GeoCube: Representação, Computação,
e Visualização de Cubos Espaciais
GeoCube: Representação, Computação,
e Visualização de Cubos Espaciais
Dissertação apresentada ao
Depar-tamento de Computação da
Univer-sidade Federal de Ouro Preto, para
a obtenção de Título de Mestre em
Ciência da Computação, na área de
Sistemas de Computação.
Orientador: Joubert de Castro Lima
Co-Orientador: Tiago Garcia de
Senna Carneiro
Ouro Preto
2012
Catalogação: [email protected]
R672g Rocha, Tárik de Melo e Silva.
GeoCube [manuscrito] : representação e visualização de cubos espaciais / Tárik de Melo e Silva Rocha. – 2012.
x, 79 f.: il. color.; grafs.; tabs.; mapas.
Orientador: Prof. Dr. Joubert de Casotro Lima.
Coorientador: Prof. Dr. Tiago Garcia de Senna Carneiro.
Dissertação (Mestrado) - Universidade Federal de Ouro Preto. Instituto de Ciências Exatas e Biológicas. Departamento de Computação. Programa de Pós-graduação em Ciência da Computação.
Área de concentração:Ciência da Computação
1. Banco de dados - Modelo OLAP - Modelo SOLAP - Teses. 2. Cubo de dados - Teses. 3. Programação paralela (Computação) - Teses. 4. Sistemas de informação geográfica (SIG) - Teses. I. Universidade Federal de Ouro Preto. II. Título.
que pelas respostas." (Voltaire).
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❆♦s ♠❡✉s ♣❛✐s ♣♦r t♦❞♦ ❛♣♦✐♦✱ s❡♠ ❡❧❡s ❡st❡ tr❛❜❛❧❤♦ ♥ã♦ s❡r✐❛ ♣♦ssí✈❡❧✳ ❆ ❋✉♥❞❛çã♦ ❞❡ ❆♠♣❛r♦ à P❡sq✉✐s❛ ❞♦ ❡st❛❞♦ ❞❡ ▼✐♥❛s ●❡r❛✐s ♣❡❧❛ ❜♦❧s❛ ❞❡ ❡s✲ t✉❞♦s✳ ❆♦ ♣r♦❢❡ss♦r ❏♦✉❜❡rt ❞❡ ❈❛str♦ ▲✐♠❛ ♠❡✉s s✐♥❝❡r♦s ❛❣r❛❞❡❝✐♠❡♥t♦s ♣❡❧❛ ♦r✐❡♥t❛çã♦✱ ❝♦♥✜❛♥ç❛✱ ♦♣♦rt✉♥✐❞❛❞❡ ❞❡ ♣❡sq✉✐s❛ ❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣❡❧❛ ♣❛❝✐ê♥❝✐❛✳ ❆♦s ❛♠✐❣♦s ❞❡ t✉r♠❛ ❡ ❞❡ ♣❡sq✉✐s❛ q✉❡ ♠❡ ❛❥✉❞❛r❛♠ ♠✉✐t♦ ❡ ❝♦♠♣❛rt✐❧❤❛r❛♠ ♦s ♠♦♠❡♥t♦s ❞✐❢í❝❡✐s ❡ ❛♦ ♣r♦❢❡ss♦r ❝♦✲♦r✐❡♥t❛❞♦r ❚✐❛❣♦ ●❛r❝✐❛ ❞❡ ❙❡♥♥❛ ❈❛r✲ ♥❡✐r♦✳ ❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛ t♦❞♦s ❛q✉❡❧❡s q✉❡ ❝♦♥tr✐❜✉ír❛♠ ♣❛r❛ ❛ r❡❛❧✐③❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳
❆ t❡❝♥♦❧♦❣✐❛ ❙❖▲❆P ✭Spatial On-Line Analytical Processing✮ ♦❢❡r❡❝❡ ❛ ❥✉♥✲ çã♦ ❞❛s ❢✉♥❝✐♦♥❛❧✐❞❛❞❡s ❖▲❆P ✭Online Analytical Processing✮ ❡ ❙■● ✭❙✐st❡♠❛ ❞❡ ■♥❢♦r♠❛çã♦ ●❡♦❣rá✜❝❛✮ ❡ ❛❜r❡ ❝❛♠✐♥❤♦ ♣❛r❛ ✉♠❛ ♥♦✈❛ ❝❛t❡❣♦r✐❛ ❞❡ ❛♣❧✐❝❛✲ çõ❡s q✉❡ ❢♦r♥❡❝❡♠ s✉♣♦rt❡ ❛ ♠❛♥✐♣✉❧❛çã♦✱ ♣r♦❝❡ss❛♠❡♥t♦ ❡ ♥❛✈❡❣❛çã♦ ❡♠ ❞❛❞♦s ❡s♣❛ç♦✲t❡♠♣♦r❛✐s ♦r❣❛♥✐③❛❞♦s ❤✐❡r❛rq✉✐❝❛♠❡♥t❡✳ ❖s ❞❛❞♦s ❡♠ ✉♠ s✐st❡♠❛ ❖▲❆P sã♦ ❛r♠❛③❡♥❛❞♦s ❝♦♠♦ ❝✉❜♦s ❡ ❡st❡s sã♦ ♦r❣❛♥✐③❛❞♦s s❡❣✉♥❞♦ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❞✐✲ ♠❡♥sõ❡s✱ ♠❡❞✐❞❛s ❡ ❤✐❡r❛rq✉✐❛s✳ ❆ ♠❛t❡r✐❛❧✐③❛çã♦ ❞❡ ✉♠ ❝✉❜♦ ❞❡ ❞❛❞♦s ♣♦ss✉✐ ♦r❞❡♠ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ❡①♣♦♥❡♥❝✐❛❧ ❡♠ r❡❧❛çã♦ ❛♦ ❝♦♥s✉♠♦ ❞❡ ♠❡♠ór✐❛ ❡ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦✳ ◗✉❛♥❞♦ ❛ss♦❝✐❛♠♦s ✐♥❢♦r♠❛çõ❡s ❡s♣❛❝✐❛✐s ❛♦ ❝✉❜♦✱ ❛ ❞❡♠❛♥❞❛ ❞❡ ♠❡♠ór✐❛ ❡ ♣r♦❝❡ss❛♠❡♥t♦ ❛✉♠❡♥t❛✱ t♦r♥❛♥❞♦ ♠❛✐s ❞✐❢í❝✐❧ ❛ t❛r❡❢❛ ❞❡ ♦❢❡r❡❝❡r r❡✲ s♣♦st❛s rá♣✐❞❛s ❛♦ ✉s✉ár✐♦✳ ❆t✉❛❧♠❡♥t❡✱ ♣♦✉❝♦s tr❛❜❛❧❤♦s ❢♦r❛♠ ♣✉❜❧✐❝❛❞♦s ♥❛ r❡♣r❡s❡♥t❛çã♦✱ ❝♦♠♣✉t❛çã♦ ❡ ❝♦♥s✉❧t❛ ❞❡ ❝✉❜♦s ❡s♣❛ç♦✲t❡♠♣♦r❛✐s ❝♦♠♣❧❡t♦s✳ ❆s té❝♥✐❝❛s ❛♣r❡s❡♥t❛❞❛s ❝♦♠♦ ♠❛t❡r✐❛❧✐③❛çã♦ s❡❧❡t✐✈❛✱ ♠❛t❡r✐❛❧✐③❛çã♦ ❜❛s❡❛❞❛ ❡♠ ❛♣r♦①✐♠❛çõ❡s ❡ ❡str✉t✉r❛s ♣❛r❛ ✐♥❞❡①❛çã♦ ❞❡ r❡❣✐õ❡s ♥ã♦ ♦❢❡r❡❝❡♠ s♦❧✉çõ❡s ♣❛r❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s ❝♦♠♣❧❡t♦s ❡ ♠✉✐t❛s ✈❡③❡s ♥ã♦ ♣♦❞❡♠ s❡r ❛♣❧✐❝❛❞❛s ♣❛r❛ ✉♠❛ ❣r❛♥❞❡ ✈❛r✐❡❞❛❞❡ ❞❡ ❢✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦ ❡s♣❛❝✐❛✐s✳ ❆rq✉✐t❡t✉r❛s ❞❡ ❝♦♠✲ ♣✉t❛❞♦r❡s ❜❛s❡❛❞❛s ❡♠ ❡♥❞❡r❡ç❛♠❡♥t♦ ❝♦♠♣❛rt✐❧❤❛❞♦ t❛♠❜é♠ ♥ã♦ sã♦ ✉t✐❧✐③❛❞❛s ♥♦s tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s✳ ◆♦s tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s ❛s ❤✐❡r❛rq✉✐❛s sã♦ ❡s♣❡❝✐✜❝❛❞❛s ♠❛♥✉❛❧♠❡♥t❡ ♣♦r ❡s♣❡❝✐❛❧✐st❛s ❞♦ ❞♦♠í♥✐♦ ❡ ♠✉✐t❛s ✈❡③❡s ❛s s♦❧✉çõ❡s ❧✐♠✐t❛♠ ❛ q✉❛♥t✐❞❛❞❡ ❡ ❛ ✈❛r✐❡❞❛❞❡ ❞❡ ♠❡❞✐❞❛s ❡s♣❛❝✐❛✐s ❡ ♥ã♦ ❡s♣❛❝✐❛✐s ♥♦ ❝✉❜♦✳ ❉✐❛♥t❡ ❞❡ t❛❧ ❝❡♥ár✐♦✱ é ♣r♦♣♦st❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ r❡♣r❡s❡♥t❛çã♦✱ ❝♦♠♣✉t❛çã♦ ❡
❆ ❛❜♦r❞❛❣❡♠ ●❡♦❈✉❜❡ ♣♦❞❡ s❡r ❡①❡❝✉t❛❞❛ ❡♠ ♠áq✉✐♥❛s ❝♦♠ ♠ú❧t✐♣❧♦s ♥ú❝❧❡♦s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✳ ▼ú❧t✐♣❧❛s ❢✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦ ❡s♣❛❝✐❛❧ ❡ ❡st❛tíst✐❝❛ ♣♦❞❡♠ s❡r ❝♦♠❜✐♥❛❞❛s✳ ❚❛♠❜é♠ é ♣r♦♣♦st❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ♣❛r❛ ❢♦r♠❛çã♦ ❛✉t♦♠át✐❝❛ ❞❡ ❤✐❡r❛rq✉✐❛s ❛tr❛✈és ❞❡ r❡❣r❛s ❞❡ ✈✐③✐♥❤❛♥ç❛ ❡♥tr❡ s❡✉s ♦❜❥❡t♦s ❡s♣❛❝✐❛✐s✳ ❆s r❡❣r❛s ❞❡ ✈✐③✐♥❤❛♥ç❛ ♣♦❞❡♠ s❡r ❞❡✜♥✐❞❛s ♣❡❧♦ ✉s✉ár✐♦ ❡ ❡①❡❝✉t❛❞❛s ♣❡❧♦ ●❡♦✲ ❈✉❜❡✳ ❖ ●❡♦❈✉❜❡ ❥á ♣♦ss✉✐ ✈✐③✐♥❤❛♥ç❛ ♥①♥✱ ♦♥❞❡ ♥❃✶✳ ❚❡st❡s ❝♦♠♣❛r❛t✐✈♦s ❝♦♠ ✉♠ s✐st❡♠❛ ✐♠♣❧❡♠❡♥t❛❞♦ ✉s❛♥❞♦ P♦st●■❙ ❡ ✈✐st❛s ♠❛t❡r✐❛❧✐③❛❞❛s ♠♦str❛♠ q✉❡ ❛ ●❡♦❈✉❜❡ ❝♦♥s❡❣✉❡ ❝♦♠♣✉t❛r ❝✉❜♦s ❞❡ ❞❛❞♦s ❡s♣❛❝✐❛✐s ❡♠ ❛té ✶✴✻ ❞♦ t❡♠♣♦ ❣❛st♦ ♣❡❧❛ t❡❝♥♦❧♦❣✐❛ P♦st●✐s ❡♠ ✉♠❛ ♠áq✉✐♥❛ ❝♦♠ ✽ ♥ú❝❧❡♦s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✳
