Sorting and Selection with Random Costs

There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work treats a natural stochastic variant of the problem where the cost of comparing two elements is a random variable. Each cost is chosen independently and is known to the algorithm. In particular we consider the following three models: each cost is chosen uniformly in the range [0, 1], each cost is 0 with some probability p and 1 otherwise, or each cost is 1 with probability p and infinite otherwise. We present lower and upper bounds (optimal in most cases) for these problems. We obtain our upper bounds by carefully designing algorithms to ensure that the costs incurred at various stages are independent and using properties of random partial orders when appropriate.

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Stanislav Angelov, Keshav Kunal, Andrew McGregor
• Keywords: CORR 2007, Education, Natural Stochastic Variant, Unit-cost Comparison Model, Upper Bounds