On-Line Difference Maximization

In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting low values followed by high values in such a way as to maximize the expected gain in rank from low values to high values. First, we consider a scenario in which only one low value and one high value may be selected. We give an optimal on-line algorithm for this scenario, and analyze it to show that, surprisingly, the expected gain is n − O(1), and so differs from the best possible off-line gain by only a constant additive term (which is, in fact, fairly small — at most 15). In a second scenario, we allow multiple nonoverlapping low/high selections, where the total gain for our algorithm is the sum of the individual pair gains. We also give an optimal on-line algorithm for this problem, where the expected gain is n2/8 − Θ(n log n). An analysi...

• Type: Conference
• Year: 1997
• Where: SODA
• Authors: Ming-Yang Kao, Stephen R. Tate
• Keywords: Algorithms, Expected Gain, Low Value, On-line Algorithms, SODA 1997