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Linear Algorithms for Partitioning Embedded Graphs of Bounded Genus
 SIAM Journal of Discrete Mathematics
, 1996
"... This paper develops new techniques for constructing separators for graphs embedded on surfaces of bounded genus. For any arbitrarily small positive " we show that any nvertex graph G of genus g can be divided in O(n + g) time into components whose sizes do not exceed "n by removing a set ..."
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Cited by 24 (4 self)
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This paper develops new techniques for constructing separators for graphs embedded on surfaces of bounded genus. For any arbitrarily small positive " we show that any nvertex graph G of genus g can be divided in O(n + g) time into components whose sizes do not exceed "n by removing a set C of O( p (g + 1=")n) vertices. Our result improves the best previous ones with respect to the size of C and the time complexity of the algorithm. Moreover, we show that one can cut off from G a piece of no more than (1 \Gamma ")n vertices by removing a set of O( p n"(g" + 1) vertices. Both results are optimal up to a constant factor. Keywords: graph separator, graph genus, algorithm, divideandconquer, topological graph theory AMS(MOS) subject classifications: 05C10, 05C85, 68R10 1 Bulgarian Academy of Sci., CICT, G.Bonchev 25A, 1113 Sofia, Bulgaria 2 Department of Comp.Sci.,Rice University, P.O.Box 1892, Houston, Texas 77251, USA 1 Introduction Let S be a class of graphs closed under t...
Nested dissection: A survey and comparison of various nested dissection algorithms
, 1992
"... Methods for solving sparse linear systems of equations can be categorized under two broad classes direct and iterative. Direct methods are methods based on gaussian elimination. This report discusses one such direct method namely Nested dissection. Nested Dissection, originally proposed by Alan Geo ..."
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Cited by 8 (1 self)
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Methods for solving sparse linear systems of equations can be categorized under two broad classes direct and iterative. Direct methods are methods based on gaussian elimination. This report discusses one such direct method namely Nested dissection. Nested Dissection, originally proposed by Alan George, is a technique for solving sparse linear systems efficiently. This report is a survey of some of the work in the area of nested dissection and attempts to put it together using a common framework.