Optimal Time-Space Tradeoff for the 2D Convex-Hull Problem
نویسندگان
چکیده
We revisit the read-only random-access model, in which the input array is read-only and a limited amount of workspace is allowed. Given a set of N two-dimensional points in a read-only input array and Θ(S) bits of extra workspace (where S ≥ lgN), we present an algorithm that runs in O(N/S + N lgS) time for constructing the convex hull formed by the given points. Following a lower bound for sorting, our algorithm is asymptotically optimal with respect to the read-only random-access model. Of independent interest, we introduce a spaceefficient data structure that we call the augmented memory-adjustable navigation pile. We expect this data structure to be a useful tool when designing other space-efficient algorithms.
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