One Torus to Rule them All: Multi-dimensional Queries in P2P Systems

1
One Torus to Rule them All Multi-dimensional
Queries in P2P Systems

• Authors Prasanna Ganesan, Beverly Yang,
  Hector Garcia-Molina
• ????µ?a ??ßa

2
MURK MUlti-Dimensional Rectangulation with
Kd-trees
3
MURK

• ????d?? ß?se?? ded?µ???? ??a multi-dimensional
  e??t?se?? se P2P d??t??
• ??a????sµ?? t?? ded?µ???? ?p?? ß??s???ta? st?
  ???? se ????????a pa?a???????aµµa (rectangles)
  p?? ?a???a t? d?a?e????eta? ??a? ??µß??
• ???s?µ?p???s? t?? kd-trees

4
Kd-trees

• ???e f???? a?t?st???e? se ??a rectangle p??
  d?a?e????eta? ??p???? ??µß??
• ??sa???? ??µß?? d?aµ???asµ?? t?? ????? p??
  ?at??e? ??p??? f???? (se µ?a d??stas?) se µ??? µe
  ?s? f??t??
• ?p?????s? ??µß??
• pa??d?s? t?? ????? st? ade?f??? f????
• a? de? ?p???e? ade?f??? f????, pa??d?s? se
  ??p???? ??µß? ap? t? ?p?-d??t??
• ?a??µ??a efa?µ??? µe t? CAN µe d?af????
• d?a????sµ?? t?? ????? se µ??? µe ?s? f??t??
• d??stas? t?? ????? e?a?t?µe?? ap? t? d??stas? t??
  ded?µ????

5
?a??de??µa
6
???µ?????s?

• ??as??des? t?? ??µß?? ?p?? st? CAN (grid
  structure)
• ???e ??µß?? ??????e? ta ???a t?? ?e?t???? t??
• ? e??t?s? ap? ??a? a????? st?? te????, p????e?ta?
  µ?s? t?? ?e?t???? µe ep????? a?t?? p?? µe???e?
  pe??ss?te?? t?? ap?stas? Manhattan µeta??
  a?????? ?a? te????? ??µß??
• ???ß??µata
• a??µ???µ??f?a t?? ????? µe ap?t??esµa ??µß?? µe
  µe???? rectangle ?a ????? p?????? ?e?t??e? ??
  ?ts? ??? ?d?? f??t?? µ???µ?t?? se ???e ??µß? ?at?
  t? d??µ?????s?
• ?? s??d?se?? µ??? µe t??? ?e?t??e? de? e??a?
  a??et?? ??a ap?d?t??? d??µ?????s?

7
?e?t??µ??? d??µ?????s?

• ?p?p???? s??d?se?? se ??µß??? (skip pointers)
  e?t?? ap? t?? ?p?????se? ???? t?? d?µ??
• ??? d?af??et???? p??se???se?? a?????a µe t??
  t??p? p?? d?µ????????ta? ?? skip pointers
• Random ???e ??µß?? d?at??e? skip pointers se s
  t??a???? ??µß??? ap? t? s????? t?? ??µß??. ?d?a
  ap?d?s? µe t?? te????? t?? realities st? CAN
• Space-filling Skip graph pa??µ??a µe t?? te?????
  skip graph. ???s?µ?p??e?ta? ??aµµ??? d??ta??
  t?? ??µß?? ? ?p??a ??e? t?? ?d??t?te? e??? skip
  graph.

8
?d??t?te? t?? te?????? MURK

• Locality a??et? ?a??, af?? d?a?????e? t? ???? se
  t?sa rectangles ?s?? ?a? ?? ??µß??
• Load balancing
• a??et? ?a?? a? ? ?ata??µ? t?? ded?µ???? e??a?
  sta?e??
• rectangles µe d?af??et??? f??t?? a? ? ?ata??µ?
  t?? ded?µ???? e??a? d??aµ???. ???s?µ?p?????ta? ??
  te?????? NBRADJUST REORDER ??a ep?te??? ?a???
  load balancing

9
???t?se??

• ?