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Spanner of an undirected graph <i>G</i> = (<i>V,E</i>) is a subgraph that is sparse and yet preserves all-pairs distances approximately. More formally, a spanner with <i>stretch</i> <i>t</i> ∈ ℕ is a subgraph (<i>V,E<sub>S</sub></i>), <i>E<sub>S</sub></i> ⊆ <i>E</i> such that the distance between any two vertices in the subgraph is at most… (More)

This paper gives gives a deterministic algorithm to transform a row reduced matrix to canonical Popov form. Given as input a row reduced matrix <i>R</i> over K[<i>x</i>], K a field, our algorithm computes the Popov form in about the same time as required to multiply together over K[<i>x</i>] two matrices of the same dimension and degree as <i>R</i>. We also… (More)

Spanner of an undirected graph <i>G</i> = <i>(V, E)</i> is a sub graph which is sparse and yet preserves all-pairs distances approximately. More precisely, a spanner with <i>stretch t</i> ∈ IN is a subgraph <i>(V, E<sub>S</sub>), E<sub>S</sub></i> ⊆ <i>E</i> such that the distance between any two vertices in the subgraph is at most <i>t</i>… (More)

Spanner of an undirected graph G = (V, E) is a sub graph which is sparse and yet preserves all-pairs distances approximately. More formally, a spanner with stretch t ∈ N is a subgraph (V, ES), ES ⊆ E such that the distance between any two vertices in the subgraph is at most t times their distance in G. We present two randomized algorithms for maintaining a… (More)

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