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

Abstract: Tiedemann, et al. [Proc. of WALCOM, LNCS 8973, 2015, pp.210-221] defined multiobjective online problems and the competitive analysis for multi-objective online problems and showed that (1) with respect to the worst component competitive analysis, the online algorithm reservation price policy rpp-high is best possible for the multi-objective time series search problem; (2) with respect to the arithmetic mean component competitive analysis, the online algorithm rpp-mult is best possible for the bi-objective time series search problem; (3) with respect to the geometric mean component competitive analysis, the online algorithm rpp-mult is best possible for the bi-objective time series search problem. In this paper, we present a simple online algorithm Balanced Price Policy bppk for the multi-objective (k-objective) time series search problem, and show that the algorithm bppk is best possible with respect to any measure of the competitive analysis. In addition, we derive exact values of the competitive ratio for the multiobjective time series search problem with respect to the worst component, the arithmetic mean component, and the geometric mean component competitive analysis.