scholarly journals Vertex Ordering Problems in Directed Graph Streams

2020 ◽  
pp. 1786-1802
Author(s):  
Amit Chakrabarti ◽  
Prantar Ghosh ◽  
Andrew McGregor ◽  
Sofya Vorotnikova
Keyword(s):  
Directed Graph ◽  
Vertex Ordering ◽  
Graph Streams

A Graph-Theoretic Approach to Comparing and Integrating Genetic, Physical and Sequence-Based Maps

Genetics ◽  
2003 ◽  
Vol 165 (4) ◽  
pp. 2235-2247
Author(s):  
Immanuel V Yap ◽  
David Schneider ◽  
Jon Kleinberg ◽  
David Matthews ◽  
Samuel Cartinhour ◽  
...  
Keyword(s):  
Directed Graph ◽  
Source Material ◽  
Complete Picture ◽  
Theoretic Approach ◽  
Research Groups ◽  
Genome Coverage ◽  
Graph Theoretic ◽  
Novel Approach ◽  
Graph Theoretic Approach ◽  
Locus Order

AbstractFor many species, multiple maps are available, often constructed independently by different research groups using different sets of markers and different source material. Integration of these maps provides a higher density of markers and greater genome coverage than is possible using a single study. In this article, we describe a novel approach to comparing and integrating maps by using abstract graphs. A map is modeled as a directed graph in which nodes represent mapped markers and edges define the order of adjacent markers. Independently constructed graphs representing corresponding maps from different studies are merged on the basis of their common loci. Absence of a path between two nodes indicates that their order is undetermined. A cycle indicates inconsistency among the mapping studies with regard to the order of the loci involved. The integrated graph thus produced represents a complete picture of all of the mapping studies that comprise it, including all of the ambiguities and inconsistencies among them. The objective of this representation is to guide additional research aimed at interpreting these ambiguities and inconsistencies in locus order rather than presenting a “consensus order” that ignores these problems.

scholarly journals A Fault Identification Method in Distillation Process Based on Dynamic Mechanism Analysis and Signed Directed Graph

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 229
Author(s):  
Wende Tian ◽  
Shifa Zhang ◽  
Zhe Cui ◽  
Zijian Liu ◽  
Shaochen Wang ◽  
...  
Keyword(s):  
Directed Graph ◽  
Process Simulation ◽  
Expert Knowledge ◽  
Dynamic Mechanism ◽  
Fault Identification ◽  
Mechanism Analysis ◽  
Distillation Process ◽  
Complex Network Theory ◽  
Identification Method ◽  
Signed Directed Graph

Due to the complexity of materials and energy cycles, the distillation system has numerous working conditions difficult to troubleshoot in time. To address the problem, a novel DMA-SDG fault identification method that combines dynamic mechanism analysis based on process simulation and signed directed graph is proposed for the distillation process. Firstly, dynamic simulation is employed to build a mechanism model to provide the potential relationships between variables. Secondly, sensitivity analysis and dynamic mechanism analysis in process simulation are introduced to the SDG model to improve the completeness of this model based on expert knowledge. Finally, a quantitative analysis based on complex network theory is used to select the most important nodes in SDG model for identifying the severe malfunctions. The application of DMA-SDG method in a benzene-toluene-xylene (BTX) hydrogenation prefractionation system shows sound fault identification performance.

scholarly journals On Directed Versions of the Hajnal–Szemerédi Theorem

2015 ◽  
Vol 24 (6) ◽  
pp. 873-928 ◽  
Author(s):  
ANDREW TREGLOWN
Keyword(s):  
Directed Graph ◽  
Minimum Degree ◽  
Directed Graphs ◽  
Perfect Matchings ◽  
Large Order ◽  
Vertex Disjoint ◽  
Removal Lemma

We say that a (di)graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. The seminal Hajnal–Szemerédi theorem characterizes the minimum degree that ensures a graph G contains a perfect Kr-packing. In this paper we prove the following analogue for directed graphs: Suppose that T is a tournament on r vertices and G is a digraph of sufficiently large order n where r divides n. If G has minimum in- and outdegree at least (1−1/r)n then G contains a perfect T-packing.In the case when T is a cyclic triangle, this result verifies a recent conjecture of Czygrinow, Kierstead and Molla [4] (for large digraphs). Furthermore, in the case when T is transitive we conjecture that it suffices for every vertex in G to have sufficiently large indegree or outdegree. We prove this conjecture for transitive triangles and asymptotically for all r ⩾ 3. Our approach makes use of a result of Keevash and Mycroft [10] concerning almost perfect matchings in hypergraphs as well as the Directed Graph Removal Lemma [1, 6].

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