞♦s ❛♣r❡s❡♥t❛❞♦s✱ ❛ ♠étr✐❝❛ ♣r♦♣♦st❛ ❢♦✐ ♠❛✐s ❞✐s❝r✐♠✐♥❛t✐✈❛ ❞♦ q✉❡ ♦ ❈❧♦s❡♥❡ss✱ ❇❡t✇❡❡♥♥❡ss ❡ ♦ ❣r❛✉ ❞♦ ♥ó✱ ✐♥❞✐✈✐❞✉❛❧♠❡♥t❡✳
✷✳✶✳ ❈❡♥tr❛❧✐❞❛❞❡ ✾
♠❛✐s ❝❡♥tr❛❧ q✉❡✱ q✉❛s❡ s❡♠♣r❡✱ é ♦ ❡❧❡♠❡♥t♦ ♠❛✐s ✐♠♣♦rt❛♥t❡✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❈♦r♦✲ ♠✐♥❛ ❡t ❛❧✳ ❬✷✵✵✽❪ ♣r♦♣õ❡♠ ✈❡rsõ❡s ❞❛s ♠étr✐❝❛s ❈❧♦s❡♥❡ss✱ ❉❡❣r❡❡ ❈❡♥tr❛❧✐t②✱ ❉❡♥s✐t② ❡ ❉✐✈❡rs✐t② ♣❛r❛ r❡❞❡s ❝♦♠ ❞✉❛s ❡♥t✐❞❛❞❡s ✐❣✉❛❧♠❡♥t❡ ❝❡♥tr❛✐s ❡ q✉❡ s❡❥❛♠ ♠❛✐s ❝❡♥✲ tr❛✐s q✉❡ ❛s ❞❡♠❛✐s✳ ❱❛❧❡♥t❡ ❛♥❞ ❋♦r❡♠❛♥ ❬✶✾✾✽❪ ♣r♦♣õ❡♠ ❞✉❛s ♠étr✐❝❛s ❜❛s❡❛❞❛s ♥♦ ❈❧♦s❡♥❡ss✿ ■♥t❡❣r❛t✐♦♥✱ q✉❡ ♠❡❞❡ ♦ q✉ã♦ ❜❡♠ ❝♦♥❡❝t❛❞♦ ✉♠ ♠❡♠❜r♦ ❞❛ r❡❞❡ ❡stá ❡ ❘❛❞✐❛❧✐t②✱ q✉❡ ♠❡♥s✉r❛ ♦ q✉❛♥t♦ ❛s ❧✐❣❛çõ❡s ❞❡ ✉♠ ♥ó ❡①♣❛♥❞❡♠✲s❡ ♣❡❧❛ r❡❞❡✳ ❱ért✐✲ ❝❡s ❝♦♠ ✐♥t❡❣r❛t✐♦♥ ❛❧t♦ ✜❝❛♠✱ ♠❛✐s ❝❡❞♦✱ ❝✐❡♥t❡s ❞❡ ✐♥❢♦r♠❛çõ❡s tr❛❢❡❣❛❞❛s ♣❡❧❛ r❡❞❡ ♣♦✐s✱ ♥❛ ♠é❞✐❛✱ ❡❧❡s ❡stã♦ ♠❛✐s ♣ró①✐♠♦s ❞♦s ❞❡♠❛✐s ✈ért✐❝❡s✱ ❡♥q✉❛♥t♦ ✈ért✐❝❡s ❝♦♠ ✈❛❧♦r ❛❧t♦ ❞❡ r❛❞✐❛❧✐t② ❞❡✈❡r✐❛♠ s❡r ❜♦♥s ❡♠✐ss♦r❡s ❞❡ ✐♥❢♦r♠❛çã♦✳ ✈❛♥ ❞❡♥ ❇r✐♥❦ ❛♥❞ ●✐❧❧❡s ❬✷✵✵✵❪ ♣r♦♣õ❡♠ ❞✉❛s ♠étr✐❝❛s ♣❛r❛ ❞✐❣r❛❢♦s ❜❛s❡❛❞❛s ♥♦ ❈❧♦s❡♥❡ss✱β✲♠❡❛s✉r❡ ❡
s♦✉r❝❡✲♠❡❛s✉r❡✱ q✉❡ t❛♠❜é♠ ♣♦ss✉❡♠ ✈❛r✐❛çã♦ ❛♣❧✐❝á✈❡❧ ♣❛r❛ ❣r❛❢♦s ♥ã♦ ❞✐r❡❝✐♦♥❛❞♦s✳ ❊♠ ❬❉❛♥❣❛❧❝❤❡✈✱✷✵✵✻❪✱ é ♣r♦♣♦st❛ ✉♠❛ ♠étr✐❝❛ ♠❛✐s s❡♥sí✈❡❧ ♣❛r❛ ✈❡r✐✜❝❛r ❛ r❡s✐stê♥✲ ❝✐❛ ❛ ❛t❛q✉❡s ❞❡ ✉♠ r❡❞❡✱ ♠❡s♠♦ q✉❡ ❛ ♠❡s♠❛ s❡❥❛ ❞❡s❝♦♥❡①❛✳ ❊♠ ❬❍❛❣❡ ❛♥❞ ❍❛r❛r②✱
