Abstract
In this paper, we consider the technique of creating artificial components to obtain good lower bounds in the fixed order algebraic decision tree model, for geometric decision problems whose solution space (set of Yes instances) consists of very few connected components. Using this technique, we obtain an Ω(log m) lower bound for the Convex Polygon Inclusion problem for convex m-gons, and an Ω(n log n) lower bound for the Max Gap problem, and the Path Testing problem.
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