Palavras-chave: ❖▲❆P✱ ❙❖▲❆P✱ ❈✉❜♦ ❞❡ ❉❛❞♦s
❙❖▲❆P ✭❙♣❛t✐❛❧ ❖♥✲▲✐♥❡ ❆♥❛❧②t✐❝❛❧ Pr♦❝❡ss✐♥❣✮ t❡❝❤♥♦❧♦❣② ♦✛❡rs t❤❡ ❥✉♥❝✲ t✐♦♥ ♦❢ ❖▲❆P ✭♦♥❧✐♥❡ ❛♥❛❧②t✐❝❛❧ ♣r♦❝❡ss✐♥❣✮ ❛♥❞ ●■❙ ✭●❡♦❣r❛♣❤✐❝ ■♥❢♦r♠❛t✐♦♥ ❙②st❡♠✮ ❢❡❛t✉r❡s✱ ❡♥❛❜❧✐♥❣ t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ ♥❡✇ ❛♣♣❧✐❝❛t✐♦♥s ❞❡s✐❣♥❡❞ ❢♦r ❤✐❡✲ r❛r❝❤✐❝❛❧ s♣❛t✐♦✲t❡♠♣♦r❛❧ ❞❛t❛✳ ❖▲❆P s②st❡♠s ✐♥❞❡① ❞❛t❛ ❛s ❞❛t❛ ❝✉❜❡s✳ ❉❛t❛ ❝✉❜❡ ✐s ❛ r❡❧❛t✐♦♥❛❧ ♦♣❡r❛t♦r ♦r❣❛♥✐③❡❞ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ❝♦♥❝❡♣t ♦❢ ❞✐♠❡♥s✐♦♥s✱ ❤✐❡r❛r❝❤✐❡s ❛♥❞ ♠❡❛s✉r❡s✳ ❚❤❡ ❞❛t❛ ❝✉❜❡ ♠❛t❡r✐❛❧✐③❛t✐♦♥ ❤❛s ❡①♣♦♥❡♥t✐❛❧ ❝♦♠✲ ♣❧❡①✐t② ✐♥ t❡r♠s ♦❢ ♠❡♠♦r② ❝♦♥s✉♠♣t✐♦♥ ❛♥❞ r✉♥t✐♠❡✳ ❲❤❡♥ ✇❡ ❛ss♦❝✐❛t❡ s♣❛t✐❛❧ ✐♥❢♦r♠❛t✐♦♥ ✐♥ ❞❛t❛ ❝✉❜❡✱ ♠❡♠♦r② ❛♥❞ ♣r♦❝❡ss✐♥❣ ❞❡♠❛♥❞ ✐♥❝r❡❛s❡s✱ t✉r♥✐♥❣ ❢❛st r❡s♣♦♥s❡s t♦ t❤❡ ✉s❡r ❛ ❡✈❡♥ ❤❛r❞ t❛s❦ t♦ s♦❧✈❡✳ ❈✉rr❡♥t❧②✱ ❢❡✇ st✉❞✐❡s ❛❞❞r❡ss s♦❧✉t✐♦♥s t♦ s♣❛t✐♦✲t❡♠♣♦r❛❧ ❝✉❜❡s r❡♣r❡s❡♥t❛t✐♦♥✱ ❝♦♠♣✉t❛t✐♦♥ ❛♥❞ q✉❡r②✳ ❚❡❝❤✲ ♥✐q✉❡s ❛s s❡❧❡❝t✐✈❡ ♠❛t❡r✐❛❧✐③❛t✐♦♥ ❛♥❞ ♠❛t❡r✐❛❧✐s❛t✐♦♥✲❜❛s❡❞ ❛♣♣r♦❛❝❤❡s ✉s❡❞ t♦ ✐♥❞❡① r❡❣✐♦♥s ❞♦ ♥♦t ♦✛❡r s♦❧✉t✐♦♥s ❢♦r ❝♦♠♣✉t✐♥❣ ❝♦♠♣❧❡t❡ ❞❛t❛ ❝✉❜❡s ❛♥❞ ♦❢t❡♥ ❝❛♥ ♥♦t ❜❡ ❛♣♣❧✐❡❞ t♦ ❛ ✇✐❞❡ ✈❛r✐❡t② ♦❢ s♣❛t✐❛❧ ❛❣❣r❡❣❛t✐♦♥ ❢✉♥❝t✐♦♥s✳ ❈♦♠♣✉t❡r ❛r❝❤✐t❡❝t✉r❡s ❜❛s❡❞ ♦♥ s❤❛r❡❞ ❛❞❞r❡ss ❛r❡ ♥♦t ✉s❡❞ ✐♥ r❡❧❛t❡❞ ✇♦r❦✳ ❋❛❝❡❞ ✇✐t❤ t❤✐s s❝❡♥❛r✐♦✱ ✇❡ ♣r♦♣♦s❡ ❛♥ ❛♣♣r♦❛❝❤ t♦ r❡♣r❡s❡♥t✱ ❝♦♠♣✉t❡ ❛♥❞ q✉❡r② s♣❛t✐♦✲ t❡♠♣♦r❛❧ ❝✉❜❡s✱ ❝❛❧❧❡❞ ●❡♦❈✉❜❡✳ ●❡♦❈✉❜❡ ❝❛♥ r✉♥ ♦♥ ♠❛❝❤✐♥❡s ✇✐t❤ ♠✉❧t✐✲❝♦r❡ ♣r♦❝❡ss♦rs✳ ▼✉❧t✐♣❧❡ ❢✉♥❝t✐♦♥s✱ ✐♥❝❧✉❞✐♥❣ ♠❛♥② st❛t✐st✐❝❛❧ ❛♥❞ s♣❛t✐❛❧ ❢✉♥❝t✐♦♥s✱ ❝❛♥ ❜❡ ❝♦♠♣✉t❡❞ ✐♥ ●❡♦❈✉❜❡✳ ●❡♦❈✉❜❡ ❛❧s♦ ♣r♦✈✐❞❡s ❛ ♥❡✇ ♠❡t❤♦❞ t♦ ❛✉t♦♠❛✲ t✐❝ ❣❡♥❡r❛t❡ s♣❛t✐❛❧ ❤✐❡r❛r❝❤✐❡s ✉s✐♥❣ ❛♥② ♥❡✐❣❤❜♦r❤♦♦❞ ❝❛❧❝✉❧✉s✳ ❈♦♠♣❛r❛t✐✈❡ t❡sts ✇✐t❤ ❛ s②st❡♠ ✐♠♣❧❡♠❡♥t❡❞ ✉s✐♥❣ P♦st●■❙ ❛♥❞ ♠❛t❡r✐❛❧✐③❡❞ ✈✐❡✇s s❤♦✇ t❤❛t ●❡♦❈✉❜❡ ❝❛♥ ❝♦♠♣✉t❡ s♣❛t✐❛❧ ❞❛t❛ ❝✉❜❡s s✐① t✐♠❡s ❢❛st❡r ♦♥ ❛ ♠❛❝❤✐♥❡ ✇✐t❤
Keywords: ❖▲❆P✱ ❙❖▲❆P✱ ❉❛t❛ ❈✉❜❡s
Lista de Figuras
✶ ❖♣❡r❛❞♦r ❈✉❜♦ ❞❡ ❉❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷
✷ ❉✐♠❡♥sõ❡s ❡ ❋❛t♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼
✸ ▼♦❞❡❧♦ ❙♥♦✇❋❧❛❦❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽
✹ ▼♦❞❡❧♦ ❈♦♥st❡❧❛çã♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✾
✺ Pr✐♥❝✐♣❛✐s ♦♣❡r❛❞♦r❡s✳ ❋♦♥t❡✿ ✭❞❡ ❈❛str♦ ▲✐♠❛✱ ✷✵✵✾✮✳✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✶
✻ ❆❜♦r❞❛❣❡♠ Top-Down ♣❛r❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✸
✼ ❈✉❜♦ ■❝❡❜❡r❣✳ ❋♦♥t❡✿ ✭❋✐♥❞❧❛t❡r ❛♥❞ ❍❛♠✐❧t♦♥✱ ✷✵✵✸✮ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✹
✽ ❆❜♦r❞❛❣❡♠ ❇♦tt♦♠✲❯♣ ♣❛r❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✺
✾ ❈❛♠❛❞❛s ❞❡ ✉♠ ♠❛♣❛✳ ❋♦♥t❡✿ ✭❤tt♣✿✴✴❣❡♦♣♦rt❛❧✳✐❝✐♠♦❞✳♦r❣✱ ✷✵✶✷✮✳ ♣✳ ✶✼
✶✵ ❉❲ ♠♦rt❛❧✐❞❛❞❡ ❝♦♠ ❛ ❞✐♠❡♥sã♦ ❡s♣❛❝✐❛❧ ▲♦❝❛❧✐③❛❝❛♦✳ ❋♦♥t❡✿
❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭❇✐♠♦♥t❡ ❙✳✱ ✷✵✵✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽
✶✶ ❖s t✐♣♦s ❞❡ ❞❛❞♦s s✉♣♦rt❛❞♦s ❡♠ ✉♠❛ ❞✐♠❡♥sã♦ ❡s♣❛❝✐❛❧✳ ❋♦♥t❡✿
✭❘✐✈❡st ❡t ❛❧✳✱ ✷✵✵✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✾
✶✷ ❉❲ ♠♦rt❛❧✐❞❛❞❡ ❝♦♠ ❛ ♠❡❞✐❞❛ ❡s♣❛❝✐❛❧ ❞❡♣❛rt❛♠❡♥t♦✳ ❋♦♥❡✿
✭❇✐♠♦♥t❡ ❙✳✱ ✷✵✵✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✵
✶✺ ■♥t❡r❢❛❝❡ ❙❖❱❆❚✳ ❋♦♥t❡✿ ✭❙❝♦t❝❤ ❛♥❞ P❛r♠❛♥t♦✱ ✷✵✵✺✮✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✶
✶✻ ■♥t❡r❢❛❝❡ ●♦❧❛♣❛✳ ❋♦♥t❡✿ ✭❞♦ ◆❛s❝✐♠❡♥t♦ ❋✐❞❛❧❣♦ ❡t ❛❧✳✱ ✷✵✵✹✮✳ ✳ ♣✳ ✸✹
✶✼ ❙✐st❡♠❛ ❏▼❛♣✳ ❋♦♥t❡✿ ✭❚❡❝❤♥♦❧♦❣✐❡s✱ ✷✵✵✺✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✺
✶✽ ❙✐st❡♠❛ ●❧♦❜❡❖❧❛♣✳ ❋♦♥t❡✿ ✭❋❡rr❛③ ❛♥❞ ❙❛♥t♦s✱ ✷✵✶✵✮✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✻
✶✾ ■♥t❡r❢❛❝❡ P♦st●❡♦❖❧❛♣✳ ❋♦♥t❡✿ ✭❈♦❧♦♥❡s❡ ❡t ❛❧✳✱ ✷✵✵✽✮✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✼
✷✵ ■♥t❡r❢❛❝❡ ❞♦ ▼❛♣❲❤❛r❡❤♦✉s❡✳ ❋♦♥t❡✿ ✭❙♦✉s❛✱ ✷✵✵✼✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✽
✷✶ ❙✐st❡♠❛ ●❡♦❈✉❜❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✹
✷✷ ❆rq✉✐t❡t✉r❛ ❞♦ ❙✐st❡♠❛ ●❡♦❈✉❜❡ ❡♠ ❞❡t❛❧❤❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻
✷✸ ❱✐s✉❛❧✐③❛çã♦ ❞❛s ✉♥✐❞❛❞❡s ❤❛❜✐t❛❝✐♦♥❛✐s ❞❡ ❖✉r♦ Pr❡t♦✴▼●✳ ✳ ✳ ♣✳ ✹✾
✷✹ ■♥t❡r❢❛❝❡ ♣❛r❛ ❝r✐❛çã♦ ❞♦ ❝✉❜♦ ❞❡ ❞❛❞♦s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✾
✷✺ ❖♣❡r❛çõ❡s ❞❡ drill-down✱ roll-up ❡ dice ❡♠ ❡s♣❛ç♦s ❝❡❧✉❧❛r❡s r❡✲
❣✉❧❛r❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✶
✷✻ ❋♦r♠❛çã♦ ❞♦ ❝✉❜♦ ❜❛s❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✸
