Optimal Algorithms for Sensitivity Analysis in Associative Multiplication Problems

AbstraeL We consider efficient ways of determining the sensitivity of a product to changes in individual factors. The task is motivated by several interesting combinatorial and numeric problems which can be given a unified formulation as the problem of findi.n~ the (associative) product of N objects. Both deterministic and probabilistic changes to the factors are considered. Algorithms for two kinds of deterministic variation schemes are considered. No atrivial lower bounds are obtained which demonstrate the algorithms to be optimal. For prob~bilistic choice of the parameter' to be varied, it is shown that optimal ordere6 binary search t~ees or Huffman trees determine the optimal strategies. A number of unsolved problems are posed.