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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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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.
The LeftRight Planarity Test
, 2009
"... A graph is planar if and only if it can be embedded in the plane without crossings. I give a detailed exposition of simple and efficient, yet poorly known algorithms for planarity testing, embedding, and Kuratowski subgraph extraction based on the leftright characterization of planarity. ..."
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A graph is planar if and only if it can be embedded in the plane without crossings. I give a detailed exposition of simple and efficient, yet poorly known algorithms for planarity testing, embedding, and Kuratowski subgraph extraction based on the leftright characterization of planarity.
Purity, Impurity and Efficiency in Graph Algorithms
"... Introduction This chapter initially considers pure lazy functional languages: their philosophy, advantages and disadvantages. We then examine how to develop efficient lazy functional programs. One way to achieve efficiency is to introduce impurities. In the final section the two schools of lazy fun ..."
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Introduction This chapter initially considers pure lazy functional languages: their philosophy, advantages and disadvantages. We then examine how to develop efficient lazy functional programs. One way to achieve efficiency is to introduce impurities. In the final section the two schools of lazy functional programming, pure and impure, are assessed. The assessment centres around two partial implementations of the Hopcroft Tarjan graph planarity algorithm. Profiling tools are used to make an experimental comparison and optimisation of each program. 4.1 Lazy Functional Programming In his book [42] Reade suggests that the user of a traditional imperative language is required to do the following: 1. describe the result to be computed; 2. impose an order on the steps required in the computation; 3. create and destroy, as required, any data structures used by the computation. 74 The first item is concerned with the extensional prope