Parallel BFS for Maximum Clique Problems April 27, 2004 Biointelligence Laboratory School of Computer Science and Engineering Seoul National University Dong-Yeon Cho (dycho@bi.snu.ac.kr)

© 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

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

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

© 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