Graph ear decompositions and graph embeddings

Chen, Jianer; Kanchi, Saroja

doi:10.1007/3-540-57899-4_67

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…In other words, Robbins' Theorem states that for a connected bridgeless graph G, an orientation D exists such that for every two vertices u and v, D contains both a directed u − v path and a directed v − u path. If the graph G represents a circulation network that is connected and contains no bridges, Robbins's Theorem would state that it is possible to walk from any given location to any other given location within G while respecting the orientation of each lane, for a strong orientation of G. The theorem can be demonstrated using ear decomposition, defined below according to [21]. Definition 14 An ear decomposition D = [P 1 , P 2 , .…”

Section: Theorem 1 (Robbins's Theorem): a Graph G Has A Strong Orientation If And Only If G Is Connected And Contains No Bridgesmentioning

confidence: 99%

Unidirectional Pedestrian Circulation: Physical Distancing in Informal Settlements

González¹,

Gongal²

2020

Preprint

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The COVID-19 pandemic has resulted in a wide range of spatial interventions to slow down the spread of the virus. The spatial limitations of narrow public circulation spaces within informal settlements, which house over one billion people around the world, make it impossible for pedestrians to practice physical distancing (or social distancing). In this paper, we propose a flexible mathematical method, named the Cluster Lane Method, for turning a planar circulation network of any size or complexity into a network of unidirectional lanes, making physical distancing possible in narrow circulation spaces by limiting face-to-face interactions. New notions and theorems about oriented graphs in graph theory are introduced. The paper ends with a discussion of the potential implementation of this cost-efficient, low-tech, sustainable solution, and with the introduction of a novel unidirectional tactile paving for the visually impaired.

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Section: Theorem 1 (Robbins's Theorem): a Graph G Has A Strong Orientation If And Only If G Is Connected And Contains No Bridgesmentioning

confidence: 99%

Unidirectional Pedestrian Circulation: Physical Distancing in Informal Settlements

González¹,

Gongal²

2020

Preprint

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“…Ear decomposition has also been used in designing efficient sequential and parallel algorithms for triconnectivity [37] and 4-connectivity [23]. In addition to graph connectivity, ear decomposition has been used in graph embeddings (see [9]).…”

Section: The Problemmentioning

confidence: 99%

Using PRAM Algorithms on a Uniform-Memory-Access Shared-Memory Architecture

Bader

Illendula

Moret

et al. 2001

Algorithm Engineering

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The ability to provide uniform shared-memory access to a significant number of processors in a single SMP node brings us much closer to the ideal PRAM parallel computer. In this paper, we develop new techniques for designing a uniform shared-memory algorithm from a PRAM algorithm and present the results of an extensive experimental study demonstrating that the resulting programs scale nearly linearly across a significant range of processors (from 1 to 64) and across the entire range of instance sizes tested. This linear speedup with the number of processors is, to our knowledge, the first ever attained in practice for intricate combinatorial problems. The example we present in detail here is a graph decomposition algorithm that also requires the computation of a spanning tree; this problem is not only of interest in its own right, but is representative of a large class of irregular combinatorial problems that have simple and efficient sequential implementations and fast PRAM algorithms, but have no known efficient parallel implementations. Our results thus offer promise for bridging the gap between the theory and practice of shared-memory parallel algorithms.

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Algorithmic graph embeddings

Chen

1995

Lecture Notes in Computer Science

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Graph ear decompositions and graph embeddings

Cited by 3 publications

References 15 publications

Unidirectional Pedestrian Circulation: Physical Distancing in Informal Settlements

Unidirectional Pedestrian Circulation: Physical Distancing in Informal Settlements

Using PRAM Algorithms on a Uniform-Memory-Access Shared-Memory Architecture

Algorithmic graph embeddings

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