✷✼ ❋♦r♠❛çã♦ ❞❛s ❛❣r❡❣❛çõ❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✻
✷✽ ❋♦r♠❛çã♦ ❞❛s ❛❣r❡❣❛çõ❡s ♣❛r❛ ✉♠❛ ♠❡❞✐❞❛ ❡s♣❛❝✐❛❧ ❡ ✉♠❛ ♠❡✲
❞✐❞❛ ♥✉♠ér✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼
✷✾ ◆♦✈❛s r❡❣✐õ❡s ❡♠ ✉♠ ❝✉❜♦ ❝♦♠ ♠❡❞✐❞❛s ❡s♣❛❝✐❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✽
✸✵ ❋♦r♠❛♥❞♦ ❤✐❡r❛rq✉✐❛s ♣❛r❛❧❡❧❛♠❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✵
✸✶ P❛r❛❧❡❧✐③❛çã♦ ❞♦ ●❡♦❈✉❜❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✷
✸✸ ❙♣❡❡❞✲❯♣ ❡ ❊✜❝✐ê♥❝✐❛ ♥❛ ❝♦♠♣✉t❛çã♦ ❞❛ ❝♦♥s✉❧t❛ ❈✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✽
✸✹ ❚❡♠♣♦ ❞❡ ❈♦♠♣✉t❛çã♦ ♣❛r❛ ❛ ❝♦♥s✉❧t❛ ❈✷✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✾
✸✺ ❙♣❡❡❞✲❯♣ ❡ ❊✜❝✐ê♥❝✐❛ ♣❛r❛ ❛ ❝♦♥s✉❧t❛ ❈✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✵
✸✻ ❈♦♠♣❛r❛çã♦ ❞♦ t❡♠♣♦ ❞❡ ❝♦♠♣✉t❛çã♦ ❞♦s s✐st❡♠❛s ●❡♦❈✉❜❡ ❡
P♦st●✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✼✶
Lista de Tabelas
✶ ❚❛❜❡❧❛ ❝♦♠♣❛r❛t✐✈❛ ❞♦s s✐st❡♠❛s ❡①✐st❡♥t❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✶
✷ ❘❡❧❛çã♦ ❞❡ t✉♣❧❛s ♥ã♦ ❛❣r❡❣❛❞❛s ❝♦♠ ✉♠❛ ♠❡❞✐❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✷
✸ ❘❡❧❛çã♦ ❞❡ t✉♣❧❛s ♥ã♦ ❛❣r❡❣❛❞❛s ❝♦♠ ✉♠❛ ♠❡❞✐❞❛ ❡s♣❛❝✐❛❧ ❡
✉♠❛ ♥✉♠ér✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼
✹ ❚❛❜❡❧❛ ❝♦♠♣❛r❛t✐✈❛ ❞♦s s✐st❡♠❛s ❡①✐st❡♥t❡s ❡ ♦ ●❡♦❈✉❜❡ ✳ ✳ ✳ ✳ ♣✳ ✻✸
✺ ◆ú♠❡r♦ ❞❡ ❝❛s♦s ❞❡ ❞❡♥❣✉❡ ♣♦r r❡❣✐ã♦✳ ❈♦♥s✉❧t❛ ❈✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✻
✻ ❋♦r♠❛♥❞♦ ❤✐❡r❛rq✉✐❛s ❛❣r❡❣❛♥❞♦ ❛s r❡❣✐õ❡s ❛ ♣♦♣✉❧❛çã♦ ❡ ♦ ♥ú✲
♠❡r♦ ❞❡ ❝❛s♦s ❞❡ ❞❡♥❣✉❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✾
✼ P❛râ♠❡tr♦s ✉s❛❞♦s ♣❛r❛ ❝♦♠♣✉t❛çã♦ ❞♦s ❝✉❜♦s ✉s❛❞♦s ♣❛r❛ ❝♦♠✲
Sumário
1 Introdução ♣✳ ✶
2 Conceitos Básicos ♣✳ ✺
✷✳✶ ❆r♠❛③é♠ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺
✷✳✷ ❈✉❜♦ ❞❡ ❉❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✽
✷✳✸ ❈♦♠♣✉t❛çã♦ ❞❡ ❈✉❜♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✷
✷✳✹ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ❞❛❞♦s ❊s♣❛❝✐❛✐s ●❡♦❣rá✜❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✻
✷✳✺ ▼❡❞✐❞❛s ❡ ❉✐♠❡♥sõ❡s ❊s♣❛❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✶✽
✷✳✻ ❍✐❡r❛rq✉✐❛ ❊s♣❛❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✶
✷✳✼ ▼❡❞✐❞❛s ❊s♣❛❝✐❛✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✷
3 Trabalhos Relacionados ♣✳ ✷✺
✸✳✶ P♦st●✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✺
✸✳✷ ●❡♦▼♦♥❞r✐❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✻
✸✳✸ ●❡❲❖❧❛P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✷✽
✸✳✻ ●❖▲❆P❆✲●❲❉✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✸
✸✳✼ ❏▼❛♣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✹
✸✳✽ ●❧♦❜❡❖❧❛♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✺
✸✳✾ P♦st●❡♦❖❧❛♣✴●❡♦❖❧❛♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✻
✸✳✶✵ ▼❛♣❲❤❛r❡❤♦✉s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✽
✸✳✶✶ ❘❡s✉♠♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✸✾
4 GeoCube ♣✳ ✹✸
✹✳✶ ❆rq✉✐t❡t✉r❛ ❞♦ ❙✐st❡♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✺
✹✳✶✳✶ ❉❲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✻
✹✳✶✳✷ ❙❖▲❆P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✼
✹✳✶✳✸ ❈❛♠❛❞❛ ❞❡ ❱✐s✉❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✹✽
✹✳✷ ❉❡t❛❧❤❛♠❡♥t♦ ❞❛ ❝❛♠❛❞❛ ❙❖▲❆P ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✵
✹✳✷✳✶ ❋♦r♠❛çã♦ ❞❛s ❍✐❡r❛rq✉✐❛s ❡ ❞♦ ❈✉❜♦ ❇❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✵
✹✳✷✳✷ ❈♦♠♣✉t❛çã♦ ❞❛s ❆❣r❡❣❛çõ❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✸
✹✳✷✳✸ ❊str❛té❣✐❛s ❞❡ ❖t✐♠✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✼
✹✳✷✳✹ P❛r❛❧❡❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✽
✹✳✷✳✹✳✶ P❛r❛❧❡❧✐③❛çã♦ ❞❛ ❡t❛♣❛ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✺✾
✹✳✷✳✹✳✷ P❛r❛❧❡❧✐③❛çã♦ ❞❛ ❡t❛♣❛ ✸ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✶
✺✳✶ ❚❡st❡s ▼✉❧t✐t❤r❡❛❞ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✻
✺✳✶✳✶ ❈♦♥s✉❧t❛ ✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✻
✺✳✶✳✷ ❈♦♥s✉❧t❛ ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✼
✺✳✷ ❚❡st❡ ❈♦♠♣❛r❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♣✳ ✻✾
6 Conclusão e Trabalhos Futuros ♣✳ ✼✸
Referências Bibliográficas ♣✳ ✼✺
Referências Bibliográficas ♣✳ ✼✺
1 Introdução
