Competitive algorithms for online conversion problems with interrelated prices

The classical uni-directional conversion algorithms are based on the assumption that prices are arbitrarily chosen from the fixed price interval[m, M] where m and M represent the estimated lower and upper bounds of possible prices 0<m<M. The estimated interval is erroneous and no attempts are made by the algorithms to update the erroneous estimates. We consider a real world setting where prices are interrelated, i.e., each price depends on its preceding price. Under this assumption, we drive a lower bound on the competitive ratio of randomized non-primitive algorithms. Motivated by the fixed and erroneous price bounds, we present an update model that progressively improves the bounds. Based on the update model, we propose a non-preemptive reservations price algorithm RP* and analyze it under competitive analysis. Finally, we report the findings of an experimental study that is conducted over the real world stock index data. We observe that RP* consistently outperforms the classical algorithm

Disparity between theory & practice beyond the worst-case competitive analysis

Online algorithms are used in a variety of situations such as forex trading, cache replacement, and job scheduling etc. In an online problem, the algorithms is presented with a sequence on input in a serial fashion such that the algorithm does not have knowledge about the future inputs. For instance, in case of forex, the online algorithm is presented daily exchange rates. The algorithm does not have knowledge about future exchange rates, and has to make an irreversible conversion decision on each day. Competitive analysis is the standard tool to analyse the performance of online algorithms. Competitive analysis measures the performance of an online algorithm against a benchmark optimum offline algorithm. Competitive analysis is a worst case measure and is criticized as a pessimistic approach for performance evaluation. The assumption of online algorithms designed under the competitive analysis paradigm also suffer from the same set of problems as competitive analysis itself. In this work, we contribute towards bridging the gap between theory and practice by considering a set of algorithms for online conversion problems and discuss the disparity between the assumed worst case competitive rations and experimentally achieved competitive ratios using real world data. We present modified worst-case input sequences in order to make them comparable to real world data. In addition, we also investigate, how the assumptions made by the algorithm differs from real world. Further, we highlight other performance measures for online algorithms with the goal of realistic performance evaluation process