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Planarizing Graphs  A Survey and Annotated Bibliography
, 1999
"... Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results abo ..."
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Cited by 33 (0 self)
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Given a finite, undirected, simple graph G, we are concerned with operations on G that transform it into a planar graph. We give a survey of results about such operations and related graph parameters. While there are many algorithmic results about planarization through edge deletion, the results about vertex splitting, thickness, and crossing number are mostly of a structural nature. We also include a brief section on vertex deletion. We do not consider parallel algorithms, nor do we deal with online algorithms.
A Better Approximation Algorithm for Finding Planar Subgraphs
 J. ALGORITHMS
, 1996
"... The MAXIMUM PLANAR SUBGRAPH problemgiven a graph G, find a largest planar subgraph of Ghas applications in circuit layout, facility layout, and graph drawing. No previous polynomialtime approximation algorithm for this NPComplete problem was known to achieve a performance ratio larger than ..."
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Cited by 29 (4 self)
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The MAXIMUM PLANAR SUBGRAPH problemgiven a graph G, find a largest planar subgraph of Ghas applications in circuit layout, facility layout, and graph drawing. No previous polynomialtime approximation algorithm for this NPComplete problem was known to achieve a performance ratio larger than 1=3, which is achieved simply by producing a spanning tree of G. We present the first approximation algorithm for MAXIMUM PLANAR SUBGRAPH with higher performance ratio (4=9 instead of 1=3). We also apply our algorithm to find large outerplanar subgraphs. Last, we show that both MAXIMUM PLANAR SUBGRAPH and its complement, the problem of removing as few edges as possible to leave a planar subgraph, are Max SNPHard.
A New Approximation Algorithm for Finding Heavy Planar Subgraphs
 ALGORITHMICA
, 1997
"... We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NPHard problem of finding a heaviest planar subgraph in an edgeweighted graph G. This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM ..."
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Cited by 9 (2 self)
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We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NPHard problem of finding a heaviest planar subgraph in an edgeweighted graph G. This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH had performance ratio exceeding 1=3, which is obtained by any algorithm that produces a maximum weight spanning tree in G. Based on the BermanRamaiyer Steiner tree algorithm, the new algorithm has performance ratio at least 1/3 + 1/72. We also show that if G is complete and its edge weights satisfy the triangle inequality, then the performance ratio is at least 3/8. Furthermore, we derive the first nontrivial performance ratio (7/12 instead of 1/2) for the NPHard MAXIMUM WEIGHT OUTERPLANAR SUBGRAPH problem.