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In the online Steiner tree problem, a sequence of points is revealed one-by-one: when a point arrives, we only have time to add a single edge connecting this point to the previous ones, and we want to minimize the total length of edges added. Here, a tight bound has been known for two decades: the greedy algorithm maintains a tree whose cost is O(log n)(More)
Matrix-vector multiplication is one of the most fundamental computing primitives that has been studied extensively. Given a matrix A ∈ FN×N and a vector b ∈ FN , it is known that in the worst-caseΘ(N 2) operations over F are needed to compute Ab. Many classes of structured dense matrices have been investigated which can be represented with O(N ) parameters,(More)
Matrix-vector multiplication is one of the most fundamental computing primitives. Given a matrix A ∈ FN×N and a vector b ∈ FN , it is known that in the worst case Θ(N2) operations over F are needed to compute Ab. Many types of structuredmatrices do admit faster multiplication. However, even given amatrix A that is known to have this property, it is hard in(More)
We examine the Sprague-Grundy values of the game of R-Wythoff, a restriction of Wythoff’s game introduced by Ho, where each move is either to remove a positive number of tokens from the larger pile or to remove the same number of tokens from both piles. Ho showed that the P -positions of R-Wythoff agree with those of Wythoff’s game, and found all positions(More)
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