TY - CHAP
T1 - Bravely, moderately
T2 - A common theme in four recent Works
AU - Goldreich, Oded
PY - 2011
Y1 - 2011
N2 - We highlight a common theme in four relatively recent works that establish remarkable results by an iterative approach. Starting from a trivial construct, each of these works applies an ingeniously designed sequence of iterations that yields the desired result, which is highly non-trivial. Furthermore, in each iteration, the construct is modified in a relatively moderate manner. The four works we refer to are 1 the polynomial-time approximation of the permanent of non-negative matrices (by Jerrum, Sinclair, and Vigoda, 33rd STOC, 2001); 2 the iterative (Zig-Zag) construction of expander graphs (by Reingold, Vadhan, and Wigderson, 41st FOCS, 2000); 3 the log-space algorithm for undirected connectivity (by Reingold, 37th STOC, 2005); 4 and, the alternative proof of the PCP Theorem (by Dinur, 38th STOC, 2006).
AB - We highlight a common theme in four relatively recent works that establish remarkable results by an iterative approach. Starting from a trivial construct, each of these works applies an ingeniously designed sequence of iterations that yields the desired result, which is highly non-trivial. Furthermore, in each iteration, the construct is modified in a relatively moderate manner. The four works we refer to are 1 the polynomial-time approximation of the permanent of non-negative matrices (by Jerrum, Sinclair, and Vigoda, 33rd STOC, 2001); 2 the iterative (Zig-Zag) construction of expander graphs (by Reingold, Vadhan, and Wigderson, 41st FOCS, 2000); 3 the log-space algorithm for undirected connectivity (by Reingold, 37th STOC, 2005); 4 and, the alternative proof of the PCP Theorem (by Dinur, 38th STOC, 2006).
UR - http://www.scopus.com/inward/record.url?scp=84857578207&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-22670-0_26
DO - 10.1007/978-3-642-22670-0_26
M3 - فصل
SN - 9783642226694
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 373
EP - 389
BT - Studies in Complexity and Cryptography
A2 - Goldreich, Oded
ER -