TY - GEN

T1 - Parallel algorithms for select and partition with noisy comparisons

AU - Braverman, Mark

AU - Mao, Jieming

AU - Weinberg, S. Matthew

N1 - Funding Information:
Research supported in part by an NSF CAREER award (CCF-1149888), NSF CCF-1215990, NSF CCF-1525342, a Packard Fellowship in Science and Engineering, and the Simons Collaboration on Algorithms and Geometry. Research completed in part while the author was a Microsoft Research Fellow at the Simons Institute for the Theory of Computing.

PY - 2016/6/19

Y1 - 2016/6/19

N2 - We consider the problem of finding the kth highest element in a totally ordered set of n elements (SELECT), and partitioning a totally ordered set into the top k and bottom n - k elements (PARTITION) using pairwise comparisons. Motivated by settings like peer grading or crowdsourcing, where multiple rounds of interaction are costly and queried comparisons may be inconsistent with the ground truth, we evaluate algorithms based both on their total runtime and the number of interactive rounds in three comparison models: noiseless (where the comparisons are correct), erasure (where comparisons are erased with probability 1 - γ), and noisy (where comparisons are correct with probability 1/2 + γ/2 and incorrect otherwise). We provide numerous matching upper and lower bounds in all three models. Even our results in the noiseless model, which is quite well-studied in the TCS literature on parallel algorithms, are novel.

AB - We consider the problem of finding the kth highest element in a totally ordered set of n elements (SELECT), and partitioning a totally ordered set into the top k and bottom n - k elements (PARTITION) using pairwise comparisons. Motivated by settings like peer grading or crowdsourcing, where multiple rounds of interaction are costly and queried comparisons may be inconsistent with the ground truth, we evaluate algorithms based both on their total runtime and the number of interactive rounds in three comparison models: noiseless (where the comparisons are correct), erasure (where comparisons are erased with probability 1 - γ), and noisy (where comparisons are correct with probability 1/2 + γ/2 and incorrect otherwise). We provide numerous matching upper and lower bounds in all three models. Even our results in the noiseless model, which is quite well-studied in the TCS literature on parallel algorithms, are novel.

KW - Median finding

KW - Noisy comparisons

KW - Parallel algorithms

KW - Rank aggregation

KW - Top-k

UR - http://www.scopus.com/inward/record.url?scp=84979248409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979248409&partnerID=8YFLogxK

U2 - 10.1145/2897518.2897642

DO - 10.1145/2897518.2897642

M3 - Conference contribution

AN - SCOPUS:84979248409

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 851

EP - 862

BT - STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing

A2 - Mansour, Yishay

A2 - Wichs, Daniel

PB - Association for Computing Machinery

T2 - 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016

Y2 - 19 June 2016 through 21 June 2016

ER -