✶✾✾✺❪✱ é ♣r♦♣♦st❛ ✉♠❛ ✈❛r✐❛çã♦ ❞♦ ❊❝❝❡♥tr✐❝✐t② ❝♦♠ ❛ ✐♥❝♦r♣♦r❛çã♦ ❞♦ ❝❛♠✐♥❤♦ ❝❡♥tr❛❧ ❞♦ ❣r❛❢♦ ♥♦ ❝á❧❝✉❧♦✳ ❊♠ ❬❑r❡ts❝❤♠❡r ❛♥❞ ❑r❡ts❝❤♠❡r✱ ✷✵✵✼❪✱ é ♣r♦♣♦st❛ ✉♠❛ ♠étr✐❝❛ s✐♠✐❧❛r ❛♦ ❉❡❣r❡❡ ❈❡♥tr❛❧✐t② ❝♦♠♦ ✉♠❛ ❢♦r♠❛ ❞❡ ❢❛③❡r ✐♥❢❡rê♥❝✐❛s s♦❜r❡ ❛ ❝♦✲❛✉t♦r✐❛ ❡ ❝✐t❛çõ❡s ❞❡ ❛rt✐❣♦s ❝✐❡♥tí✜❝♦s✳
✷✳✶✳✸ ❘♦t❡❛♠❡♥t♦ ❡♠ r❡❞❡s ❛❞✲❤♦❝
❆♣❡s❛r ❞♦s ❡st✉❞♦s ❞❡ ♠étr✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡ ❡♠ ❞✐✈❡rs♦s ❝♦♥t❡①t♦s✱ ❡①✐st❡♠ ♣♦✉✲ ❝♦s tr❛❜❛❧❤♦s ❡♠ r♦t❡❛♠❡♥t♦ ♣❛r❛ ❘❙❙❋s q✉❡ ✉s❛♠ ❡ss❛s ♠étr✐❝❛s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r ❝❛✉s❛ ❞❛s r❡str✐çõ❡s ❝♦♠♣✉t❛❝✐♦♥❛✐s q✉❡ ✐♥✈✐❛❜✐❧✐③❛♠ ❛ ❝♦♠♣✉t❛çã♦ ❞❡ ✈ár✐❛s ❞❛s ♠étr✐❝❛s ❝❧áss✐❝❛s ❞❡ ❝❡♥tr❛❧✐❞❛❞❡✳
❑r❛✉s❡ ❡t ❛❧✳ ❬✷✵✵✻❪ ♣r♦♣õ❡♠ ✉♠❛ ❡str✉t✉r❛ ❞❡ r♦t❡❛♠❡♥t♦ ♣❛r❛ r❡❞❡s ❛❞✲❤♦❝ ❞❡ ✈ár✐♦s s❛❧t♦s q✉❡ ✈✐s❛ ♠❛①✐♠✐③❛r ❛ ✈❛③ã♦ ✜♠✲❛✲✜♠ ❝♦♠ ❛ ❛❞✐çã♦ ❞❡ ❡♥❧❛❝❡s ♥❛ ♣❡r✐❢❡r✐❛ ❞❛ r❡❞❡✳ ❖ ♦❜❥❡t✐✈♦ é ♠♦❞✐✜❝❛r ❛ ❡str✉t✉r❛ ❞❛ r❡❞❡ ❝♦♠♦ ❢♦r♠❛ ❞❡ ♠✐♥✐♠✐③❛r ❛ q✉❛♥t✐✲ ❞❛❞❡ ❞❡ ♥ós ❝♦♠ ❝❡♥tr❛❧✐❞❛❞❡ ♠✉✐t♦ s✉♣❡r✐♦r ❛♦s ❞❡♠❛✐s ♣♦✐s✱ ❡ss❡s ♥ós ♣r♦✈❛✈❡❧♠❡♥t❡ s❡rã♦ ♣♦♥t♦s ❞❡ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦✳ ❆❧é♠ ❞✐st♦✱ é ♣r♦♣♦st❛ ✉♠❛ ♠étr✐❝❛ ❜❛s❡❛❞❛ ♥♦ ❇❡t✇❡❡♥♥❡ss q✉❡ é ❝♦♠♣✉t❛❞❛ ❞❡ ♠❛♥❡✐r❛ ❝❡♥tr❛❧✐③❛❞❛ ❝♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ❛✈❛❧✐❛r ♦ ❣❛✲ ♥❤♦ ❞❛ ♠♦❞✐✜❝❛çã♦ ♥❛ ❡str✉t✉r❛ ❞❛ r❡❞❡✳ P♦st❡r✐♦r♠❡♥t❡✱ ❨✉ ❡t ❛❧✳ ❬✷✵✵✼❪ ✉t✐❧✐③❛r❛♠ ❛ ♠❡s♠❛ ♠étr✐❝❛ ❝♦♠♦ ❢♦r♠❛ ❞❡ ❡✈✐t❛r ♦ ❝♦♥❣❡st✐♦♥❛♠❡♥t♦ ❡♠ ♥ós ♠❛✐s ❝❡♥tr❛✐s✱ s❡♠ ♠♦❞✐✜❝❛çõ❡s ❡str✉t✉r❛✐s ♥❛ r❡❞❡✳
❯♠❛ ❛❜♦r❞❛❣❡♠ s❡♠❡❧❤❛♥t❡ ❛♦ tr❛❜❛❧❤♦ ❛q✉✐ ♣r♦♣♦st♦ é ❡st✉❞❛❞❛ ❡♠ ❬❙♦✉✐❤❧✐ ❡t ❛❧✳✱ ✷✵✵✾❪✳ ❊ss❡ tr❛❜❛❧❤♦ ❡st❛❜❡❧❡❝❡ ✉♠ ♠❡❝❛♥✐s♠♦ ❞❡ ❜❛❧❛♥❝❡❛♠❡♥t♦ ❞❡ ❝❛r❣❛ q✉❡ ❡✈✐t❛ ♦ trá❢❡❣♦ ❡♠ r❡❣✐õ❡s ❝❡♥tr❛✐s ❞❛ r❡❞❡ q✉❡ sã♦ ✐❞❡♥t✐✜❝❛❞❛s ♣❡❧❛ ♠étr✐❝❛ ♣r♦♣♦st❛
✶✵ ❈❛♣ít✉❧♦ ✷✳ ❚r❛❜❛❧❤♦s ❘❡❧❛❝✐♦♥❛❞♦s
♥ú♠❡r♦ ❞❡ ♥ós ❡♥tr❡ ♦r✐❣❡♠ ❡ ❞❡st✐♥♦✱ ♦✉ s❡❥❛✱ r♦t❛s ❝❡♥tr❛✐s✱ q✉❡ ❣❡r❛❧♠❡♥t❡ ♣♦ss✉❡♠ ♣♦✉❝♦s ♥ós✱ s❡rã♦ ❡✈✐t❛❞❛s✳
✷✳✷ ❆❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ❘❙❙❋s
✷✳✷✳✶ ❉❡s❛✜♦s
❖ r♦t❡❛♠❡♥t♦ ❡♠ ❘❙❙❋s é t❛r❡❢❛ ❢✉♥❞❛♠❡♥t❛❧ ❡ ❞❡s❛✜❛❞♦r❛✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ♣♦ss✐✲ ❜✐❧✐❞❛❞❡ ❞❡ ❤❛✈❡r ♠✐❧❤❛r❡s ❛ ❝❡♥t❡♥❛s ❞❡ ♠✐❧❤❛r❡s ❞❡ ♥ós s❡♥s♦r❡s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ❛ ✐♥✈✐❛❜✐❧✐❞❛❞❡ ❞❡ s❡ ❝r✐❛r ✉♠❛ t❛❜❡❧❛ ❞❡ ❡♥❞❡r❡ç❛♠❡♥t♦ ❣❧♦❜❛❧ ❬❆❧✲❦❛r❛❦✐ ❛♥❞ ❑❛♠❛❧✱
✷✵✵✹❪✳ ●❡r❛❧♠❡♥t❡✱ ❛❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ♣❛r❛ ❘❙❙❋s tê♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ❧❡✈❛r ♦s ❞❛❞♦s ♣♦r r♦t❛s q✉❡ ♠✐♥✐♠✐③❛♠ ♦ ♥ú♠❡r♦ ❞❡ r❡tr❛♥s♠✐ssõ❡s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♦ ❣❛st♦ ❞❡ ❡♥❡r❣✐❛ ❞❛ r❡❞❡✳ P❛r❛ t❛♥t♦✱ ❛ ❡str✉t✉r❛ ❞❡ r♦t❡❛♠❡♥t♦ ♣r❡❝✐s❛ s❡r ❝♦♥❝❡❜✐❞❛ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ t♦❞♦s ♦s ♥ós ❢♦♥t❡✱ ❡✳❣✳✱ ♥ós q✉❡ ❞❡t❡❝t❛r❛♠ ✉♠ ❡✈❡♥t♦✱ ♣♦ss❛♠ ❡s❝♦❛r s✉❛s ❧❡✐t✉r❛s ❛té ♦ s✐♥❦ ❞❛ ♠❛♥❡✐r❛ ♠❛✐s ❡✜❝✐❡♥t❡✱ ♦✉ s❡❥❛✱ r❡q✉✐s✐t❛♥❞♦ ♦ ♠❡♥♦r ♥ú♠❡r♦ ❞❡ r❡tr❛♥s♠✐ssõ❡s ♣♦ssí✈❡❧✳ ❆❧é♠ ❞✐st♦✱ ❛♦ r♦t❡❛r ♣❛❝♦t❡s✱ ♦ ❛❧❣♦r✐t♠♦ ♣♦❞❡ ✉t✐❧✐③❛r té❝♥✐❝❛s ❝♦♠♦ ❛❣r❡❣❛çã♦ ❞❡ ❞❛❞♦s ❬◆❛❦❛♠✉r❛ ❡t ❛❧✳✱✷✵✵✾❪✱ q✉❡ ❡①♣❧♦r❛ ❛ ❝♦rr❡❧❛çã♦ ❞♦s ❞❛❞♦s ❡ r❡❛❧✐③❛ ❛ ❛❣r❡❣❛çã♦ ❡♠ ♥ós ✐♥t❡r♠❡❞✐ár✐♦s r❡❞✉③✐♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ ♠❡♥s❛❣❡♥s tr♦❝❛❞❛s ♥❛ r❡❞❡✳
❆ ❝♦♥str✉çã♦ ❞❛ ár✈♦r❡ ❞❡ ❛❣r❡❣❛çã♦ ót✐♠❛ é ✉♠ ♣r♦❜❧❡♠❛ ◆P✲❉✐❢í❝✐❧ ❬❆❧✲❑❛r❛❦✐ ❡t ❛❧✳✱✷✵✵✹❪ q✉❡ é ❡q✉✐✈❛❧❡♥t❡ ❛♦ ♣r♦❜❧❡♠❛ ❞❛ ➪r✈♦r❡ ❞❡ ❙t❡✐♥❡r ❬❑r✐s❤♥❛♠❛❝❤❛r✐ ❡t ❛❧✳✱
✷✵✵✷❪✳ ❊st❡ ♣r♦❜❧❡♠❛ é ❛♠♣❧❛♠❡♥t❡ ❝♦♥❤❡❝✐❞♦ ❡✱ ❢♦r♠❛❧♠❡♥t❡✱ ❡❧❡ ♣♦❞❡ s❡r ❛♣r❡s❡♥t❛❞♦ ❝♦♠♦ s❡ s❡❣✉❡✿ s❡❥❛ ✉♠❛ r❡❞❡ r❡♣r❡s❡♥t❛❞❛ ❝♦♠♦ ✉♠ ❣r❛❢♦ G = (V, E)✱ ♦♥❞❡ V =
{v1, v2, v3, ..., vn} é ♦ ❝♦♥❥✉♥t♦ ❞❡ ♥ós s❡♥s♦r❡s ❡ E = {e1, e2, e3, ..., ei} r❡♣r❡s❡♥t❛ ♦ ❝♦♥❥✉♥t♦ ❞❡ ❛r❡st❛s✱ ❝♦♠ ✉♠ ♣❡s♦ ❛ss♦❝✐❛❞♦✱ q✉❡ ❢❛③❡♠ ❛s ❝♦♥❡①õ❡s ❡♥tr❡ ♦s ♥ós ❞❡
V✳ ❈♦♠♦ ❝♦♥str✉✐r ✉♠❛ ár✈♦r❡ ❞❡ ❝✉st♦ ♠í♥✐♠♦ q✉❡ ❝♦♥❡❝t❡ t♦❞♦s ♦s ♥ós ❢♦♥t❡ F =
