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Engineering Planar Separator Algorithms
, 2009
"... We consider classical lineartime planar separator algorithms, determining for a given planar graph a small subset of its nodes whose removal divides the graph into two components of similar size. These algorithms are based on planar separator theorems, which guarantee separators of size O ( √ n) a ..."
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Cited by 8 (3 self)
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We consider classical lineartime planar separator algorithms, determining for a given planar graph a small subset of its nodes whose removal divides the graph into two components of similar size. These algorithms are based on planar separator theorems, which guarantee separators of size O ( √ n
Planar separators and the Euclidean norm
 IN 1ST INTERNATIONAL SYMPOSIUM ON ALGORITHMS
, 1990
"... In this paper we show that every 2connected embedded planar graph with faces of sizes d!..... df has a simple cycle separator of size 1.58~,/dl 2 +...+d} and we give an almost linear time algorithm for finding these separators, O(m~(n. n)). We show that the new upper bound expressed as a function o ..."
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Cited by 17 (1 self)
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In this paper we show that every 2connected embedded planar graph with faces of sizes d!..... df has a simple cycle separator of size 1.58~,/dl 2 +...+d} and we give an almost linear time algorithm for finding these separators, O(m~(n. n)). We show that the new upper bound expressed as a function
Application of A Planar Separator Theorem
"... Through the paper Application of A Planar Separator Theorem by RICHARD J. LIPTON and ROBERT TAR JAN, we get that any nvertex planar graph can be divided into components of roughly equal size by removing only O(x/) vertices. This separator theorem with a divideandconquer strategy can help us reso ..."
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Through the paper Application of A Planar Separator Theorem by RICHARD J. LIPTON and ROBERT TAR JAN, we get that any nvertex planar graph can be divided into components of roughly equal size by removing only O(x/) vertices. This separator theorem with a divideandconquer strategy can help us
Planar Separators and Parallel Polygon Triangulation
"... We show how to construct an O ( p n)separator decomposition of a planar graph G in O(n) time. Such a decomposition defines a binary tree where each node corresponds to a subgraph of G and stores an O ( p n)separator of that subgraph. We also show how to construct an O(n)way decomposition tree in ..."
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Cited by 54 (8 self)
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We show how to construct an O ( p n)separator decomposition of a planar graph G in O(n) time. Such a decomposition defines a binary tree where each node corresponds to a subgraph of G and stores an O ( p n)separator of that subgraph. We also show how to construct an O(n)way decomposition tree
NPcompleteness of the Planar Separator Problems
, 2001
"... For a given graph G, the Separator Problem asks whether a vertex or edge set of small cardinality (or weight) exists whose removal partitions G into two disjoint graphs of approximately equal sizes. Called the Vertex Separator Problem when the removed set is a vertex set, and the Edge Separator Prob ..."
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Cited by 5 (0 self)
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Problem when it is an edge set, both problems are NPcomplete for general unweighted graphs [6]. Despite the significance of planar graphs, it has not been known whether the Planar Separator Problem, which considers a planar graph and a threshold as an input, is NPcomplete or not. In this paper, we prove
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 461 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
I/Oefficient planar separators
 SIAM JOURNAL ON COMPUTING
, 2008
"... We present I/Oefficient algorithms for computing optimal separator partitions of planar graphs. Our main result shows that, given a planar graph G with N vertices and an integer r> 0, a vertex separator of size O(N / √ r) that partitions G into O(N/r) subgraphs of size at most r and boundary s ..."
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Cited by 3 (1 self)
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We present I/Oefficient algorithms for computing optimal separator partitions of planar graphs. Our main result shows that, given a planar graph G with N vertices and an integer r> 0, a vertex separator of size O(N / √ r) that partitions G into O(N/r) subgraphs of size at most r and boundary
0.1 Generalizations of the Planar Separator Theorem
"... In the previous section we saw that the planar separator theorem provides us with a procedure to separate the vertices of a planar graph G = (V,E), V  = n, into three sets A,B,C, where A, B  ≤ 2n/3, C  ≤ 4√n, and there exists no edge between A and B. In this section we will consider sever ..."
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In the previous section we saw that the planar separator theorem provides us with a procedure to separate the vertices of a planar graph G = (V,E), V  = n, into three sets A,B,C, where A, B  ≤ 2n/3, C  ≤ 4√n, and there exists no edge between A and B. In this section we will consider
I/OEfficient Planar Separators and Applications
, 2001
"... We present a new algorithm to compute a subset S of vertices of a planar graph G whose removal partitions G into O(N/h) subgraphs of size O(h) and with boundary size O( p h) each. The size of S is O(N= p h). Computing S takes O(sort(N)) I/Os and linear space, provided that M 56hlog² B. Together with ..."
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Cited by 3 (1 self)
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with recent reducibility results, this leads to O(sort(N)) I/O algorithms for breadthfirst search (BFS), depthfirst search (DFS), and single source shortest paths (SSSP) on undirected embedded planar graphs. Our separator algorithm does not need a BFS tree or an embedding of G to be given as part
Abstract On Gazit and Miller’s parallel algorithm for planar separators: achieving
"... greater efficiency through random sampling We show how to obtain a workefficient parallel algorithm for finding a planar separator. The algorithm requires O(rz ’) time for any given positive constant e. 1 ..."
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greater efficiency through random sampling We show how to obtain a workefficient parallel algorithm for finding a planar separator. The algorithm requires O(rz ’) time for any given positive constant e. 1
Results 1  10
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