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

Satsangi, Dharna; Srivastava, Kamal; Srivastava, Govind

doi:10.1007/s12293-013-0115-5

Cited by 4 publications

(13 citation statements)

References 20 publications

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“…For other graphs, the vertex order has a strong effect on the results. In our experiments we first compared three state-of-the-art vertex order heuristics (breadth-first search (rbfs [13]), depth-first search (AVSDF [7]) and connectivity (conGreedy [10])) before applying the page assignment heuristics. It turned out that for all of them the same vertex order heuristic performed best on the same graph class, so that all experiments could be run without bias on exactly the same input order.…”

Section: Methodsmentioning

confidence: 99%

Mixed Linear Layouts: Complexity, Heuristics, and Experiments

Col

Klute

Nöllenburg

2019

Lecture Notes in Computer Science

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A k-page linear graph layout of a graph G = (V, E) draws all vertices along a line and each edge in one of k disjoint halfplanes called pages, which are bounded by . We consider two types of pages. In a stack page no two edges should cross and in a queue page no edge should be nested by another edge. A crossing (nesting) in a stack (queue) page is called a conflict. The algorithmic problem is twofold and requires to compute (i) a vertex ordering and (ii) a page assignment of the edges such that the resulting layout is either conflict-free or conflict-minimal. While linear layouts with only stack or only queue pages are well-studied, mixed s-stack q-queue layouts for s, q ≥ 1 have received less attention. We show NP-completeness results on the recognition problem of certain mixed linear layouts and present a new heuristic for minimizing conflicts. In a computational experiment for the case s, q = 1 we show that the new heuristic is an improvement over previous heuristics for linear layouts.

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Section: Methodsmentioning

confidence: 99%

Mixed Linear Layouts: Complexity, Heuristics, and Experiments

Col

Klute

Nöllenburg

2019

Lecture Notes in Computer Science

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“…Heuristics excluded, due to relatively poor performance, are among others a maximum neighborhood heuristic, a vertex-cover heuristic, a simple BFS heuristic [33], and variations of conCro [4].…”

Section: Constructive Heuristicsmentioning

confidence: 99%

“…In this strategy the edges are ordered non-increasingly by their length in a circular drawing. length (eLen) [8,33]. Here the edges are ordered non-increasingly by the distance of their end vertices on a spine.…”

Section: Constructive 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%

“…Experimental evaluations have been performed by Satsangi et al [33], who, however, excluded previously best performing algorithms by Baur and Brandes [4] and tested algorithms for VO and PA problems only independently from each other, not in combination. He et al [23] performed an experimental study of several heuristics, but only for the 2-page crossing minimization problem.…”

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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