Soumojit Sarkar

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Deterministic algorithms are given for some computational problems that take as input a nonsingular polynomial matrix A over K[x], K an abstract field, including solving a linear system involving A and computing a row reduced form of A. The fastest known algorithms for linear system solving based on the technique of high-order lifting by Storjohann (2003),(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> &#8712; IN is a subgraph <i>(V, E<sub>S</sub>), E<sub>S</sub></i> &#8838; <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 <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> &#8712; &Nopf; is a subgraph (<i>V,E<sub>S</sub></i>), <i>E<sub>S</sub></i> &#8838; <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 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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