An Experimental Study on Generating Planar Graphs

Meinert, Sascha; Wagner, Dorothea

doi:10.1007/978-3-642-21204-8_39

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…Several models of planar graphs that are easier to generate have been considered [107]. The most scalable of these models consider Delaunay triangulations of random point sets (Section 5.4.1).…”

Section: Random Planar Graphsmentioning

confidence: 99%

Recent Advances in Scalable Network Generation

Penschuck¹,

Brandes²,

Hamann³

et al. 2020

Preprint

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Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically spanning multiple areas of expertise. Challenges begin with the identification of relevant domain-specific network features, continue with the question of how to compile such features into a tractable model, and culminate in algorithmic details arising while implementing the pertaining model.In the present survey, we explore crucial aspects of random graph models with known scalable generators. We begin by briefly introducing network features considered by such models, and then discuss random graphs alongside with generation algorithms. Our focus lies on modelling techniques and algorithmic primitives that have proven successful in obtaining massive graphs. We consider concepts and graph models for various domains (such as social network, infrastructure, ecology, and numerical simulations), and discuss generators for different models of computation (including shared-memory parallelism, massive-parallel GPUs, and distributed systems).

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Section: Random Planar Graphsmentioning

confidence: 99%

Recent Advances in Scalable Network Generation

Penschuck¹,

Brandes²,

Hamann³

et al. 2020

Preprint

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“…Planar graphs are the class of graphs that can be embedded in a two-dimensional plane without edge crossings. Designing efficient algorithms for planar graphs is an important subfield in the area of algorithm development and optimization [4]. From the practical perspective, the planarity is also an important characteristic of many physical networks such as roads, utilities, water distribution systems, and some circuit designs.…”

Section: Planar Graph Generationmentioning

confidence: 99%

Multiscale planar graph generation

2019

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A network is a representation of a set of entities and the relationships between them. The network paradigm is often used to represent physical, biological, engineered and social systems [1]. Networks can help us better understand the structural and functional dynamics of these systems and formulate predictive models. However, collecting real-world network data often requires time and can be expensive. Also, for many applications, the sensitivity of real-world data towards theft and misuse further adds to the cost of protection and security of the data, which sharply limits its availability.The problem of data scarcity can be tackled by using synthetic data which can mimic both the properties and diversity of real world networks. Such synthetic data can be used for simulations, analysis, and performance/quality verification of algorithms -a crucial task in algorithm engineering. Synthetic network generation is one of the most important fields in network science from both theoretical and practical perspectives. We refer the reader for an in-depth discussion to recent reviews in [2,3].

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“…They show that even such a simple generator exhibits an interesting phenomena of phase change. Namely, there exists a narrow range for p values for which the number of connected components drop significantly for very small increment in p. Planar triangulated graphs [22] are another class of random graph generators in which the points are embedded on a Euclidean plane. The Delaunay triangulation of the points yields a random graph.…”

Section: Existing Graph Generatorsmentioning

confidence: 99%

Citations, Sequence Alignments, Contagion, and Semantics: On Acyclic Structures and their Randomness

Gupta

2012

Preprint

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Datasets from several domains, such as life-sciences, semantic web, machine learning, natural language processing, etc. are naturally structured as acyclic graphs. These datasets, particularly those in bio-informatics and computational epidemiology, have grown tremendously over the last decade or so. Increasingly, as a consequence, there is a need to build and evaluate various strategies for processing acyclic structured graphs. Most of the proposed research models the real world acyclic structures as random graphs, i.e., they are generated by randomly selecting a subset of edges from all possible edges. Unfortunately the graphs thus generated have predictable and degenerate structures, i.e., the resulting graphs will always have almost the same degree distribution and very short paths. Specifically, we show that if O(n log n log n) edges are added to a binary tree of n nodes then with probability more than O(1/(log n) 1/n ) the depth of all but O(log log n log log n ) vertices of the dag collapses to 1. Experiments show that irregularity, as measured by distribution of length of random walks from root to leaves, is also predictable and small. The degree distribution and random walk length properties of real world graphs from these domains are significantly different from random graphs of similar vertex and edge size.

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An Experimental Study on Generating Planar Graphs

Cited by 6 publications

References 18 publications

Recent Advances in Scalable Network Generation

Recent Advances in Scalable Network Generation

Multiscale planar graph generation

Citations, Sequence Alignments, Contagion, and Semantics: On Acyclic Structures and their Randomness

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