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SIAM Journal on Computing
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Journal of Computer and System Sciences - 27th IEEE Conference on Foundations of Computer Science October 27-29, 1986
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SIAM Journal on Computing
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Applied numerical linear algebra
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Min—max-boundary domain decomposition
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CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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PTAS for geometric hitting set problems via local search
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We present a linear work parallel iterative algorithm for solving linear systems involving Laplacians of planar graphs. In particular, if Ax = b, where A is the Laplacian of any planar graph with n nodes, the algorithm produces a vector x such that ||x--x||A ≤ ε, in O(n1/6+clog(1/ε)) parallel time, doing O(nlog(1/ε)) work, where c is any positive constant. One of the key ingredients of the solver, is an O(nklog2k) work, O(klogn) time, parallel algorithm for decomposing any embedded planar graph into components of size O(k) that are delimited by O(n/√k) boundary edges. The result also applies to symmetric diagonally dominant matrices of planar structure.