The Element Distinctness Lower Bound theory establishes that comparison-based algorithms require Ω(n log n) time by proving that decision tree regions accepting distinct inputs must be convex, preventing non-adjacent permutations from sharing leaves. This principle relies on the intersection of linear inequalities defining connected geometric regions within an input space and utilizes topological connectivity arguments to bound computational complexity in abstract decision models. The theory formally connects combinatorial information content (n! possible sorted outcomes) with algebraic geometry constraints to derive strict limits applicable across both standard random access machine comparisons and more general algebraic computation trees.
The Element Distinctness Lower Bound theory establishes that comparison-based algorithms require Ω(n log n) time by proving that decision tree regions accepting distinct inputs must be convex, preven…