❉❛t❛ ❲❛r❡❤♦✉s❡ ✭❉❲✮ é ✉♠ r❡♣♦s✐tór✐♦ ♦✉ ❝♦❧❡çã♦ ❞❡ ❞❛❞♦s ✐♥t❡❣r❛❞♦✱ ♦r✐❡♥✲ t❛❞♦ ♣♦r ❛ss✉♥t♦✱ ✈❛r✐á✈❡❧ ❝♦♠ ♦ t❡♠♣♦ ❡ ♥ã♦✲✈♦❧át✐❧ q✉❡ ♦❢❡r❡❝❡ s✉♣♦rt❡ ❛ ♣r♦✲ ❝❡ss♦s ❞❡ t♦♠❛❞❛ ❞❡ ❞❡❝✐sã♦ ✭■♥♠♦♥ ❛♥❞ ❍❛❝❦❛t❤♦r♥✱ ✶✾✾✹✮✳ ❙❡r✈✐❞♦r❡s ❖▲❆P ✭Online Analytical Processing✮ ♥♦r♠❛❧♠❡♥t❡ ❝♦♠♣✉t❛♠ ❝✉❜♦s ❛ ♣❛rt✐r ❞❡ ❉❲s✳ ❖s ❞❛❞♦s ❡♠ ✉♠ s✐st❡♠❛ ❖▲❆P sã♦ ❛r♠❛③❡♥❛❞♦s ❝♦♠♦ ❝✉❜♦s ❡ ❡st❡s sã♦ ♦r❣❛✲ ♥✐③❛❞♦s s❡❣✉♥❞♦ ♦ ❝♦♥❝❡✐t♦ ❞❡ ❞✐♠❡♥sõ❡s✱ ❢❛t♦s✱ ♠❡❞✐❞❛s ❡ ❤✐❡r❛rq✉✐❛s✳
❖ ♦♣❡r❛❞♦r ❝✉❜♦ ❞❡ ❞❛❞♦s✱ ♦✉ s✐♠♣❧❡s♠❡♥t❡ ❝✉❜♦✱ ❢♦✐ ♣r♦♣♦st♦ ♣♦r ❏✐♠ ●r❛② ❡♠ ✭●r❛② ❡t ❛❧✳✱ ✶✾✾✼✮✳ ❯♠ ❝✉❜♦ é ❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦ ♦♣❡r❛❞♦r Group-by s♦❜r❡ t♦❞❛s ❛s ❝♦♠❜✐♥❛çõ❡s ❞❡ ❞✐♠❡♥sõ❡s✱ s❡♥❞♦ ❛s ❞✐♠❡♥sõ❡s ❝♦♠♣♦st❛s ❞❡ ♠ú❧t✐♣❧❛s ❤✐❡r❛rq✉✐❛s✳ ❆ ❣r❛♥✉❧❛r✐❞❛❞❡ é ♦ ♥í✈❡❧ ❞❡ ❞❡t❛❧❤❡ ❡♠ q✉❡ ♦s ❞❛❞♦s sã♦ ♠❛♥t✐❞♦s ♥♦ ❝✉❜♦✳ ❈❛❞❛ Group-by é ❝❤❛♠❛❞♦ ❞❡ ❝✉❜ó✐❞❡ ❡ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝é❧✉❧❛s ♦✉ t✉♣❧❛s s♦❜r❡ ❛s ❞✐♠❡♥sõ❡s✳ P❛r❛ ❣❡r❛r t♦❞❛s ❛s s✉♠❛r✐③❛çõ❡s ♦ ❛❧❣♦r✐t♠♦ ❢❛③ ♦ ✉s♦ ❞♦ ✈❛❧♦r ❆▲▲✳ ❆ ❋✐❣✉r❛ ✶✐❧✉str❛ ♦ ♦♣❡r❛❞♦r ❝✉❜♦ ✐♠♣❧❡♠❡♥t❛❞♦ ❝♦♠♦ ✉♠❛ t❛❜❡❧❛ ❝♦♠♣♦st❛ ❞❡ t✉♣❧❛s✳ ◆❡st❡ ❡①❡♠♣❧♦ ❤á ❛♣❡♥❛s três ❞✐♠❡♥sõ❡s ❡ ✉♠❛ ♠❡❞✐❞❛✳
❋✐❣✉r❛ ✶✿ ❖♣❡r❛❞♦r ❈✉❜♦ ❞❡ ❉❛❞♦s✳
✈❡í❝✉❧♦s ✈❡♥❞✐❞♦s✱ r❡♣r❡s❡♥t❛❞❛ ♣❡❧❛ ❝♦❧✉♥❛ ❱❡♥❞❛✳ ❈✉❜♦s ❞❡ ❞❛❞♦s ❝♦♠♣❧❡t♦s ♣r♦❞✉③❡♠ ❛s ❛❣r❡❣❛çõ❡s ♣♦ssí✈❡✐s s♦❜r❡ ♦ ❝♦♥❥✉♥t♦ ❞❡ t✉♣❧❛s ✐♥✐❝✐❛❧✳ ◆♦ ❡①❡♠♣❧♦ ❞❛ ❋✐❣✉r❛ ✶✱ ✉♠ ❝✉❜♦ ❝♦♠♣❧❡t♦ ❢♦✐ ❝r✐❛❞♦ ❛ ♣❛rt✐r ❞❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ s❡✐s t✉♣❧❛s ❞❡ ❡♥tr❛❞❛✳ ❖ ❝✉❜♦ ❝♦♠♣❧❡t♦ r❡s✉❧t❛♥t❡ ♣♦ss✉✐ ✈✐♥t❡ ❡ s❡✐s t✉♣❧❛s✱ ♦✉ s❡❥❛✱ ❡♥q✉❛♥t♦ ♦ ♥ú♠❡r♦ ❞❡ ❝♦❧✉♥❛s ♦✉ ❞✐♠❡♥sõ❡s ❝r❡s❝❡ ❧✐♥❡❛r♠❡♥t❡ ♦ ♥ú♠❡r♦ ❞❡ t✉♣❧❛s ♦✉ ❝é❧✉❧❛s ❡♠ ✉♠ ❝✉❜♦ ❝r❡s❝❡ ❡①♣♦♥❡♥❝✐❛❧♠❡♥t❡✳
❞❡ ❢❡rr❛♠❡♥t❛s ❙❖▲❆P✭Spatial On-Line Analytical Processing✮✳
❋❡rr❛♠❡♥t❛s ❙❖▲❆P ❣❡r❛♠ ❝✉❜♦s ❡s♣❛❝✐❛✐s✳ ❈✉❜♦s ❡s♣❛❝✐❛✐s ♣♦ss✉❡♠ ♠❡❞✐✲ ❞❛s✱ ❞✐♠❡♥sõ❡s ❡ ❤✐❡r❛rq✉✐❛s ❡s♣❛❝✐❛✐s ❡ ♥ã♦✲❡s♣❛❝✐❛✐s ❡ ♣♦ss✉❡♠ s✉♣♦rt❡ ♣❛r❛ ❛❣r❡❣❛çã♦ ❞❡ ♦❜❥❡t♦s ❡s♣❛❝✐❛✐s ❡ ♥ã♦ ❡s♣❛❝✐❛✐s✳ ■♥❢❡❧✐③♠❡♥t❡✱ ❛s ❢❡rr❛♠❡♥t❛s ❙❖▲❆P ♠❛✐s ❝♦♠✉♥s✱ ❞❡s❝r✐t❛s ♥♦ ❝❛♣ít✉❧♦ ✸✱ ♣♦ss✉❡♠ ❧✐♠✐t❛çõ❡s q✉❛♥t♦ ❛♦ ♥ú♠❡r♦ ❡ t✐♣♦ ❞❡ ♦♣❡r❛❞♦r❡s ❡s♣❛❝✐❛✐s✳ ❆ ❝♦♠❜✐♥❛çã♦ ❞❡ ♠❡❞✐❞❛s ❡st❛tíst✐❝❛s ❡ ❡s♣❛❝✐❛✐s é ♦✉tr❛ ❧✐♠✐t❛çã♦ ❞♦s tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s✳ ❆ ❣❡r❛çã♦ ❞❡ ❤✐❡r❛rq✉✐❛s ❡s♣❛❝✐❛✐s ❞❡ ❢♦r♠❛ ❛✉t♦♠át✐❝❛✱ ✉s❛♥❞♦ ♣❛r❛ ✐st♦ r❡❣r❛s ❞❡ ✈✐③✐♥❤❛♥ç❛ ❡s♣❛❝✐❛✐s ✈❛r✐❛❞❛s✱ é ♠✉✐t♦ út✐❧ ❛♦ t♦♠❛❞♦r ❞❡ ❞❡❝✐sã♦✱ ♣♦ré♠ ♥ã♦ sã♦ ♦❢❡r❡❝✐❞❛s ♥❛s ❛❜♦r✲ ❞❛❣❡♥s ❡st✉❞❛❞❛s ♥❡st❡ tr❛❜❛❧❤♦✳ P♦r ✜♠ ♦ ✉s♦ ❞❡ ❝♦♠♣✉t❛❞♦r❡s ❝♦♠ ♠ú❧t✐♣❧♦s ♥ú❝❧❡♦s t♦♠❛ ❝❛❞❛ ✈❡③ ♠❛✐s ✐♠♣♦rtâ♥❝✐❛✱ ♣♦ré♠ ♦s tr❛❜❛❧❤♦s ❝♦rr❡❧❛t♦s s✐♠♣❧❡s✲ ♠❡♥t❡ ♥ã♦ ❢♦r❛♠ ❞❡s❡♥❤❛❞♦s ♣❛r❛ t❛✐s ❛rq✉✐t❡t✉r❛s ❞❡ ❝♦♠♣✉t❛❞♦r✳
❉✐❛♥t❡ ❞❡ t❛❧ ❝❡♥ár✐♦✱ é ♣r♦♣♦st♦ ♦ ●❡♦❈✉❜❡✱ ✉♠ s✐st❡♠❛ ❙❖▲❆P ❝♦♠ s✉♣♦rt❡ ❛ ♠ú❧t✐♣❧❛s ♠❡❞✐❞❛s ❡s♣❛❝✐❛✐s ❡ ❡st❛tíst✐❝❛s✱ s✉♣♦rt❡ ❛ ❤✐❡r❛rq✉✐③❛çã♦ ❛✉t♦♠át✐❝❛ ❞❡ ❡s♣❛ç♦s r❡❣✉❧❛r❡s ❡ ♥ã♦ r❡❣✉❧❛r❡s s❡❣✉♥❞♦ q✉❛✐sq✉❡r r❡❣r❛ ❞❡ ✈✐③✐♥❤❛♥ç❛ ❡s♣❛✲ ❝✐❛❧✳ ❖ ●❡♦❈✉❜❡ s❡ ♠♦str❛ ♠✉✐t♦ ♣r♦♠✐ss♦r t❛♠❜é♠ ❡♠ t❡r♠♦s ❞❡ ❞❡s❡♠♣❡♥❤♦✳ ❚❡st❡s ❝♦♠♣❛r❛t✐✈♦s ❝♦♠ ✉♠ s✐st❡♠❛ ✐♠♣❧❡♠❡♥t❛❞♦ ✉s❛♥❞♦ P♦st●■❙ ❡ ✈✐st❛s ♠❛✲ t❡r✐❛❧✐③❛❞❛s ♠♦str❛♠ q✉❡ ♦ ●❡♦❈✉❜❡ ❝♦♥s❡❣✉❡ ❝♦♠♣✉t❛r ❝✉❜♦s ❞❡ ❞❛❞♦s ❡s♣❛❝✐❛✐s ❡♠ ❛té ✶✴✻ ❞♦ t❡♠♣♦ ❣❛st♦ ♣❡❧❛ t❡❝♥♦❧♦❣✐❛ P♦st●■❙✳
2 Conceitos Básicos
2.1 Armazém de Dados
Data Warehouse ♦✉ ❛r♠❛③é♠ ❞❡ ❞❛❞♦s é ✉♠❛ ❝♦❧❡çã♦ ❞❡ ❞❛❞♦s ♦r✐❡♥t❛❞♦ ♣♦r ❛ss✉♥t♦✱ ♥ã♦ ✈♦❧át✐❧✱ ✈❛r✐á✈❡❧ ❝♦♠ ♦ t❡♠♣♦ ❡ q✉❡ ♣♦❞❡ ✐♥t❡❣r❛r ❢♦♥t❡s ❞❡ ❞❛✲ ❞♦s ❤❡t❡r♦❣ê♥❡❛s✳ ❊st❛s ❝❛r❛❝t❡ríst✐❝❛s t♦r♥❛♠ ♦s ❛r♠❛③é♥s ❞❡ ❞❛❞♦s út❡✐s ♣❛r❛ ❢❡rr❛♠❡♥t❛s ❞❡ s✉♣♦rt❡ ❛ t♦♠❛❞❛s ❞❡ ❞❡❝✐sã♦✱ ❝♦♠♦ ❖▲❆P ✭Online Analytical Processing✮ ❡ ▼✐♥❡r❛çã♦ ❞❡ ❉❛❞♦s✳ ❋r❡q✉❡♥t❡♠❡♥t❡✱ ♦s ❛r♠❛③é♠ ❞❡ ❞❛❞♦s sã♦ ♠❛♥t✐❞♦s s❡♣❛r❛❞❛♠❡♥t❡ ❞♦s ❜❛♥❝♦s ❞❡ ❞❛❞♦s ♦♣❡r❛❝✐♦♥❛✐s ❞❛s ♦r❣❛♥✐③❛çõ❡s q✉❡ ❡①✐❣❡♠ ❞✐❢❡r❡♥t❡s r❡q✉✐s✐t♦s ❞❡ ❞❡s❡♠♣❡♥❤♦ ❡ ❢✉♥❝✐♦♥❛❧✐❞❛❞❡✳ ❆s tr❛♥s❛çõ❡s ♦♣❡✲ r❛❝✐♦♥❛✐s ❞♦ ❞✐❛✲❛✲❞✐❛ ❞❛s ♦r❣❛♥✐③❛çõ❡s sã♦ s✉♣♦rt❛❞❛s ♣❡❧❛s ❢❡rr❛♠❡♥t❛s ❖▲❚P ✭Online Transaction Processing✮✳ ❆♦ ❝♦♥trár✐♦ ❞♦s ❜❛♥❝♦s ❞❡ ❞❛❞♦s ❖▲❚P✱ ♦ ❛r♠❛③é♠ ❞❡ ❞❛❞♦s ♣r✐♦r✐③❛ ❛ ♣❡rs✐stê♥❝✐❛ ❞❡ ❞❛❞♦s ❤✐stór✐❝♦s✱ s✉♠❛r✐③❛❞♦s ❡ ❝♦♥s♦❧✐❞❛❞♦s ❛♦ ✐♥✈és ❞❡ tr❛♥s❛çõ❡s ✐♥❞✐✈✐❞✉❛✐s✳ ❈♦♠♦ ❡st❡s ❛r♠❛③é♥s ♣♦ss✉❡♠ ❞❛❞♦s ❞❡ ❧♦♥❣♦s ♣❡rí♦❞♦s ❡ ❞❡ ❞✐❢❡r❡♥t❡s ❢♦♥t❡s✱ s❡✉ t❛♠❛♥❤♦ é ❣❡r❛❧♠❡♥t❡ ♠❛✐♦r ❞♦ q✉❡ ♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ♦♣❡r❛❝✐♦♥❛❧✳ P♦r ✜♠✱ ♦s ❛r♠❛③é♥s ❞❡ ❞❛❞♦s ❞ã♦ s✉♣♦rt❡ ❛ ❝♦♥s✉❧t❛s ❛❞✲❤♦❝ ❝♦♠♣❧❡①❛s q✉❡ ♣♦❞❡♠ ❛❝❡ss❛r ♠✐❧❤õ❡s ❞❡ r❡❣✐str♦s ❡ ❡①❡❝✉t❛r ✈ár✐❛s ✈❛rr❡❞✉r❛s✱ ❥✉♥çõ❡s ❡ ❛❣r❡❣❛çõ❡s✳ ✭✭❈❤❛✉❞❤✉r✐ ❛♥❞ ❉❛②❛❧✱ ✶✾✾✼✮✮
❝♦♠♦ ❛rq✉✐✈♦s ❜✐♥ár✐♦s✱ ♦❜❥❡t♦s s❡r✐❛❧✐③❛❞♦s✱ ❛rq✉✐✈♦s ①♠❧ ❡ t❛❜❡❧❛s r❡❧❛❝✐♦♥❛✐s✳ ❚é❝♥✐❝❛s ❞❡ ❧✐♠♣❡③❛ ❡ ✐♥t❡❣r❛çã♦ ❞❡ ❞❛❞♦s sã♦ ❛♣❧✐❝❛❞❛s ♣❛r❛ ❣❛r❛♥t✐r ❛ ❝♦♥s✐s✲ tê♥❝✐❛ ❞♦s ♥♦♠❡s✱ ❡str✉t✉r❛s ❞❛s ❞✐♠❡♥sõ❡s✱ ♠❡❞✐❞❛s✱ ❡♥tr❡ ♦✉tr♦s✳
