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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 ∈ F N ×N and a vector b ∈ F N , it is known that in the worst-case Θ(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)… (More)

- Albert Gu
- 2015

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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