TY - EJOUR
DO - 10.1007/s10107-018-1269-1
AB - The goal of scenario reduction is to approximate a given discrete distribution with another discrete distribution that has fewer atoms. We distinguish continuous scenario reduction, where the new atoms may be chosen freely, and discrete scenario reduction, where the new atoms must be chosen from among the existing ones. Using the Wasserstein distance as measure of proximity between distributions, we identify those n-point distributions on the unit ball that are least susceptible to scenario reduction, i.e., that have maximum Wasserstein distance to their closest m-point distributions for some prescribed m < n. We also provide sharp bounds on the added benefit of continuous over discrete scenario reduction. Finally, to our best knowledge, we propose the first polynomial-time constant-factor approximations for both discrete and continuous scenario reduction as well as the first exact exponential-time algorithms for continuous scenario reduction.
T1 - Scenario Reduction Revisited: Fundamental Limits and Guarantees
DA - 2018
AU - Rujeerapaiboon, Napat
AU - Schindler, Kilian
AU - Kuhn, Daniel
AU - Wiesemann, Wolfram
JF - Mathematical Programming
N1 - Available from Optimization Online
ID - 224448
KW - Scenario reduction
KW - Wasserstein distance
KW - Constant-factor approximation algorithm
KW - k-median clustering
KW - k-means clustering
UR - http://www.optimization-online.org/DB_HTML/2017/01/5816.html
ER -