❆ ❡①♣❧♦r❛çã♦ ❡ ♦r❣❛♥✐③❛çã♦ ❞♦s ❞❛❞♦s ❞❡ ✉♠ ❛r♠❛③é♠ ❞❡ ❞❛❞♦s ♣♦❞❡♠ s❡r ❢❡✐t❛s ♣♦r ❢❡rr❛♠❡♥t❛s ❖▲❆P q✉❡ s✉♠❛r✐③❛♠ ❡ ♦r❣❛♥✐③❛♠ ❣r❛♥❞❡s q✉❛♥t✐❞❛❞❡s ❞❡ ❞❛❞♦s ❡♠ ❡str✉t✉r❛s ♠✉❧t✐❞✐♠❡♥s✐♦♥❛✐s ♦♥❞❡ ♠ú❧t✐♣❧❛s ❤✐❡r❛rq✉✐❛s ❢❛❝✐❧✐t❛♠ ❛ ♥❛✈❡❣❛çã♦ ❡ ❛s ❡str✉t✉r❛s ♠✉❧t✐❞✐♠❡♥s✐♦♥❛✐s ✐♥❞❡①❛♠ ❡✜❝✐❡♥t❡♠❡♥t❡ ♦s ❞❛❞♦s✳
❉✐♠❡♥sõ❡s sã♦ ♣❡rs♣❡❝t✐✈❛s ❞♦ ♣r♦❝❡ss♦ ❞❡ ❞❡❝✐sã♦ q✉❡ ❞❡s❝r❡✈❡♠ í♥❞✐❝❡s✱ ❝❤❛♠❛❞♦s ♠❡❞✐❞❛s✱ q✉❡ ❞❡s❡❥❛♠♦s ❛♥❛❧✐s❛r✳ ❊st❛s ❞✐♠❡♥sõ❡s ♣♦ss✉❡♠ ♣❡❧♦ ♠❡♥♦s ✉♠ ❛tr✐❜✉t♦ q✉❡ ❛s ❞❡s❝r❡✈❡♠✳ ❈♦♠♦ ❡①❡♠♣❧♦✱ ❛ ❞✐♠❡♥sã♦ ❝✐❞❛❞❡ ♣♦❞❡ ♣♦ss✉✐r ♦s ❛tr✐❜✉t♦s ♣♦♣✉❧❛çã♦✱ ❞❛t❛ ❞❡ ❢✉♥❞❛çã♦✱ ♥♦♠❡✱ s✐❣❧❛✱ ❡♥tr❡ ♦✉tr♦s✳ ◗✉❛♥❞♦ ♦s ❞❛❞♦s sã♦ ❛♥❛❧✐s❛❞♦s ❡♠ ✉♠❛ ♣❡rs♣❡❝t✐✈❛ ♠✉❧t✐❞✐♠❡♥s✐♦♥❛❧ é ❛ss✉♠✐❞♦ ✉♠ t❡♠❛ ❝❡♥tr❛❧✳ ❊st❡ t❡♠❛ ❝❡♥tr❛❧ é r❡♣r❡s❡♥t❛❞♦ ♣♦r ❢❛t♦s✳ ❋❛t♦s sã♦ ❛s ♠❡❞✐❞❛s q✉❡ ❛♥❛❧✐s❛♠♦s ❛tr❛✈és ❞❛s r❡❧❛çõ❡s ❡♥tr❡ ❛s ❞✐♠❡♥sõ❡s✳ ❖s ❢❛t♦s r❡♣r❡s❡♥t❛♠ ♦ ❞❡s❡♠♣❡♥❤♦ ❞❡ ✉♠ ✐♥❞✐❝❛❞♦r ❡ ❡stá s❡♠♣r❡ ❛ss♦❝✐❛❞♦ ❛ ✉♠❛ ♦✉ ✈ár✐❛s ❞✐♠❡♥sõ❡s✳ ❙ã♦ ❡①❡♠♣❧♦s ❞❡ ❢❛t♦s✿ t❡♠♣❡r❛t✉r❛✱ í♥❞✐❝❡ ♣❧✉✈✐❛❧✱ ♣r❡ç♦✱ ❡♥tr❡ ♦✉tr♦s✳
♥❡✈❡✳
❋✐❣✉r❛ ✷✿ ❉✐♠❡♥sõ❡s ❡ ❋❛t♦s✳
❋✐❣✉r❛ ✸✿ ▼♦❞❡❧♦ ❙♥♦✇❋❧❛❦❡✳
❖ ❡sq✉❡♠❛ ❝♦♥st❡❧❛çã♦ ✭constellation model✮ é ♦ ♠❛✐s ❝♦♠♣❧❡①♦ ❡ é ✉s❛❞❛ ♣♦r ❛♣❧✐❝❛çõ❡s ♠❛✐s s♦✜st✐❝❛❞❛s✳ ❊st❡ ❡sq✉❡♠❛ ♣♦ss✉✐ ✈ár✐❛s t❛❜❡❧❛s ❞❡ ❢❛t♦s q✉❡ ❝♦♠♣❛rt✐❧❤❛♠ ❛s t❛❜❡❧❛s ❞❡ ❞✐♠❡♥sã♦✳ ❊st❡ ❡sq✉❡♠❛ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❡sq✉❡♠❛s ❡str❡❧❛s✱ ♣♦r ✐ss♦ ♦ ♥♦♠❡ ❝♦♥st❡❧❛çã♦ ✭❋✐❣✉r❛ ✹✮✳
2.2 Cubo de Dados
❖ ♠♦❞❡❧♦ ♠✉❧t✐❞✐♠❡♥s✐♦♥❛❧ ♦r❣❛♥✐③❛ ♦s ❞❛❞♦s ❝♦♥❝❡✐t✉❛❧♠❡♥t❡ ❝♦♠♦ ✉♠ ❝✉❜♦ ❞❡ ❞❛❞♦s q✉❡ é ✉♠❛ ❣❡♥❡r❛❧✐③❛çã♦ ❞♦ ♦♣❡r❛❞♦r Group-By s♦❜r❡ t♦❞❛s ♣♦ssí✈❡✐s ❝♦♠❜✐♥❛çõ❡s ❞❡ ❞✐♠❡♥sõ❡s✳ ❈❛❞❛ ❝♦♠❜✐♥❛çã♦ ❞❡ ❞✐♠❡♥sõ❡s ❛❣r❡❣❛ s♦❜r❡ ✉♠❛ ♠❡❞✐❞❛✱ ♣♦rt❛♥t♦ ✉♠ ❝✉❜♦ ❛❣r❡❣❛ s❡❣✉♥❞♦ ✈ár✐❛s ❣r❛♥✉❧❛r✐❞❛❞❡s✳ ❈❛❞❛ Group-by✱ ❝❤❛♠❛❞♦ ❝✉❜♦✐❞❡✱ ❝♦rr❡s♣♦♥❞❡ ❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ t✉♣❧❛s✳
❋✐❣✉r❛ ✹✿ ▼♦❞❡❧♦ ❈♦♥st❡❧❛çã♦✳
❡ ❤♦❧íst✐❝❛✳ ❯♠ ❝✉❜♦ ♥♦r♠❛❧♠❡♥t❡ s✉♣♦rt❛ ♠ú❧t✐♣❧❛s ♠❡❞✐❞❛s✳
❼ Distributiva: ❙✉♣♦♥❤❛ q✉❡ ♦s ❞❛❞♦s ❡stã♦ ♣❛rt✐❝✐♦♥❛❞♦s ❡♠ ♥ ❝♦♥❥✉♥t♦s✳ ❆ ❢✉♥çã♦ ❞❡ ❛❣r❡❣❛çã♦ é ❛♣❧✐❝❛❞❛ ❡♠ ❝❛❞❛ ♣❛rt✐çã♦ r❡s✉❧t❛♥❞♦ ❡♠ ♥ r❡s✉❧t❛✲ ❞♦s ❛❣r❡❣❛❞♦s✳ ❙❡ ♦ r❡s✉❧t❛❞♦ ❞❡r✐✈❛❞♦ ♥❛s ♥ ♣❛rt✐çõ❡s ❢♦r ✐❣✉❛❧ ❛♦ r❡s✉❧t❛❞♦ ❞❛ ❢✉♥çã♦ ❛♣❧✐❝❛❞❛ ❛♦ ❞❛❞♦ s❡♠ ♣❛rt✐❝✐♦♥❛♠❡♥t♦✱ ♣♦❞❡✲s❡ ❞✐③❡r q✉❡ ❛ ❢✉♥✲ çã♦ ♣♦❞❡ s❡r ❝♦♠♣✉t❛❞❛ ❞❡ ✉♠❛ ♠❛♥❡✐r❛ ❞✐str✐❜✉t✐✈❛✳ ◆❡st❡ ❣r✉♣♦ ❡stã♦ ❛s ❢✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦ ♠❛✐s s✐♠♣❧❡s ❞❡ s❡r❡♠ ❝❛❧❝✉❧❛❞❛s✱ ❝♦♠♦ ❝♦✉♥t✭✮✱ s✉♠✭✮✱ ♠✐♥✭✮ ❡ ♠❛①✭✮❀
tr✐❜✉t✐✈❛s✳ ❆s ❢✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦ q✉❡ ♣❡rt❡♥❝❡♠ ❛ ❡st❡ ❣r✉♣♦ sã♦✿ ❛✈❣✭✮✱ ♠✐♥✲◆✭✮ ❡ ♠❛①✲◆✭✮❀
❼ Holística: ◆ã♦ é ♣♦ssí✈❡❧ ❞❡r✐✈❛r ✉♠❛ ❢✉♥çã♦ ❤♦❧íst✐❝❛ ❡♠ ❢✉♥çõ❡s ❛❧❣é✲ ❜r✐❝❛s ♦✉ ❞✐str✐❜✉t✐✈❛s✳ ❚r❛t❛✲s❡ ❞❛ ❝❧❛ss❡ ❞❡ ❢✉♥çõ❡s ♠❛✐s ❝♦♠♣❧❡①❛s ❞❡ s❡r❡♠ ❝♦♠♣✉t❛❞❛s✳ ➱ ♦ t✐♣♦ ❞❡ ❢✉♥çã♦ ❞❡ ❛❣r❡❣❛çã♦ ♠❛✐s ❞✐❢í❝✐❧ ❞❡ s❡r ❝♦♠♣✉t❛❞❛✳ ❙ã♦ ❡①❡♠♣❧♦s ❞❡ ❢✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦ ❤♦❧íst✐❝❛s✿ ♠❡❞✐❛♥❛✭✮✱ ♠♦❞❛✭✮ ❡ r❛♥❦✭✮✳
❋✐❣✉r❛ ✺✿ Pr✐♥❝✐♣❛✐s ♦♣❡r❛❞♦r❡s✳ ❋♦♥t❡✿ ✭❞❡ ❈❛str♦ ▲✐♠❛✱ ✷✵✵✾✮✳
❼ Slicing-Dicing: ❊st❛ ♦♣❡r❛çã♦ s❡❧❡❝✐♦♥❛ ✉♠❛ ♣♦rçã♦ ❞♦ ❝✉❜♦✳ P❛r❛ ❢❛✲ ③❡r ❡st❛ ♦♣❡r❛çã♦✱ é ♥❡❝❡ssár✐♦ ❡s❝♦❧❤❡r ✉♠ ✈❛❧♦r ✜①♦ ❞❡ ✉♠❛ ❞✐♠❡♥sã♦ ❡ r❡❧❛❝✐♦♥❛r ❡st❡ ✈❛❧♦r ❝♦♠ t♦❞♦s ♦s ✈❛❧♦r❡s ❞❛s ♦✉tr❛s ❞✐♠❡♥sõ❡s❀
❼ Pivoting: ◗✉❛♥❞♦ é ❢❡✐t♦ ♦ ♣✐✈♦t❡❛♠❡♥t♦ ❞❡ ✉♠ ❝✉❜♦✱ é ❢❡✐t♦ ❛ r♦t❛çã♦ ❞❛s ❞✐♠❡♥sõ❡s✳ ❊♠ ✉♠ ❝✉❜♦ ❝♦♠ ❞✉❛s ❞✐♠❡♥sõ❡s✱ ♣♦❞❡♠♦s ❞✐③❡r q✉❡ ♦❝♦rr❡ ❛ tr♦❝❛ ❞❡ ✉♠❛ ❧✐♥❤❛ ♣♦r ✉♠❛ ❝♦❧✉♥❛❀
✭◗✶✱ ◗✷✱ ◗✸ ❡ ◗✹✮ ♣❛r❛ s❡♠❡str❡ ✭❙✶ ❡ ❙✷✮✳
❼ Drill-Down: ❊ss❛ ♦♣❡r❛çã♦ ♦❝♦rr❡ ❡♠ ❞✐r❡çã♦ ♦♣♦st❛ ❛ ♦♣❡r❛çã♦ ❞❡ Roll Up✳ ◆❛ ❋✐❣✉r❛ ✺ ♦ r❡s✉❧t❛❞♦ ❞❛ ♦♣❡r❛çã♦ ❞❡ Drill-Down t❡♠♦s ❛ ❞❡s❝✐❞❛ ♥♦ ❝♦♥❝❡✐t♦ ❞❡ ❤✐❡r❛rq✉✐❛ ❞❡ t❡♠♣♦ ❞♦ ♥í✈❡❧ ❞❡ tr✐♠❡str❡ ✭◗✶✱ ◗✷✱ ◗✸ ❡ ◗✹✮ ♣❛r❛ ♠ês ✭❏❛♥✱ ❋❡✈✱ ▼❛r✱ ❆❜r✱ ▼❛✐✱ ❏✉♥✱ ❏✉❧✱ ❆❣♦✱ ❙❡t✱ ❖✉t✱ ◆♦✈ ❡ ❉❡③✮✳
2.3 Computação de Cubos
❆ ❝r✐❛çã♦ ❞❡ ✉♠ ❝✉❜♦ é ✉♠ ♣r♦❜❧❡♠❛ ❞❡ ❝♦♠♣❧❡①✐❞❛❞❡ ❡①♣♦♥❡♥❝✐❛❧ ❡♠ ❢✉♥✲ çã♦ ❞♦ ♥ú♠❡r♦ ❞❡ ❞✐♠❡♥sõ❡s✳ ❙❡♥❞♦ ❛ss✐♠ ❛ ♠❛t❡r✐❛❧✐③❛çã♦ ❞❡ ✉♠ ❝✉❜♦ ❡♥✈♦❧✈❡ ❣r❛♥❞❡ q✉❛♥t✐❞❛❞❡ ❞❡ ♠❡♠ór✐❛ ❡ t❡♠♣♦ ❞❡ ❡①❡❝✉çã♦✳ ❆♦ ❝♦♠♣✉t❛r ❝✉❜♦s ❡s✲ ♣❛❝✐❛✐s ❡st❡ ❣❛st♦ ❞❡ t❡♠♣♦ ❡ ♠❡♠ór✐❛ ❛✉♠❡♥t❛✱ ♣♦✐s ❛ ♠❛t❡r✐❛❧✐③❛çã♦ ❞♦ ❝✉❜♦ ❡♥✈♦❧✈❡ ♦ ❛r♠❛③❡♥❛♠❡♥t♦ ❞❡ ❞❛❞♦s ❡s♣❛❝✐❛✐s ❡ ❛ ❝♦♠♣✉t❛çã♦ ❞❡ ♦♣❡r❛❞♦r❡s ❡s✲ ♣❛❝✐❛✐s ❝♦♠♦ t♦❝❛✱ ✉♥✐ã♦✱ ✐♥t❡rs❡çã♦✱ ❡♥tr❡ ♦✉tr♦s✳
❯♠ ❞♦s ♣r✐♠❡✐r♦s ❛❧❣♦r✐t♠♦s ♥❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s ✉s❛♥❞♦ ❡str✉t✉r❛s ❡♠ ♠❡♠ór✐❛ ♣r✐♠❛r✐❛ é ❛ ❛❜♦r❞❛❣❡♠ Multi-way ✭❩❤❛♦ ❡t ❛❧✳✱ ✶✾✾✽✮✳ ❖ ❛❧❣♦r✐t♠♦ ❝❛rr❡❣❛ ♦s ❞❛❞♦s ❡♠ ✈❡t♦r❡s ❡ ♥ã♦ ✉t✐❧✐③❛ t❛❜❡❧❛s ❞❡ ❜❛♥❝♦s ❞❡ ❞❛❞♦s r❡❧❛❝✐♦✲ ♥❛✐s✳ ❖s ✈❡t♦r❡s sã♦ ♣❛rt✐❝✐♦♥❛❞♦s ❡♠ ♣á❣✐♥❛s✱ ♦♥❞❡ ❝❛❞❛ ♣á❣✐♥❛ ❝♦♥s❡❣✉❡ s❡r ❛r♠❛③❡♥❛❞❛ ❡♠ ♠❡♠ór✐❛ ♣r✐♥❝✐♣❛❧✳
♣❛r❛ ♦ ❛❧❣♦r✐t♠♦ ❝❛❧❝✉❧❛r t♦❞♦s ❛s ❛❣r❡❣❛çõ❡s ❡♠ ✉♠❛ só ✈❛rr❡❞✉r❛✱ ❡✈✐t❛♥❞♦ ♠ú❧t✐♣❧♦s ❡ ❝✉st♦s♦s ❛❝❡ss♦s ❛♦s ❞❛❞♦s ❞❡ ❡♥tr❛❞❛✳
