Technical Report CS0313

Title: A Ramsey-Theorem Based Technique for Proving Lower Bounds on Decisions Trees
Authors: Shlomo Moran
Abstract: Let EU be tlie set of sequences (a1,...,an) in which ai!=aj for i!=j. Ramsey Theorem is used to show that in every decision tree T that accept EU, for every permutation pi there must be a computation path in T that 'compares' all pairs of consecutive elements of pi. This result is then used to prove a lower bound of OMEGA(nlogn) on decision trees that accepts EU and in which every query involves at most n^c input elements for some c<1/2. (If queries are allowed to use n^(1/2) input elements, then O(n) upper bound for this problem exists). In a forthcoming paper we generalize the technique presented here for proving lower bounds on other "order invariant" problems.
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