An evolutionary algorithm for the 2-page crossing number problem

Bansal, Roli; Srivastava, Kamal; Shweta, .; Varshney, Kush R.; Sharma, Nirmala

doi:10.1109/cec.2008.4630933

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…The smlDgrDFS heuristic starts with a smallest degree vertex and chooses a neighbor with smallest degree to proceed. random DFS (randDFS) [3]. In contrast to smlDgrDFS, randDFS starts with a random vertex and proceeds with a random neighbor.…”

Section: Vo Heuristicsmentioning

confidence: 99%

“…There are several heuristics for 2-page crossing minimization [8][9][10] with a fixed linear vertex ordering, as well as algorithms for the general 2-page crossing minimization problem [21,22]. Genetic and evolutionary crossing minimization algorithms have been proposed for one page [18], two pages [3,19,31], and any number of pages [33]. Further, neural networks have been used for 2-page crossing minimization [20,37] and for k-page crossing minimization [28].…”

Section: Introductionmentioning

confidence: 99%

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Experimental Evaluation of Book Drawing Algorithms

Klawitter

Mchedlidze

Nöllenburg

2018

Lecture Notes in Computer Science

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A k-page book drawing of a graph G = (V, E) consists of a linear ordering of its vertices along a spine and an assignment of each edge to one of the k pages, which are half-planes bounded by the spine. In a book drawing, two edges cross if and only if they are assigned to the same page and their vertices alternate along the spine. Crossing minimization in a k-page book drawing is NP-hard, yet book drawings have multiple applications in visualization and beyond. Therefore several heuristic book drawing algorithms exist, but there is no broader comparative study on their relative performance. In this paper, we propose a comprehensive benchmark set of challenging graph classes for book drawing algorithms and provide an extensive experimental study of the performance of existing book drawing algorithms.

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Section: Vo Heuristicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Experimental Evaluation of Book Drawing Algorithms

Klawitter

Mchedlidze

Nöllenburg

2018

Lecture Notes in Computer Science

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“…It is worthy to mention here that the use of unary operator for producing a child is suggested by Fogel et al (1966), Eiben and Schippers (1998). In addition, such operators have been used in the EAs designed for graph layout problems (Bansal et al 2008;Sharma and Srivastava 2009). …”

Section: Reproductionmentioning

confidence: 99%

A memetic algorithm for the cyclic antibandwidth maximization problem

Bansal

Srivastava

2009

Soft Comput

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The cyclic antibandwidth problem is to embed the vertices of a graph G of n vertices on a cycle C n such that the minimum distance (measured in the cycle) of adjacent vertices is maximized. Exact results/conjectures for this problem exist in the literature for some standard graphs, such as paths, cycles, two-dimensional meshes, and tori, but no algorithm has been proposed for the general graphs in the literature reviewed by us so far. In this paper, we propose a memetic algorithm for the cyclic antibandwidth problem (MACAB) that can be applied on arbitrary graphs. An important feature of this algorithm is the use of breadth first search generated level structures of a graph to explore a variety of solutions. A novel greedy heuristic is designed which explores these level structures to label the vertices of the graph. The algorithm achieves the exact cyclic antibandwidth of all the standard graphs with known optimal values. Based on our experiments we conjecture the cyclic antibandwidth of three-dimensional meshes, hypercubes, and double stars. Experiments show that results obtained by MACAB are substantially better than those given by genetic algorithm.

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$$K$$ -page crossing number minimization problem: An evaluation of heuristics and its solution using GESAKP

Satsangi

Srivastava

2013

Memetic Comp.

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An evolutionary algorithm for the 2-page crossing number problem

Cited by 3 publications

References 8 publications

Experimental Evaluation of Book Drawing Algorithms

Experimental Evaluation of Book Drawing Algorithms

A memetic algorithm for the cyclic antibandwidth maximization problem

$$K$$ -page crossing number minimization problem: An evaluation of heuristics and its solution using GESAKP

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