◆❛ ❋✐❣✉r❛ ✻ ✐❧✉str❛✲s❡ ❛ ❝♦♠♣✉t❛çã♦ ❞♦ ❝✉❜♦ ✉s❛♥❞♦ ❛ ❡str❛té❣✐❛ top-down✳ ■♥✐❝✐❛❧♠❡♥t❡✱ s❡ ❝♦♠♣✉t❛ ❛ t✉♣❧❛ ❞❛ ❜❛s❡ ❞❡ ❡♥tr❛❞❛✱ ♥❡st❡ ❡①❡♠♣❧♦ ❝♦♠♣♦st❛ ♣♦r q✉❛tr♦ ❛tr✐❜✉t♦s ❆❇❈❉✳ ❯♠❛ ✈❡③ ❣❡r❛❞♦ ❛ ❛❣r❡❣❛çã♦ ❆❇❈❉✱ ♣♦❞❡✲s❡ ❣❡r❛r ❛ ❛❣r❡❣❛çã♦ ❇❈❉ r❡♠♦✈❡♥❞♦ ♦ ❛tr✐❜✉t♦ ❆✳ ❊st❡ ♣r♦❝❡❞✐♠❡♥t♦ s❡ r❡♣❡t❡ r❡♠♦✈❡♥❞♦✲ s❡ ❇✱ ❈ ❡ ❉✳ ❆♦ ❣❡r❛r ❛ ❛❣r❡❣❛çã♦ ❇❈❉✱ t❛♠❜é♠ é ♣♦ssí✈❡❧ ❣❡r❛r ❛ ❛❣r❡❣❛çã♦ ❇❉ ❡ ❧♦❣♦ ❡ s❡❣✉✐❞❛ ❇✳ ❆ ♣❛rt✐r ❞❡ ❇❈❉ t❛♠❜é♠ é ♣♦ssí✈❡❧ ❣❡r❛r ❇❈✳ ❉❡ ✉♠❛ ❢♦r♠❛ ❣❡r❛❧✱ ❡st❛ ❡str❛té❣✐❛ s❡ ❜❡♥❡✜❝✐❛ ❞♦ ❢❛t♦ q✉❡ ❛s ❛❣r❡❣❛çõ❡s ♠❛✐s ❣❡r❛✐s✱ ♦✉ s❡❥❛✱ ❝♦♠ ♠❡♥♦s ❛tr✐❜✉t♦s✱ ♣♦❞❡♠ s❡r ❞❡r✐✈❛❞❛s ❢❛❝✐❧♠❡♥t❡ ❛ ♣❛rt✐r ❞❛s ❛❣r❡❣❛çõ❡s ♠❛✐s ❡s♣❡❝í✜❝❛s✱ ♦✉ s❡❥❛✱ ❝♦♠ ♠❛✐♦r ♥ú♠❡r♦ ❞❡ ❛tr✐❜✉t♦s✳
❋✐❣✉r❛ ✻✿ ❆❜♦r❞❛❣❡♠ Top-Down ♣❛r❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s✳
❞❡ ✷✳
❋✐❣✉r❛ ✼✿ ❈✉❜♦ ■❝❡❜❡r❣✳ ❋♦♥t❡✿ ✭❋✐♥❞❧❛t❡r ❛♥❞ ❍❛♠✐❧t♦♥✱ ✷✵✵✸✮
❖ ❛❧❣♦r✐t♠♦ ♣r♦♣♦st♦ r❡❝❡❜❡✉ ♦ ♥♦♠❡ ❞❡ ❇❯❈ ✭Botton-Up Cube✮✱ ♣♦✐s ❛❞♦t❛ ❛ ❡str❛té❣✐❛ Bottom-up✱ ♦♥❞❡ s❡ ♣r♦❝❡ss❛ ♦ ❝✉❜♦ ❛ ♣❛rt✐r ❞♦s Group-bys ♠❛✐s ❛❣r❡❣❛❞♦s ♣❛r❛ ♦s Group-bys ♠❡♥♦s ❛❣r❡❣❛❞♦s✱ ❞✐❢❡r❡♥t❡ ❞♦ ❛❧❣♦r✐t♠♦ Multi-way ♣r❡✈✐❛♠❡♥t❡ ❡①♣❧✐❝❛❞♦✳ ❆ ♣r✐♥❝✐♣❛❧ ✈❛♥t❛❣❡♠ ❞❡st❡ ❛❧❣♦r✐t♠♦ é r❡❛❧✐③❛r ❛ ♣♦❞❛ ❞❛s ❛❣r❡❣❛çõ❡s q✉❡ ✈✐♦❧❛♠ ♦ ❧✐♠✐❛r ♠í♥✐♠♦ ♦ ♠❛✐s ❝❡❞♦ ♣♦ssí✈❡❧✱ s❡♠ t❡r q✉❡ ❣❛st❛r ♣r♦❝❡ss❛♠❡♥t♦ ❣❡r❛♥❞♦ ❛❣r❡❣❛çõ❡s ❞❡s♥❡❝❡ssár✐❛s ❛♦ Iceberg Cube✳ ❆ ♣r♦✲ ♣r✐❡❞❛❞❡ ❛♥t✐♠♦♥♦tô♥✐❝❛✱ ❞❡s❝r✐t❛ ❡♠ ✭❆❣r❛✇❛❧ ❛♥❞ ❙r✐❦❛♥t✱ ✶✾✾✹✮✱ ❣❛r❛♥t❡ q✉❡ s❡ ✉♠ ❞❛❞♦ ❝♦♥❥✉♥t♦ ❞❡ ❛tr✐❜✉t♦s ❙ é ✐♥❢r❡q✉❡♥t❡✱ t♦❞♦s ♦s ❛♥❝❡str❛✐s t❛♠❜é♠ sã♦✳ ❖s ❛♥❝❡str❛✐s ❞❡ ❙ ❞❡✈❡♠ ♣♦ss✉✐r ❙✲♥ ❛tr✐❜✉t♦s ✐❣✉❛✐s ❛ ❙✱ ♦♥❞❡ n > 1✳
◆♦ ❡①❡♠♣❧♦ ❞❛ ❋✐❣✉r❛ ✽ ❣❡r❛♠♦s ❛s ❛❣r❡❣❛çõ❡s ❆✱ ❇✱ ❈ ❡ ❉ s❡♣❛r❛❞❛♠❡♥t❡✳
é q✉❡ ❛s ❛❣r❡❣❛çõ❡s ✐♥❢r❡q✉❡♥t❡s ♣♦❞❡♠ s❡ t♦r♥❛r ❢r❡q✉❡♥t❡s ♥✉♠ s❡r✈✐❞♦r ❖▲❆P à ♠❡❞✐❞❛ q✉❡ ❛t✉❛❧✐③❛çõ❡s sã♦ ❝♦♠♣✉t❛❞❛s✱ ♣♦ré♠ ♦s Iceberg Cube ♥ã♦ ♣❡r♠✐t❡♠ ❞❡t❡❝t❛r ❛✉t♦♠❛t✐❝❛♠❡♥t❡ t❛❧ ❝❡♥ár✐♦✳
❆ ❛❜♦r❞❛❣❡♠ ❙t❛r ♣r♦♣♦st❛ ❡♠ ✭❳✐♥ ❡t ❛❧✳✱ ✷✵✵✼✮ é ❛ ♣r✐♠❡✐r❛ q✉❡ ✐♥t❡❣r❛ ❛s ✈❛♥t❛❣❡♥s ❞❛s ❡str❛té❣✐❛s bottom-up ❡ top-down✳ ❯♠❛ ♥♦✈❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❝✉❜♦s é ♣r♦♣♦st❛ ❡ ❡st❛ ♣❡r♠✐t❡ q✉❡ ❛❣r❡❣❛çõ❡s s❡❥❛♠ ❛r♠❛③❡♥❛❞❛s ❡♠ ♥ós ✐♥t❡r✲ ♠❡❞✐ár✐♦s ❞❡ ✉♠❛ ❣r❛❢♦ ❛❝í❝❧✐❝♦ ❞✐r❡❝✐♦♥❛❞♦ ✭❉❆●✮ ❝❤❛♠❛❞♦ star-tree✳ ❖✉tr❛s ❛❜♦r❞❛❣❡♥s✱ ❝♦♠♦ ❉✇❛r❢✱ ❈✲❈✉❜✐♥❣✱ ▼❈● ❡ ▼❉❆●✱ ✐♥✈❡st✐r❛♠ ❡♠ r❡❞✉③✐r ♦ t❛♠❛♥❤♦ ❞♦ ❣r❛❢♦✱ s✉♣r✐♥❞♦ ♥ós ❞❡s♥❡❝❡ssár✐♦s ❞❛ r❡♣r❡s❡♥t❛çã♦ ❞♦ ❝✉❜♦✳ ◆❡st❡ tr❛❜❛❧❤♦ é ❛❞♦t❛❞♦ ❛ ❛❜♦r❞❛❣❡♠ ❙t❛r ♣❛r❛ ❣❡r❛çã♦ ❞❡ ❛❣r❡❣❛çõ❡s ❞❡ ✉♠ ❝✉❜♦ ❞❡ ❞❛❞♦s✳ ❆ ❛❜♦r❞❛❣❡♠ ❙t❛r ♣❡r♠✐t❡ ❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s ❝♦♠♣❧❡t♦s ♦✉ ♣❛r❝✐❛✐s✱ ✐♥❝❧✉✐♥❞♦ Iceberg Cubes✳ ▼❛✐♦r❡s ❞❡t❛❧❤❡s ❞❛ r❡♣r❡s❡♥t❛çã♦ ❙t❛r✲❚r❡❡ ♥♦ ❝❛♣ít✉❧♦ ✹✳✷✳✷✳
2.4 Representação de dados Espaciais Geográficos
P❛r❛ ❡♥t❡♥❞❡r ❝♦♠♦ é ❢❡✐t❛ ❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s ❡s♣❛❝✐❛✐s ♣r✐♠❡✐r♦ é ❡ss❡♥✲ ❝✐❛❧ ❡♥t❡♥❞❡r ❝♦♠♦ é ❢❡✐t❛ ❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ♠❛♣❛s ❡♠ s✐st❡♠❛s ❝♦♠♣✉t❛❝✐♦♥❛✐s✳ ❯♠ ♠❛♣❛ é r❡♣r❡s❡♥t❛❞♦ ❡♠ ❝❛♠❛❞❛s ♦♥❞❡ ❝❛❞❛ ❝❛♠❛❞❛ r❡♣r❡s❡♥t❛ ✉♠ t✐♣♦ ❞❡ ✐♥❢♦r♠❛çã♦✳ ❆❜❛✐①♦ ❤á ✉♠❛ ❜r❡✈❡ ❞❡s❝r✐çã♦ ❞♦s t✐♣♦s ❞❡ ❝❛♠❛❞❛s q✉❡ sã♦ ✉s❛❞❛s ♣❡❧♦s ♣r✐♥❝✐♣❛✐s ❙✐st❡♠❛s ❞❡ ■♥❢♦r♠❛çõ❡s ●❡♦❣rá✜❝❛s✿
❼ Vetorial: ➱ ❛ ❝❛♠❛❞❛ ♦♥❞❡ ♦❝♦rr❡ ❛s ❛❣r❡❣❛çõ❡s ❞♦s ❝✉❜♦s ❡s♣❛❝✐❛✐s✱ s❡♥❞♦ ❢♦r♠❛❞❛ ♣♦r ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✈❡t♦r❡s q✉❡ ♣♦❞❡♠ r❡♣r❡s❡♥t❛r ♣♦♥t♦s✱ ❧✐♥❤❛s ❡ ♣♦❧í❣♦♥♦s✳ ❈❛❞❛ ❡❧❡♠❡♥t♦ ❞❡st❛ ❝❛♠❛❞❛ é ❝❤❛♠❛❞♦ ❣❡♦✲♦❜❥❡t♦ ❡ ❡stá ❛ss♦❝✐❛❞♦ ❛ ❛tr✐❜✉t♦s ♥ã♦ ❡s♣❛❝✐❛✐s q✉❡ ♦ ❞❡s❝r❡✈❡♠✳ ❈❛❞❛ ❣❡♦✲♦❜❥❡t♦ ♣♦s✲ s✉✐ ✉♠ ✐❞❡♥t✐✜❝❛❞♦r ú♥✐❝♦ q✉❡ s❡r✈❡ ❝♦♠♦ ❝❤❛✈❡ ❞❡ ♥❛✈❡❣❛❜✐❧✐❞❛❞❡ ❡♥tr❡ ❛ ♣♦rçã♦ ❡s♣❛❝✐❛❧ ❡ ❛❧❢❛♥ú♠❡r✐❝❛ ❞❡ ♣♦❧í❣♦♥♦✱ ♣♦♥t♦ ♦✉ ❧✐♥❤❛❀
❼ Matricial: ❘❡♣r❡s❡♥t❛ ✐♠❛❣❡♥s q✉❡ ❣❡r❛❧♠❡♥t❡ sã♦ ❝♦❧❡t❛❞❛s ♣♦r s❡♥s♦r❡s r❡♠♦t♦s à ❜♦r❞♦ ❞❡ s❛té❧✐t❡s ♦✉ ❛❡r♦♥❛✈❡s✳ ◆❡st❛ ❝❛♠❛❞❛ ♦ ❡s♣❛ç♦ é ❞✐✈✐❞✐❞♦ ❡♠ ❝é❧✉❧❛s q✉❡ ❢♦r♠❛♠ ✉♠❛ ♠❛tr✐③✳ ❈❛❞❛ ❝é❧✉❧❛ ♣♦❞❡ ❡st❛r ❛ss♦❝✐❛❞❛ ❛ ✉♠❛ ❝❧❛ss✐✜❝❛çã♦ ♣ré✈✐❛ q✉❡ ❛ ❞❡s❝r❡✈❡✳ ❈❧❛ss✐✜❝❛r ❛s ❝é❧✉❧❛s ❡①✐❣❡ té❝♥✐❝❛s ❛✈❛♥ç❛❞❛s ❞❡ ♣r♦❝❡ss❛♠❡♥t♦s ❞❡ ✐♠❛❣❡♥s❀
❆ ❡s❝❛❧❛ ❞❡ ✉♠ ❢❡♥ô♠❡♥♦ é ❞❡t❡r♠✐♥❛❞❛ ♣❡❧❛ s✉❛ r❡s♦❧✉çã♦ ♦✉ ❣r❛♥✉❧❛r✐❞❛❞❡ ❡ ♣❡❧❛ ❡①t❡♥sã♦ ❡♠ q✉❡ ♦ ❢❡♥ô♠❡♥♦ é ❝❛r❛❝t❡r✐③❛❞♦ ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ❡ ❡s♣❛ç♦✳ ❊♠ s✉♠❛✱ ❡①t❡♥sã♦ s❡ r❡❢❡r❡ ❛ ár❡❛ ❡♠ q✉❡ ♦ ❢❡♥ô♠❡♥♦ ❛❝♦♥t❡❝❡ ❡♥q✉❛♥t♦ ❛ r❡s♦❧✉çã♦ s❡ r❡❢❡r❡ ❛ ♣r❡❝✐sã♦ ✉s❛❞❛ ♥❛s ♠❡❞✐❞❛s r❡❛❧✐③❛❞❛s s♦❜r❡ ♦ ❢❡♥ô♥❡♠♦ ✭❲❤✐t❡ ❛♥❞ ❘✉♥♥✐♥❣✱ ✶✾✾✹✮✳
◆❛ ✜❣✉r❛ ✾ ❡stá ✉♠ ❡①❡♠♣❧♦ ❞♦s três t✐♣♦s ❞❡ r❡♣r❡s❡♥t❛çõ❡s ❞❡ ♠❛♣❛s ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ✐♥❢♦r♠❛çã♦ ❣❡♦❣rá✜❝❛ ✭❱❡t♦r✐❛❧✱ ▼❛tr✐③ ❡ ❊s♣❛ç♦ ❈❡❧✉❧❛r✮✳
