A new lower bound technique and its application: tight lower bound for a polygon triangulation problem

A new technique for obtaining lower bounds on the worst-case time-complexity of optimization problems in the linear decision tree model of computation is presented. This technique is then used to obtain a tight $\Omega (n\log n)$ lower bound for a problem of finding a minimum cost triangulation of a convex polygon with weighted vertices. This problem is similar to the problem of finding an optimal order of computing a matrix chain product. If the lower bound technique could be extended to bounded degree algebraic decision trees, a tight $\Omega (n\log n)$ lower bound for this latter problem would be obtained.