Abstract
Given a geometric graph G = ( S , E ) in R d with constant dilation t, and a positive constant ε, we show how to construct a ( 1 + ε ) -spanner of G with O ( | S | ) edges using O ( sort ( | E | ) ) memory transfers in the cache-oblivious model of computation. The main building block of our algorithm, and of independent interest in itself, is a new cache-oblivious algorithm for constructing a well-separated pair decomposition which builds such a data structure for a given point set S ⊂ R d using O ( sort ( | S | ) ) memory transfers.
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