1. Parallel BFS for Maximum Clique Problems
April 27, 2004
Biointelligence Laboratory
School of Computer Science and Engineering
Seoul National University
Dong-Yeon Cho

2. © 2004 SNU CSE Biointelligence Lab
Introduction
Breadth First Search (BFS)
Investigation of all the states at a given depth before looking at any states that are deeper in the search tree
Search space complexity
Time complexity
Heuristics for Maximum Clique
Eliminate all states containing connections in the complementary graph
Ex) 1x1xxx, x1x1xx, x1xxx1, 1xxxx1 2 3 1 4 5 2 3 1 4 5
© 2004 SNU CSE Biointelligence Lab

3. Breadth First Search (BFS)
00, 01, 10, 11
One bit extension by POA
GEL for specific length
NAND
(x0 = 0 or x2 = 0)
000, 010, 100, 110, 001, 011, 101, 111
One bit extension by POA
GEL for specific length
0000, 0100, 1000, 1100, 0010, 0110,
0001, 0101, 1001, 1101, 0011, 0111
NAND
(x1 = 0 or x3 = 0)
One bit extension by POA
GEL for specific length
00000, 01000, 10000, 11000, 00100, 01100, 00010, 10010, 00110,
00001, 01001, 10001, 11001, 00101, 01101, 00011, 10011, 00111 …
© 2004 SNU CSE Biointelligence Lab

4. One Bit Extension By POA
Parallel Overlap Assembly 5’ 3’ 3’ 5’
P’iV’i(0)P’i+1 5’ 3’ 3’ 5’
P’iV’i(1)P’i+1
© 2004 SNU CSE Biointelligence Lab

5. © 2004 SNU CSE Biointelligence Lab
NAND Gate
xi = 0 or xj = 0
OR Gate using positive selection and arranged in series [Livstone and Landweber, 2003]
Efficiency (): the fraction of strands applied to a microreactor that should bind and actually do (+=1) 00 01 10 11
© 2004 SNU CSE Biointelligence Lab