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 Ω (nlog 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 Ω (nlog n) lower bound for this latter problem would be obtained.