Optimal Mixed Graph Augmentation

1987 ◽  
Vol 16 (4) ◽  
pp. 599-612 ◽  
Author(s):  
Dan Gusfield
Keyword(s):  
Graph Augmentation ◽  
Mixed Graph

Mixed graph convolution and residual transformation network for skeleton-based action recognition

2021 ◽  
Author(s):  
Shuhua Liu ◽  
Xiaoying Bai ◽  
Ming Fang ◽  
Lanting Li ◽  
Chih-Cheng Hung
Keyword(s):  
Action Recognition ◽  
Mixed Graph

Population-specific genome graphs improve high-throughput sequencing data analysis: A case study on the Pan-African genome

2021 ◽  
Author(s):  
H. Serhat Tetikol ◽  
Kubra Narci ◽  
Deniz Turgut ◽  
Gungor Budak ◽  
Ozem Kalay ◽  
...  
Keyword(s):  
High Throughput Sequencing ◽  
Information Overload ◽  
African Ancestry ◽  
Sample Selection ◽  
Variant Calling ◽  
Population Diversity ◽  
Human Populations ◽  
Sequencing Data ◽  
Bioinformatics Pipeline ◽  
Graph Augmentation

ABSTRACTGraph-based genome reference representations have seen significant development, motivated by the inadequacy of the current human genome reference for capturing the diverse genetic information from different human populations and its inability to maintain the same level of accuracy for non-European ancestries. While there have been many efforts to develop computationally efficient graph-based bioinformatics toolkits, how to curate genomic variants and subsequently construct genome graphs remains an understudied problem that inevitably determines the effectiveness of the end-to-end bioinformatics pipeline. In this study, we discuss major obstacles encountered during graph construction and propose methods for sample selection based on population diversity, graph augmentation with structural variants and resolution of graph reference ambiguity caused by information overload. Moreover, we present the case for iteratively augmenting tailored genome graphs for targeted populations and test the proposed approach on the whole-genome samples of African ancestry. Our results show that, as more representative alternatives to linear or generic graph references, population-specific graphs can achieve significantly lower read mapping errors, increased variant calling sensitivity and provide the improvements of joint variant calling without the need of computationally intensive post-processing steps.

scholarly journals A Self-Stabilizing Algorithm for Constructing a Maximal (1,1)-Directed Acyclic Mixed Graph

2018 ◽  
Vol 8 (1) ◽  
pp. 53-72 ◽  
Author(s):  
Yonghwan Kim ◽  
Haruka Ohno ◽  
Yoshiaki Katayama ◽  
Toshimitsu Masuzawa
Keyword(s):  
Mixed Graph

scholarly journals Scheduling Multiprocessor Tasks with Equal Processing Times as a Mixed Graph Coloring Problem

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 246
Author(s):  
Yuri N. Sotskov ◽  
Еvangelina I. Mihova
Keyword(s):  
Graph Coloring ◽  
Precedence Constraints ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Due Dates ◽  
Mixed Graph ◽  
Coloring Problem ◽  
Release Times ◽  
Schedule Length ◽  
Graph Coloring Problem

This article extends the scheduling problem with dedicated processors, unit-time tasks, and minimizing maximal lateness for integer due dates to the scheduling problem, where along with precedence constraints given on the set of the multiprocessor tasks, a subset of tasks must be processed simultaneously. Contrary to a classical shop-scheduling problem, several processors must fulfill a multiprocessor task. Furthermore, two types of the precedence constraints may be given on the task set . We prove that the extended scheduling problem with integer release times of the jobs to minimize schedule length may be solved as an optimal mixed graph coloring problem that consists of the assignment of a minimal number of colors (positive integers) to the vertices of the mixed graph such that, if two vertices and are joined by the edge , their colors have to be different. Further, if two vertices and are joined by the arc , the color of vertex has to be no greater than the color of vertex . We prove two theorems, which imply that most analytical results proved so far for optimal colorings of the mixed graphs , have analogous results, which are valid for the extended scheduling problems to minimize the schedule length or maximal lateness, and vice versa.

scholarly journals The Unique Mixed Almost Moore Graph with Parameters k = 2, r = 2 and z = 1

2017 ◽  
Vol 17 (03n04) ◽  
pp. 1741005 ◽  
Author(s):  
DOMINIQUE BUSET ◽  
NACHO LÓPEZ ◽  
JOSEP M. MIRET
Keyword(s):  
Upper Bound ◽  
Mixed Graph ◽  
Moore Graph

A natural upper bound for the maximum number of vertices in a mixed graph with maximum undirected degree r, maximum directed out-degree z and diameter k is given by the mixed Moore bound. Graphs with order attaining the Moore bound are known as Moore graphs, and they are very rare. Besides, graphs with prescribed parameters and order one less than the corresponding Moore bound are known as almost Moore graphs. In this paper we prove that there is a unique mixed almost Moore graph of diameter k = 2 and parameters r = 2 and z = 1.

scholarly journals On Total Regularity of Mixed Graphs with Order Close to the Moore Bound

2019 ◽  
Vol 35 (6) ◽  
pp. 1253-1272
Author(s):  
James Tuite ◽  
Grahame Erskine
Keyword(s):  
Open Problem ◽  
Mixed Graph ◽  
Difficult Question ◽  
Moore Graph ◽  
Network Topologies ◽  
Mixed Graphs

Abstract The undirected degree/diameter and degree/girth problems and their directed analogues have been studied for many decades in the search for efficient network topologies. Recently such questions have received much attention in the setting of mixed graphs, i.e. networks that admit both undirected edges and directed arcs. The degree/diameter problem for mixed graphs asks for the largest possible order of a network with diameter k, maximum undirected degree $$\le r$$≤r and maximum directed out-degree $$\le z$$≤z. Similarly one can search for the smallest possible k-geodetic mixed graphs with minimum undirected degree $$\ge r$$≥r and minimum directed out-degree $$\ge z$$≥z. A simple counting argument reveals the existence of a natural bound, the Moore bound, on the order of such graphs; a graph that meets this limit is a mixed Moore graph. Mixed Moore graphs can exist only for $$k = 2$$k=2 and even in this case it is known that they are extremely rare. It is therefore of interest to search for graphs with order one away from the Moore bound. Such graphs must be out-regular; a much more difficult question is whether they must be totally regular. For $$k = 2$$k=2, we answer this question in the affirmative, thereby resolving an open problem stated in a recent paper of López and Miret. We also present partial results for larger k. We finally put these results to practical use by proving the uniqueness of a 2-geodetic mixed graph with order exceeding the Moore bound by one.

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