2.5 Medidas e Dimensões Espaciais
❖ q✉❡ ❝❛r❛❝t❡r✐③❛ ✉♠ ❝✉❜♦ ❞❡ ❞❛❞♦s ❝♦♠♦ ❡s♣❛❝✐❛❧ é ❛ ✉t✐❧✐③❛çã♦ ❞❡ ❣❡♦✲ ♦❜❥❡t♦s✱ s❡❥❛ ❝♦♠♦ ✉♠❛ ♠❡❞✐❞❛ ♦✉ ❝♦♠♦ ❛tr✐❜✉t♦ ❡♠ ✉♠❛ ❞✐♠❡♥sã♦✳ ◆❛ ❋✐❣✉r❛
✶✵ t❡♠♦s ♦ ❡①❡♠♣❧♦ ❞❡ ✉♠❛ ❞✐♠❡♥sã♦ ❡s♣❛❝✐❛❧ ❡♠ ✉♠ ❉❲ q✉❡ ✉s❛ ♦ ❡sq✉❡♠❛
✢♦❝♦s ❞❡ ♥❡✈❡✳ ❆ ❧♦❝❛❧✐❞❛❞❡ é ❝♦♠♣♦st❛ ♣♦r ✈ár✐♦s ❛tr✐❜✉t♦s ❛❧❢❛♥✉♠ér✐❝♦s ✭❝❡♣✱ ♥♦♠❡✱ ♣♦♣✉❧❛çã♦✱ ◆✳ ❞❡ ❍♦s♣✐t❛✐s✮ ❡ ✉♠ ❛tr✐❜✉t♦ ❣❡♦♠étr✐❝♦ ✭❣❡♦♠❡tr✐❛✮✳ ❆ ❡♥t✐❞❛❞❡ ❘❡❣✐ã♦ s❡r✈❡ ♣❛r❛ ❞❡✜♥✐r ✉♠❛ r❡❣✐ã♦ s❡❣✉♥❞♦ s✉❛ ❤✐❡r❛rq✉✐❛ ✭❘❡❣✐ã♦ ≺
▲♦❝❛❧✐③❛çã♦✮✳
❋✐❣✉r❛ ✶✵✿ ❉❲ ♠♦rt❛❧✐❞❛❞❡ ❝♦♠ ❛ ❞✐♠❡♥sã♦ ❡s♣❛❝✐❛❧ ▲♦❝❛❧✐③❛❝❛♦✳ ❋♦♥t❡✿ ❋✐❣✉r❛ ❛❞❛♣t❛❞❛ ❞❡ ✭❇✐♠♦♥t❡ ❙✳✱ ✷✵✵✺✮✳
r❡♣r❡s❡♥t❛❞♦s ♣♦r ♦❜❥❡t♦s ❣❡♦❣rá✜❝♦s ♣♦ss✐❜✐❧✐t❛♥❞♦ ✈✐s✉❛❧✐③❛çã♦ ❝❛rt♦❣rá✜❝❛ ❞❛s ❝♦♥s✉❧t❛s ❣❡r❛❞❛s ♣❡❧♦ ✉s✉ár✐♦✳ ❖ t❡r❝❡✐r♦ t✐♣♦ é ❛ ♠✐st❛ q✉❡ é ✉♠❛ ❝♦♠❜✐♥❛çã♦ ❞♦s ♦✉tr♦s ❞♦✐s t✐♣♦s✳ ❆ r❡♣r❡s❡♥t❛çã♦ ♠✐st❛ ✈❛r✐❛ ❡♥tr❡ ❛ r❡♣r❡s❡♥t❛çã♦ ♥ã♦✲ ❡s♣❛❝✐❛❧ ❡♠ ❛❧❣✉♥s ♥í✈❡✐s ❞❡ ❤✐❡r❛rq✉✐❛ ❡ ❛ r❡♣r❡s❡♥t❛çã♦ ❝❛rt♦❣rá✜❝❛ ❡♠ ♦✉tr♦s ♥í✈❡✐s✳ ❖s três ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ r❡♣r❡s❡♥t❛çã♦ ♣♦❞❡♠ s❡r ✈✐st♦s ♥❛ ❋✐❣✉r❛ ✶✶✳
❋✐❣✉r❛ ✶✶✿ ❖s t✐♣♦s ❞❡ ❞❛❞♦s s✉♣♦rt❛❞♦s ❡♠ ✉♠❛ ❞✐♠❡♥sã♦ ❡s♣❛❝✐❛❧✳ ❋♦♥t❡✿ ✭❘✐✈❡st ❡t ❛❧✳✱ ✷✵✵✺✮✳
❯♠❛ ♠❡❞✐❞❛ ❡s♣❛❝✐❛❧ ♣♦ss✉✐ ✉♠ ♦✉ ♠❛✐s ♣♦♥t❡✐r♦s ♣❛r❛ ♦❜❥❡t♦s ❣❡♦❣rá✜✲ ❝♦s ✭❍❛♥ ❡t ❛❧✳✱ ✶✾✾✽❜✮ ❞❡♣❡♥❞❡♥❞♦ ❞♦ ♥í✈❡❧ ❞❡ ❛❣r❡❣❛çã♦✳ ◆❛ ✜❣✉r❛ ✶✷ ❡stá ✉♠ ❡①❡♠♣❧♦ ❞❛ ♠❡❞✐❞❛ ❡s♣❛❝✐❛❧ ✬❣❡♦♠❡tr✐❛✬ q✉❡ é ✉♠ ♣♦♥t❡✐r♦ ♣❛r❛ ✉♠ ♦❜❥❡t♦ ❡s♣❛❝✐❛❧✳
❡♥tr❡ ❛tr✐❜✉t♦s✱ ♣♦✐s ♥♦ ♠♦♠❡♥t♦ ❞❛ ❛❣r❡❣❛çã♦ ❡st❡s ❛tr✐❜✉t♦s ♣♦❞❡♠ ♣♦ss✉✐r ❞❡♣❡♥❞ê♥❝✐❛s ❡♥tr❡ s✐ ✭❇✐♠♦♥t❡ ❙✳✱ ✷✵✵✺✮✳
❋✐❣✉r❛ ✶✷✿ ❉❲ ♠♦rt❛❧✐❞❛❞❡ ❝♦♠ ❛ ♠❡❞✐❞❛ ❡s♣❛❝✐❛❧ ❞❡♣❛rt❛♠❡♥t♦✳ ❋♦♥❡✿ ✭❇✐♠♦♥t❡ ❙✳✱ ✷✵✵✺✮✳
❈♦♠♦ r❡s✉❧t❛❞♦ ❞❛ ❛❣r❡❣❛çã♦ ❞❡ ❞♦✐s ♦❜❥❡t♦s ❡s♣❛❝✐❛✐s ❝♦♠♣❧❡①♦s é ❣❡r❛❞♦ ✉♠ ♥♦✈♦ ♦❜❥❡t♦ ❡s♣❛❝✐❛❧ ❝♦♠♣❧❡①♦ ❝♦♠ ♦s ♠❡s♠♦s ❛tr✐❜✉t♦s✳ ❆♦ r❡❛❧✐③❛r♠♦s ❛ ❛❣r❡❣❛çã♦ ❞❡ ❞♦✐s ❛tr✐❜✉t♦s ❡s♣❛❝✐❛✐s ❞❡✈❡✲s❡ ❝❛❧❝✉❧❛r ♦ ✈❛❧♦r ❞❛s ❛❣r❡❣❛çõ❡s ❞❡ t♦❞♦s ♦s ♦✉tr♦s ❛tr✐❜✉t♦s✳ P❛r❛ ✐ss♦ ❞❡✈❡✲s❡ ❛♣❧✐❝❛r ✉♠❛ ❢✉♥çã♦ ❞❡ ❛❣r❡❣❛çã♦ ❡q✉✐✈❛❧❡♥t❡ ❛ q✉❡ ❢♦✐ ❛♣❧✐❝❛❞❛ ♥♦ ❛tr✐❜✉t♦ ❡s♣❛❝✐❛❧✳ ❱❛♠♦s ❛♦ ❡①❡♠♣❧♦✿
❞❡st❡s ❛tr✐❜✉t♦s✳ ❉❡✜♥✐r ❛s ❞❡♣❡♥❞ê♥❝✐❛s ❡♥tr❡ ♦s ❛tr✐❜✉t♦s ♣❛r❛ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❛❣r❡❣❛çõ❡s ❡s♣❛❝✐❛✐s ❡ ♣❛r❛ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❛tr✐❜✉t♦s é ✉♠ ♦❜stá❝✉❧♦ ♣❛r❛ ❣❡r❛çã♦ ❞❡ ♥♦✈♦s ♦❜❥❡t♦s ❡s♣❛❝✐❛✐s ❛ ♣❛rt✐r ❞❛ ❛❣r❡❣❛çã♦ ❞❡ ♦❜❥❡t♦s ❤✐❡r❛rq✉✐✲ ❝❛♠❡♥t❡ ✐♥❢❡r✐♦r❡s✳ ◆❛ ❛❜♦r❞❛❣❡♠ ●❡♦❈✉❜❡ ♦ ✉s✉ár✐♦ é r❡s♣♦♥sá✈❡❧ ♣♦r ❞❡✜♥✐r ❡st❛s ❞❡♣❡♥❞ê♥❝✐❛s✳
2.6 Hierarquia Espacial
❆ss✐♠ ❝♦♠♦ ♥♦ ❝✉❜♦ ❛❧❢❛✲♥✉♠ér✐❝♦ ♦ ❝✉❜♦ ❡s♣❛❝✐❛❧ t❛♠❜é♠ é ❤✐❡r❛rq✉✐③❛❞♦ ❛ ✜♠ ❞❡ ♣♦ss✐❜✐❧✐t❛r ♦♣❡r❛çõ❡s ❝♦♠♦ roll-up✱ drill-down✱ slice ❡ dice✳
❆ ❤✐❡r❛rq✉✐❛ ❞❡ ✉♠❛ ❞✐♠❡♥sã♦ ❡s♣❛❝✐❛❧ ♦❝♦rr❡ ♣♦r ✐♥s❡rçã♦ ❞❡ ♥♦✈♦s ❛tr✐✲ ❜✉t♦s q✉❡ ❝❧❛ss✐✜❝❛♠ ♦ ♦❜❥❡t♦ ♥♦s ❞✐❢❡r❡♥t❡s ♥í✈❡✐s ❞❡ ❤✐❡r❛rq✉✐❛ ♦✉ ♣♦r ❛❞✐çã♦ ❞❡ ❞✐♠❡♥sõ❡s✳ ❈❛❞❛ ♥í✈❡❧ ❞❡ ❤✐❡r❛rq✉✐❛ ♣♦ss✉✐ ✉♠ ✐❞❡♥t✐✜❝❛❞♦r ♣❛r❛ ♦ ♦❜❥❡t♦ ❣❡♦❣rá✜❝♦ ❝♦rr❡s♣♦♥❞❡♥t❡✱ ♦ q✉❡ ♣❡r♠✐t❡ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ r❡♣r❡s❡♥t❛çõ❡s ♣❛r❛ ♦s ❞✐❢❡r❡♥t❡s ♥í✈❡✐s✳ ❆ ♠❡❞✐❞❛ q✉❡ ♠✉❞❛♠♦s ♦ ♥í✈❡❧ ❞❛ ❤✐❡r❛rq✉✐❛ ♠✉❞❛♠♦s s✉❛ ✈✐s✉❛❧✐③❛çã♦✳ ❊st❡ t✐♣♦ ❞❡ ❛❜♦r❞❛❣❡♠ ❢❛❝✐❧✐t❛ ❛ ♥❛✈❡❣❛çã♦ ♥♦ ❝✉❜♦ ❞❡ ❞❛❞♦s ❡ t❛♠❜é♠ ❡✈✐t❛ q✉❡ s❡❥❛ ❢❡✐t❛ ♦♣❡r❛çõ❡s ❝♦♠♣❧❡①❛s s♦❜r❡ ♣♦❧í❣♦♥♦s✳
◆❛ ❋✐❣✉r❛ ✶✸ ✐❧✉str❛✲s❡ ✉♠❛ r❡♣r❡s❡♥t❛çã♦ ❞❡ ❤✐❡r❛rq✉✐❛ t❡♠♣♦r❛❧ ❝♦♠ ❛
s❡❣✉✐♥t❡ ♦r❞❡♠ ✭❆♥♦ ≺ ❙❡♠❡str❡ ≺ ▼❡s ≺ ❉✐❛✮ ✭❆♥♦ ≺ ❙❡♠❛♥❛ ≺ ❉✐❛✮✳ ◆❛
♠❡s♠❛ ❋✐❣✉r❛ ❤á ✉♠❛ ❤✐❡r❛rq✉✐❛ ❡s♣❛❝✐❛❧ ❝♦♠ ❛ s❡❣✉✐♥t❡ ♦r❞❡♠ ✭P❛✐s≺ ❊st❛❞♦
❋✐❣✉r❛ ✶✸✿ ❍✐❡r❛rq✉✐❛ t❡♠♣♦r❛❧ ✭❆✮ ❡ ❤✐❡r❛rq✉✐❛ ❡s♣❛❝✐❛❧ ✭❇✮✳
2.7 Medidas Espaciais
❆ss✐♠ ❝♦♠♦ é ❝❧❛ss✐✜❝❛❞❛ ❛s ♠❡❞✐❞❛s ♥ã♦ ❡s♣❛❝✐❛✐s t❛♠❜é♠ é ❝❧❛ss✐✜❝❛❞❛ ❛s ♠❡❞✐❞❛s ❡s♣❛❝✐❛✐s✿
❼ Distributiva: ◆❡st❡ ❣r✉♣♦ ❡stã♦ ❛s ❢✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦ ♠❛✐s s✐♠♣❧❡s ❞❡ s❡r❡♠ ❝❛❧❝✉❧❛❞❛s✱ ❝♦♠♦ ✉♥✐ã♦ ❣❡♦♠étr✐❝❛✱ ✐♥t❡rs❡çã♦ ❣❡♦♠étr✐❝❛ ❡ Minimal Orthogonal Bounding Box✳ ➱ ♣♦ssí✈❡❧ ❝❛❧❝✉❧❛r ❡st❡ t✐♣♦ ❞❡ ❢✉♥çã♦ ❞❡ ❛❣r❡✲ ❣❛çã♦ ❛ ♣❛rt✐r ❞♦ ♥í✈❡❧ ♠❛✐s ❜❛✐①♦ ❞❛ ❤✐❡r❛rq✉✐❛✳ ◆♦t❡ q✉❡ só é ♣r❡❝✐s♦ ♦ ✉s♦ ❞♦s ♥í✈❡✐s ✐♠❡❞✐❛t❛♠❡♥t❡ ❛❜❛✐①♦ ♥❛ ❤✐❡r❛rq✉✐❛ ❡ ♥ã♦ t♦❞♦s ♦s ♥í✈❡✐s ✐♥❢❡r✐♦r❡s ❞❛ ❤✐❡r❛rq✉✐❛✳ ❈♦♥❢♦r♠❡ ❥á ❡①♣❧✐❝❛❞♦✱ ❡st❛ ♣r♦♣r✐❡❞❛❞❡ ♦t✐♠✐③❛ ❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s❀
sã♦✿ ❝❡♥tr♦✐❞❡✱ ❝❡♥tr♦ ❞❡ ♠❛ss❛ ❡ ❝❡♥tr♦ ❞❡ ❣r❛✈✐❞❛❞❡❀
3 Trabalhos Relacionados
❖s tr❛❜❛❧❤♦s r❡❧❛❝✐♦♥❛❞♦s ❢♦r❛♠ ❛✈❛❧✐❛❞♦s s❡❣✉♥❞♦ ❛s s❡❣✉✐♥t❡s ♣r♦♣r✐❡❞❛❞❡s✿
❼ Visualização: ❱✐s✉❛❧✐③❛çã♦ ✸❉❀
❼ Recursos Espaciais: ▼❡❞✐❞❛s ❡ ❋✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦ ❡s♣❛❝✐❛✐s ❞✐✈❡rs❛s✱ ❉✐♠❡♥sã♦ ❡s♣❛❝✐❛❧✱ ▼❡❞✐❞❛s ❍✐❜r✐❞❛s✱ ❍✐❡r❛rq✉✐③❛çã♦ ❆✉t♦♠át✐❝❛✱ ♠ú❧t✐✲ ♣❧❛s ♠❡❞✐❞❛s ❡s♣❛❝✐❛✐s✱ ♥ã♦ ❡s♣❛❝✐❛s ♦✉ ❝♦♠❜✐♥❛çõ❡s❀
