A03? ??????????? ????????????

1
A03????????????????????????

• ?????? ?? ??
• ????? ? ??

2
????????
??????????
?????????
OBDD? ?????
?????? ??????
OBDD????????????????????????
3
????
??????????? ??????
?????????
OBDD???????? ??????????
4
1.??????????

• Tree-Shellable???????
• ??????????????????
• ??????????????
• (Ordered)Tree-Shellable????
• ????????(??????)
• ???1???????????
• ????????

1
0
1
0
1
1
1
1
1
1
5
Tree-Shellable????
??????DNF????tree-shellability
DNF???????????????????? ??????????????
DNF????????? ?? ???? ? ?? ?????
tree-shellable?????? ???????????????
6
Tree-Shellable????

• ??????DNF????Tree-Shellability
• ?????
• ???????????????
• tree-shellable ?????
• ordered tree-shellable NP??
• ??????tree-shellability??????
• ?????????????
• ???????????
• ???????????

7
2. ???????????????????

• ???????OBDD????????
• ??????????????????????
• ??????
• OBDD(???????)
• ??????????
• ??????????????
• ????????????????
• ?????????????
• OBDD???????????????

8
???????????????????

• ???????????????
• ??????????????
• ????????????
• BMD?????????????
• ?????????OBDD??
• ZBDD????????????????????
• ???????BDD??
• OBDD?????????????? ??

9
??????OBDD???????????????

• ????????OBDD??
• ?????(?????????)???????
• ?????????????????????
• ?????????????k????????????
• ??

10
OBDD???????????????

• ????????????????????????
• ????????????
• ?????????????
• ??????????????????????
• ?nn???????

n ??? ??? OBDD???
2 4 2 13
3 9 42 87
4 16 24024 431
5 25 ? 1925
11
OBDD???????????????

• ???????????????OBDD??????
• ??????OBDD????
• ??????????????????????????
• ?????????????
• ????????OBDD???????
• 44?55????????8788??
• ???????????????

12
Compilation of Bayesian Networks Using ZBDDs

• ?Compilation of Bayesian Networks?
  ??????????????????BDD???????????Minato et al.
  IJCAI-2007
• ???????BDD ? ???????????????????????????????
• ???ZBDD???????????(?????)???????????????????????
  ???????????
• ????????????????????????????????????
• ? ??????????????(??????????)

13
Compilation of Bayesian Networks Using ZBDDs
????????
??????? (?????)
?????? (ZBDD)
?????????
14
???????BDD??

• ???????BDD??(DDMF, QMDD)?????????CAD????
• (?????????A07?????)
• ????????????????????
• ??????????????????
• ??????

15
OBDD??????????????

• ????????????????????
• ?????????????????????????
• ????
• ??????
• ??(x,y)????
• OBDD??
• SBDD??
• ?????????????????
• ???????????????????????

16
3.?????????

• ???????????????????
• ????NP???????????????
• ??????????????????
• ?
• ????????????????????
• ???????????????????????
• ???????

17
????????????????????

• Cke(-ke)???C?????(??????)?k???
• (??)?????????
• ????ke????????-ke????
• ????????
• Chordalk1e-k2e??????????

18
????ke????-ke??????????

• ???????
• ???????????????????
• ????????????????
• ??????????
• ????ke???
• k1 ?????
• k2 NP??
• ????-ke???
• k1 ?????

19
????ke????-ke??????????
??????????(????)

• ????1e??????
• ???????????
• ??????????????????????
• ????1?
• ????2e???
• ????1?????
• 2????????NP??

??????
20
Chordalk1e-k2e??????????

• ?????????????????????
• ??????????
• Fixed parameter tractable?????????
• Chordalke?????????????
• tree-decomposition???
• ?????????????????
• Fixed parameter tractable??????n?
• ?????k???? ??????

21
???

• ????????????????
• ??????????????????
• ????OBDD?????????????
• ?????????????????
• ????????????????
• ???????????????
• ?????????