Optimal online algorithms for the multi-objective time series search problem

Tiedemann et al. (2015) [8] formulated multi-objective online problems and several measures of the competitive analysis, and showed best possible online algorithms for the multi-objective time series search problem with respect to those measures of the competitive analysis. In this paper, we present modified definitions of the competitive analysis for multi-objective online problems and propose a simple online algorithm Balanced Price Policy (BPPk) for the multi-objective (k-objective) time series search problem. Under the modified framework, we show that the algorithm BPPk is best possible with respect to any measure of the competitive analysis and we also derive best possible values of the competitive ratio for the multi-objective time series search problem with respect to several natural measures of the competitive analysis.