TY - GEN
T1 - A linear work, O(n1/6) time, parallel algorithm for solving planar Laplacians
AU - Koutis, Ioannis
AU - Miller, Gary L.
N1 - Publisher Copyright:
Copyright © 2007 by the Association for Computing Machinery, Inc. and the Society for Industrial and Applied Mathematics.
PY - 2007
Y1 - 2007
N2 - 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 ≤ ∈, in O(n1/6+c log(1/∈)) parallel time, doing O(n log(1/∈)) work, where c is any positive constant. One of the key ingredients of the solver, is an O(nk log2 k) work, O(k log n) 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.
AB - 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 ≤ ∈, in O(n1/6+c log(1/∈)) parallel time, doing O(n log(1/∈)) work, where c is any positive constant. One of the key ingredients of the solver, is an O(nk log2 k) work, O(k log n) 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.
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M3 - Conference contribution
AN - SCOPUS:79959646222
T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
SP - 1002
EP - 1011
BT - Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007
PB - Association for Computing Machinery
T2 - 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007
Y2 - 7 January 2007 through 9 January 2007
ER -