❼ Desempenho: ❆❜♦r❞❛❣❡♠ P❛r❛❧❡❧❛✱ ❆t✉❛❧✐③❛çã♦ ■♥❝r❡♠❡♥t❛❧✳
3.1 PostGis
❖ s✐st❡♠❛ P♦st●✐s1 é ✉♠❛ ❡①t❡♥sã♦ ❡s♣❛❝✐❛❧ ❞♦ ❙●❇❉ P♦st●r❡❙◗▲2 q✉❡
♦❢❡r❡❝❡ s✉♣♦rt❡ ❛ ♦❜❥❡t♦s ❣❡♦❣rá✜❝♦s✱ ♠❡❞✐❞❛s ❡ ❢✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦ ❡s♣❛❝✐❛✐s✳ ◆♦r♠❛❧♠❡♥t❡✱ é ✉t✐❧✐③❛❞♦ ❝♦♠♦ r❡♣♦s✐tór✐♦ ❞❡ ❞❛❞♦s ♣❛r❛ s✐st❡♠❛s ❙❖▲❆P✳ ❖ P♦st●✐s ✉s❛ ❛ ❜✐❜❧✐♦t❡❝❛ ❏❚❙3 ♣❛r❛ r❡❛❧✐③❛r ❛ ♠❛♥✐♣✉❧❛çã♦ ❞♦s ❞❛❞♦s ❡s♣❛❝✐❛✐s✳ ❖ P♦st●✐s t❛♠❜é♠ ♦❢❡r❡❝❡ ❛ ✐♥❞❡①❛çã♦ ❞♦s ♦❜❥❡t♦s ❣❡♦❣rá✜❝♦s ❛tr❛✈és ❞♦s í♥❞✐❝❡s
1http://postgis.refractions.net/ 2http://www.postgresql.org/
●✐❙❚ ✭Generalized Search Tree✮✱ ❘✲❚r❡❡ ❡ ❇✲❚r❡❡ ♦ q✉❡ t♦r♥❛ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❞❡ ❝♦♥s✉❧t❛s ♠❛✐s ❡✜❝✐❡♥t❡✳
❈♦♠♦ ❛❧t❡r♥❛t✐✈❛ ♣❛r❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s ♦ P♦st●✐s ♦❢❡r❡❝❡ ❛ ♣ré✲❝♦♠♣✉t❛çã♦ ❞❡ ❝♦♥s✉❧t❛s ❛tr❛✈és ❞❛s ✈✐st❛s ♠❛t❡r✐❛❧✐③❛❞❛s✳ ❖ ♣r♦♣ós✐t♦ ❞❛s ✈✐st❛s ♠❛t❡✲ r✐❛❧✐③❛❞❛s é ❞✐♠✐♥✉✐r ♦ t❡♠♣♦ ❞❡ r❡s♣♦st❛ ❞❡ ❝♦♥s✉❧t❛s q✉❡ ♣r♦❝❡ss❛♠ ❣r❛♥❞❡s q✉❛♥t✐❞❛❞❡s ❞❡ ❞❛❞♦s✱ ❛❣r❡❣❛çõ❡s ❡ r❡❧❛❝✐♦♥❛♠❡♥t♦s✳ P❛r❛ ✐ss♦✱ ❛ ❝♦♥s✉❧t❛ é ♣ré✲❝♦♠♣✉t❛❞❛ ❡ s❡✉ r❡s✉❧t❛❞♦ é ♣❡rs✐st✐❞♦ ♥♦ r❡♣♦s✐tór✐♦ ❞❡ ❞❛❞♦s ❡✈✐t❛♥❞♦ q✉❡ ❡st❛ s❡❥❛ r❡✲❝♦♠♣✉t❛❞❛ t♦❞❛ ✈❡③ q✉❡ ❢♦r r❡q✉✐s✐t❛❞❛ ♣❡❧♦ ✉s✉ár✐♦✳ ■♥❢❡❧✐③♠❡♥t❡ ♦ P♦st●✐s ♥ã♦ ♦❢❡r❡❝❡ s✉♣♦rt❡ ♥❛t✐✈♦ ❛ ❝♦♠♣✉t❛çã♦ ❞❡ ❝✉❜♦s✱ ♣♦rt❛♥t♦ ♥ã♦ ♣♦ss✉✐ ♦t✐♠✐③❛çõ❡s ❛♦ ❣❡r❛r ❛s ❛❣r❡❣❛çõ❡s✳ ❊str❛té❣✐❛s ❞❡ ❛t✉❛❧✐③❛çã♦ ❞❡✈❡♠ s❡r ❞❡✜✲ ♥✐❞❛s ♣❛r❛ s❡ ♠♦❞✐✜❝❛r ❛s ✈✐❡✇s ♠❛t❡r✐❛❧✐③❛❞❛s✳ ❖ P♦st●✐s ♥ã♦ ♣♦ss✉✐ ✈❡rsã♦ ❞❡s❡♥❤❛❞❛ ♣❛r❛ ❛rq✉✐t❡t✉r❛s ❞❡ ❝♦♠♣✉t❛❞♦r❡s ❝♦♠ ♠ú❧t✐♣❧♦s ♥ú❝❧❡♦s ❞❡ ♣r♦❝❡s✲ s❛♠❡♥t♦ ♦✉ ♠ú❧t✐♣❧♦s ❝♦♠♣✉t❛❞♦r❡s✱ ♣♦rt❛♥t♦ ❛s ♦♣❡r❛çõ❡s ❞❡ ❝❛r❣❛ ❡ ❝♦♥s✉❧t❛ ✉s✉❢r✉❡♠ s♦♠❡♥t❡ ❞♦ ♣❛r❛❧❡❧✐s♠♦ ✐♠♣❧í❝✐t♦✱ ♦ q✉❡ ♠✉✐t❛s ✈❡③❡s ♥ã♦ ❝♦♥s♦♠❡ t♦❞♦ ♦ r❡❝✉rs♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❞✐s♣♦♥í✈❡❧✳ P♦st●✐s t❛♠❜é♠ ♥ã♦ ♦❢❡r❡❝❡ ❛ ✈✐s✉❛❧✐③❛çã♦ ❞♦s ♠❛♣❛s✳ ❖ P♦st●■❙ é ✉♠ ❙●❇❉ r❡❧❛❝✐♦♥❛❧ ❝♦♠ ❡①t❡♥sõ❡s ❡s♣❛❝✐❛✐s✱ ♣♦r✲ t❛♥t♦ ❤á ❛❧❣✉♥s ✈✐s✉❛❧✐③❛❞♦r❡s ✷❉ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ✈✐s✉❛❧✐③❛r ❡sq✉❡♠❛s ❡s♣❛❝✐❛✐s ♣♦st●■❙✱ ❞❡♥tr❡ ❡❧❡s ♦ ♠❛✐s ✉s❛❞♦ é ♦ P♦st●■❙ ❱✐❡✇❡r 4✳
3.2 GeoMondrian
❖ ●❡♦▼♦♥❞r✐❛♥5 é ✉♠ s✐st❡♠❛ ❙❖▲❆P ❞❡ ❝ó❞✐❣♦ ❛❜❡rt♦ ❡s❝r✐t♦ ❡♠ ❏❛✈❛ q✉❡ ♦❢❡r❡❝❡ ❢✉♥çõ❡s ❝♦♠♦✿ ❡①♣❧♦r❛çã♦ ❞♦s ❞❛❞♦s ❞❡ ❢♦r♠❛ ✐♥t❡r❛t✐✈❛✱ ❝♦♥s✉❧t❛s ❛❞✲❤♦❝
4
http://geotux.tuxfamily.org/index.php/en/component/k2/item/293-consola-sql-para-plugin-pgadmin-postgis-viewer
❡♠ ♠❛♣❛s ❡s♣❛❝✐❛✐s✱ ❢✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦ ❡ ♠❡❞✐❞❛s ❡s♣❛❝✐❛s ❡ s✉♣♦rt❡ ❛ ❞❛❞♦s ❣❡♦♠étr✐❝♦s ✈❡t♦r✐❛✐s✳ ❖ ●❡♦▼♦♥❞r✐❛♥ é ❛ ✈❡rsã♦ ❡s♣❛❝✐❛❧ ❞♦ s❡r✈✐❞♦r ❖▲❆P ▼♦♥❞r✐❛♥ ❡✱ ❛ss✐♠ ❝♦♠♦ ♦ P♦st●✐s✱ ✉s❛ ❛ ❜✐❜❧✐♦t❡❝❛ ❏❚❙ ♣❛r❛ ♠❛♥✐♣✉❧❛çã♦ ❞♦s ❞❛❞♦s ❡s♣❛❝✐❛✐s✳
❆ ♠❛♥✐♣✉❧❛çã♦ ❞♦ ❝✉❜♦ ✉t✐❧✐③❛ ❛ ❧✐♥❣✉❛❣❡♠ ▼❉❳✱ ❞❡s❡♥✈♦❧✈✐❞❛ ♣❡❧❛ ▼✐❝r♦✲ s♦❢t✳ ❆s ❞❡✜♥✐çõ❡s ❞♦ ❝✉❜♦ ✉t✐❧✐③❛♠ ❡sq✉❡♠❛s ❳▼▲✳ ❖ ●❡♦▼♦♥❞r✐❛♠ ❝❛rr❡❣❛ ♦s ❞❛❞♦s ♣❡rs✐st✐❞♦s ♥♦ ❙●❇❉ P♦st●✐s ❡ ❛r♠❛③❡♥❛ ♦ ❝✉❜♦ r❡s✉❧t❛♥t❡ ❡♠ ♠❡♠ór✐❛ ♣r✐♠ár✐❛✱ ♣♦rt❛♥t♦ ❝✉❜♦s ❝♦♠♣✉t❛❞♦s ❛ ♣❛rt✐r ❞❡ ❜❛s❡s ♠❛ss✐✈❛s r❡q✉❡r❡♠ ♠✉✐t❛ q✉❛♥t✐❞❛❞❡ ❞❡ ♠❡♠ór✐❛ ❘❆▼✳ ❖ ●❡♦❈✉❜❡ t❛♠❜é♠ ♣♦ss✉✐ t❛❧ ❧✐♠✐t❛çã♦✱ s❡♥❞♦ ♥❡❝❡ssár✐♦ ✈❡rsõ❡s q✉❡ ❢❛③❡♠ ✉s♦ ❡✜❝✐❡♥t❡ ❞❡ ♠❡♠ór✐❛ ❡①t❡r♥❛✳ ❆t✉❛❧✐③❛çõ❡s ✐♥✲ ❝r❡♠❡♥t❛✐s ❞♦s ❞❛❞♦s sã♦ ❢❡✐t❛s ♣♦r ♠❡✐♦ ❞❡ ♥♦t✐✜❝❛çõ❡s✱ ♦✉ s❡❥❛✱ ♦ ❙●❇❉ ♥♦t✐✜❝❛ ♦ ●❡♦▼♦♥❞r✐❛♠ q✉❛♥❞♦ ❛❧❣✉♠ ❞❛❞♦ s♦❢r❡ ✉♠ ♠♦❞✐✜❝❛çã♦✱ ♦ ●❡♦▼♦♥❞r✐❛♥ ✐❞❡♥✲ t✐✜❝❛ ❛s ❝é❧✉❧❛s ❛❢❡t❛❞❛s ❡ r❡❢❛③ ❛s ❛❣r❡❣❛çõ❡s✳ ❖ ●❡♦❈✉❜❡ ♥ã♦ ✐♠♣❧❡♠❡♥t❛ ♦ s❡r✈✐ç♦ ❞❡ ❛t✉❛❧✐③❛çã♦ ❛té ♦ ♠♦♠❡♥t♦✳
3.3 GeWOlaP
❊♠ ✭❇✐♠♦♥t❡ ❡t ❛❧✳✱ ✷✵✵✼✮ ♦s ❛✉t♦r❡s ❝✐t❛♠ ❛s ♣r✐♥❝✐♣❛✐s ❝❛r❛❝t❡ríst✐❝❛s ❞♦s s✐st❡♠❛s ❙❖▲❆P ❡ ❛ ❞✐✜❝✉❧❞❛❞❡ ❡♠ ✐♠♣❧❡♠❡♥t❛r t❛✐s s✐st❡♠❛s✳ ❊♥tr❡ ♦s ♣r✐♥❝✐✲ ♣❛✐s ❞❡s❛✜♦s ❡stã♦✿ ❛ ❞❡✜♥✐çã♦ ❞❡ ♠❡❞✐❞❛s ❡s♣❛❝✐❛✐s ❡ s✉❛s ❢✉♥çõ❡s ❞❡ ❛❣r❡❣❛çã♦✱ ❞✐♠❡♥sõ❡s ❡s♣❛❝✐❛✐s ❡ s✉❛s ❤✐❡r❛rq✉✐❛s ❡ ❡①t❡♥sã♦ ❞♦s ♦♣❡r❛❞♦r❡s ❙■● ♣❛r❛ ♦s s✐st❡♠❛s ❙❖▲❆P✳
❖s ❛✉t♦r❡s t❛♠❜é♠ ♣r♦♣õ❡♠ ♦ s✐st❡♠❛ ●❡✇❖❧❛♣ q✉❡ é ✉♠ s✐st❡♠❛ ❙❖✲ ▲❆P ❲❡❜ ❜❛s❡❛❞♦ ♥♦ ♠♦❞❡❧♦ ♠✉❧t✐❞✐♠❡♥s✐♦♥❛❧ ❛♣r❡s❡♥t❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡ ❡♠ ✭❙❛♥❞r♦ ❇✐♠♦♥t❡✱ ✷✵✵✻✮✳ ❖ ●❡✇❖❧❛♣ é ❝♦♥str✉í❞♦ ❡♠ ✸ ❝❛♠❛❞❛s✳ ❆ ♣r✐♠❡✐r❛ ❝❛♠❛❞❛ é ✉♠ ❜❛♥❝♦ ❞❡ ❞❛❞♦s ❖❘❆❈▲❊ q✉❡ s✉♣♦rt❛ ♦♣❡r❛çõ❡s ❡s♣❛❝✐❛✐s✱ ❛ s❡✲ ❣✉♥❞❛ é ♦ s❡r✈✐❞♦r ❖▲❆P ▼♦♥❞r✐❛♥ q✉❡ r❡❛❧✐③❛ ❛s ❛❣r❡❣❛çõ❡s ❡ ♣❡rs✐stê♥❝✐❛ ❞♦s ❞❛❞♦s ❡ ❛ t❡r❝❡✐r❛ é ❛ ❝❛♠❛❞❛ ❞❡ ✈✐s✉❛❧✐③❛çã♦ r❡♣r❡s❡♥t❛❞❛ ♣♦r ✉♠ ❝❧✐❡♥t❡ ❙■● ❲❡❜ ❝♦♠♣♦st❛ ♣❡❧♦s ❝♦♠♣♦♥❡♥t❡s ❏P✐✈♦t✱ q✉❡ ♣♦ss✐❜✐❧✐t❛ ❛ ✈✐s✉❛❧✐③❛çã♦ ❞♦s ❞❛❞♦s ❞❡ ❢♦r♠❛ t❛❜✉❧❛r ❡ ❞♦ ▼❛♣❳tr❡♠❡✱ q✉❡ ❢♦r♥❡❝❡ ❛ ✈✐s✉❛❧✐③❛çã♦ ❡s♣❛❝✐❛❧✳ ❖s ❝♦♠✲ ♣♦♥❡♥t❡s ▼❛♣❳tr❡♠❡ ❡ ♦ ❙●❇❉ ❖r❛❝❧❡ ✉s❛❞♦ ♣❡❧❛ s♦❧✉çã♦ ♥ã♦ ♣♦ss✉❡♠ ❝ó❞✐❣♦ ❛❜❡rt♦✳
❋✐❣✉r❛ ✶✹✿ ■♥t❡r❢❛❝❡ ●❡❲❖❧❛♣✳ ❋♦♥t❡✿ ✭❇✐♠♦♥t❡ ❡t ❛❧✳✱ ✷✵✵✼✮✳