{f1, f2, f3, ..., fn} ❡ ♦ s✐♥❦ s❡♥❞♦ q✉❡ F ⊆V✳ ❖ ❝✉st♦ ❞❛ ár✈♦r❡ ❞❡ ❙t❡✐♥❡r r❡s✉❧t❛♥t❡ s❡rá ♦ s♦♠❛tór✐♦ ❞♦ ❝✉st♦ ❞❛s ❛r❡st❛s ❞❛ ár✈♦r❡✳
◆❛ ❧✐t❡r❛t✉r❛✱ ❞✐✈❡rs❛s ❤❡✉ríst✐❝❛s ❡ ❛❧❣♦r✐t♠♦s ❛♣r♦①✐♠❛❞♦s ❢♦r❛♠ ♣r♦♣♦st♦s ♣❛r❛ ❛ r❡s♦❧✉çã♦ ❞♦ ♣r♦❜❧❡♠❛ ❞❛ ➪r✈♦r❡ ❞❡ ❙t❡✐♥❡r✳ ❊♠ ❬❍♦✉❣❛r❞② ❛♥❞ Prö♠❡❧✱ ✶✾✾✾❪ ❡ ❬❘♦❜✐♥s ❛♥❞ ❩❡❧✐❦♦✈s❦②✱ ✷✵✵✵❪ sã♦ ♣r♦♣♦st♦s ❛❧❣♦r✐t♠♦s ❝♦♠ ❢❛t♦r ❞❡ ❛♣r♦①✐♠❛çã♦ ♣❡q✉❡♥♦✱ ✐❣✉❛❧ ❛ ✶✳✺✺✳ ❖ ♣r✐♥❝✐♣❛❧ ♣r♦❜❧❡♠❛ ❞❡st❛s s♦❧✉çõ❡s é q✉❡✱ s❡ ✐♠♣❧❡♠❡♥t❛❞❛s ❝♦♠♦ ❛❧❣♦r✐t♠♦ ❞✐str✐❜✉í❞♦✱ ❛s ♠❡s♠❛s ♥ã♦ s❡rã♦ ❛❞❡q✉❛❞❛s ❛ ✉♠ ❝♦♥t❡①t♦ r❡str✐t♦ ❡♠ t❡r♠♦s ❞❡ ❡♥❡r❣✐❛✱ ❝♦♠♦ é ♦ ❝❛s♦ ❞❛s ❘❙❙❋s✱ ♣♦✐s s❡r✐❛ ♥❡❝❡ssár✐♦ ✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ tr♦❝❛ ❞❡ ♠❡♥s❛❣❡♥s ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞❛ ár✈♦r❡✳
✷✳✷✳ ❆❧❣♦r✐t♠♦s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ❘❙❙❋s ✶✶
❡♠ ❝❧✉st❡r ❬❍✉❛♥❣ ❡t ❛❧✳✱ ✷✵✵✾❀ ❏✐❛ ❡t ❛❧✳✱ ✷✵✵✽❪✱ ❜❛s❡❛❞♦s ❡♠ ár✈♦r❡ ❡ ♥ã♦ ❡str✉t✉✲ r❛❞♦s✳ ❆❧❣♦r✐t♠♦s ❜❛s❡❛❞♦s ❡♠ ár✈♦r❡ ❡ ❡♠ ❝❧✉st❡r sã♦ ❢✉♥❞❛♠❡♥t❛❧♠❡♥t❡ ❞✐st✐♥t♦s✳ Pr♦t♦❝♦❧♦ ❜❛s❡❛❞♦ ❡♠ ❝❧✉st❡r ❝r✐❛ ❣r✉♣♦s ❞❡ ♥ós ❡ ❡s❝♦❧❤❡ ✉♠ ❧í❞❡r ♣❛r❛ ♦ ♠❡s♠♦✱ ♣♦rt❛♥t♦✱ ❡st❡s ♣r♦t♦❝♦❧♦s t❡♠ ♦ ♣♦t❡♥❝✐❛❧ ❞❡ ❛❣r❡❣❛r ♦s ❞❛❞♦s ❞❡♥tr♦ ❞♦ ❝❧✉st❡r✱ s❡♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ tr❛♥s♠✐t✐r ❞❛❞♦s r❡❞✉♥❞❛♥t❡s ❛té ♦ s✐♥❦✳ ❆❧❣♦r✐t♠♦s ❜❛s❡❛❞♦s ❡♠ ár✈♦r❡ ♣r♦❝✉r❛♠ ❝♦♥str✉✐r ❡str✉t✉r❛s ❞❡ r♦t❡❛♠❡♥t♦ ❡♠ ❢♦r♠❛t♦ ❞❡ ár✈♦r❡ q✉❡ ♣♦ss❛ ❡s❝♦❛r ❛s ❧❡✐t✉r❛s ❞♦s ♥ós q✉❡ s❡♥s♦r❡❛r❛♠ ❡✈❡♥t♦s ❛té ♦ s✐♥❦✳ ❉❡st❛ ❢♦r♠❛✱ ❛ ♣r✐♥❝✐♣❛❧ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ❛❣r❡❣❛çã♦ ❞❡st❡s ❛❧❣♦r✐t♠♦s ❡stá ♥♦s ♣♦♥t♦s ❞❡ ❛❣r❡❣❛çã♦✱ q✉❡ sã♦✱ ❣❡r❛❧♠❡♥t❡✱ ♥ós q✉❡ t❡♠ ♠❛✐s ❞❡ ✉♠ ❞❡s❝❡♥❞❡♥t❡ ♥❛ ár✈♦r❡✳ ➱ ✐♠♣♦rt❛♥t❡ r❡ss❛❧t❛r q✉❡ ❡st❛s ❞✉❛s ❛❜♦r❞❛❣❡♥s ♥ã♦ sã♦ ♠✉t✉❛♠❡♥t❡ ❡①❝❧✉s✐✈❛s✱ ♦✉ s❡❥❛✱ ❡①✐st❡♠ ❛❧❣♦r✐t♠♦s q✉❡ ✉t✐❧✐③❛♠ ❛♠❜❛s ❛s ♣♦❧ít✐❝❛s✳ ❆❧❣♦r✐t♠♦s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ■♥❋❘❆ ❬◆❛❦❛♠✉r❛ ❡t ❛❧✳✱✷✵✵✾❪ ❡ ❉❆❆❘P ❬❱✐❧❧❛s ❡t ❛❧✳✱ ✷✵✵✾❪ ❝r✐❛♠ ❝❧✉st❡rs ❡ ♣r♦❝✉r❛♠ ❝r✐❛r ár✈♦r❡s q✉❡ ❢❛✈♦r❡ç❛♠ ❛ ❡①✐stê♥❝✐❛ ❞❡ ♣♦♥t♦s ❞❡ ❛❣r❡❣❛çã♦✳ ❆s ♣ró①✐♠❛s três s❡çõ❡s ❞❡s❝r❡✈❡♠ ❛❧❣✉♠❛s ♣r♦♣♦st❛s ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s ❝❧❛ss✐✜❝❛çõ❡s ❞❡s❝r✐t❛s✳
✷✳✷✳✷ ❆❧❣♦r✐t♠♦s ❤✐❡rárq✉✐❝♦s
❉❡ ♠♦❞♦ ❣❡r❛❧✱ ♦s ❛❧❣♦r✐t♠♦s ❤✐❡rárq✉✐❝♦s✱ ♦✉ ❜❛s❡❛❞♦s ❡♠ ❝❧✉st❡r✱ ❞❡✜♥❡♠ ✉♠ ♣❛♣❡❧ ❡s♣❡❝✐❛❧ ♣❛r❛ ❛❧❣✉♥s ♥ós✱ ❝♦♥❤❡❝✐❞♦s ❝♦♠♦ ❝❧✉st❡r ❤❡❛❞s✳ ❊ss❡s ♥ós s❡rã♦ ❡♥❝✉❜✐❞♦s ❞❡ r❡❛❧✐③❛r t❛r❡❢❛s ❝♦♠♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❡♥✈✐♦ ❡ ❛❣r❡❣❛çã♦ ❞❛s ❧❡✐t✉r❛s ❞❡ ✈ár✐♦s ♥ós s❡♥s♦r❡s ♣❛r❛ ♦ s✐♥❦
