Testing Euclidean minimum spanning trees in the plane
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A sublinear-time approximation scheme for bin packing
Theoretical Computer Science
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SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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Property testing
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A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size
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SIAM Journal on Discrete Mathematics
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FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
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We consider the problem of computing the weight of a Euclidean minimum spanning tree for a set of n points in $\mathbb R^d$. We focus on the setting where the input point set is supported by certain basic (and commonly used) geometric data structures that can provide efficient access to the input in a structured way. We present an algorithm that estimates with high probability the weight of a Euclidean minimum spanning tree of a set of points to within $1 + \eps$ using only $\widetilde{\O}(\sqrt{n} \, \text{poly} (1/\eps))$ queries for constant d. The algorithm assumes that the input is supported by a minimal bounding cube enclosing it, by orthogonal range queries, and by cone approximate nearest neighbor queries.