scholarly journals Equitable list vertex colourability and arboricity of grids

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6353-6374 ◽  
Author(s):  
Ewa Drgas-Burchardt ◽  
Janusz Dybizbański ◽  
Hanna Furmańczyk ◽  
Elżbieta Sidorowicz
Keyword(s):  
General Graph ◽  
Acyclic Graph ◽  
Colour Class ◽  
Vertex Arboricity ◽  
General Graphs

A graph G is equitably k-list arborable if for any k-uniform list assignment L, there is an equitable L-colouring of G whose each colour class induces an acyclic graph. The smallest number k admitting such a coloring is named equitable list vertex arboricity and is denoted by ?=l (G). Zhang in 2016 posed the conjecture that if k ? ?(?(G) + 1)/2? then G is equitably k-list arborable. We give some new tools that are helpful in determining values of k for which a general graph is equitably k-list arborable. We use them to prove the Zhang?s conjecture for d-dimensional grids where d 2 {2,3,4} and give new bounds on ?=l (G) for general graphs and for d-dimensional grids with d ? 5.

scholarly journals QUANTUM WALKS ON GENERAL GRAPHS

2006 ◽  
Vol 04 (05) ◽  
pp. 791-805 ◽  
Author(s):  
VIV KENDON
Keyword(s):  
Continuous Time ◽  
Prior Information ◽  
Quantum Computer ◽  
Quantum Walk ◽  
Quantum Walks ◽  
General Graph ◽  
Resource Requirements ◽  
General Graphs

Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are compared and found to be very similar for both discrete and continuous time walks. The role of the oracle, and how it changes if more prior information about the graph is available, is also discussed.

scholarly journals IoT-enabled directed acyclic graph in spark cluster

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Jahwan Koo ◽  
Nawab Muhammad Faseeh Qureshi ◽  
Isma Farah Siddiqui ◽  
Asad Abbas ◽  
Ali Kashif Bashir
Keyword(s):  
Distributed Computing ◽  
Real Time ◽  
Directed Acyclic Graph ◽  
Random Access ◽  
Heterogeneous Data ◽  
The Body ◽  
Computing Environment ◽  
Time Data ◽  
Acyclic Graph ◽  
Sensory Data

Abstract Real-time data streaming fetches live sensory segments of the dataset in the heterogeneous distributed computing environment. This process assembles data chunks at a rapid encapsulation rate through a streaming technique that bundles sensor segments into multiple micro-batches and extracts into a repository, respectively. Recently, the acquisition process is enhanced with an additional feature of exchanging IoT devices’ dataset comprised of two components: (i) sensory data and (ii) metadata. The body of sensory data includes record information, and the metadata part consists of logs, heterogeneous events, and routing path tables to transmit micro-batch streams into the repository. Real-time acquisition procedure uses the Directed Acyclic Graph (DAG) to extract live query outcomes from in-place micro-batches through MapReduce stages and returns a result set. However, few bottlenecks affect the performance during the execution process, such as (i) homogeneous micro-batches formation only, (ii) complexity of dataset diversification, (iii) heterogeneous data tuples processing, and (iv) linear DAG workflow only. As a result, it produces huge processing latency and the additional cost of extracting event-enabled IoT datasets. Thus, the Spark cluster that processes Resilient Distributed Dataset (RDD) in a fast-pace using Random access memory (RAM) defies expected robustness in processing IoT streams in the distributed computing environment. This paper presents an IoT-enabled Directed Acyclic Graph (I-DAG) technique that labels micro-batches at the stage of building a stream event and arranges stream elements with event labels. In the next step, heterogeneous stream events are processed through the I-DAG workflow, which has non-linear DAG operation for extracting queries’ results in a Spark cluster. The performance evaluation shows that I-DAG resolves homogeneous IoT-enabled stream event issues and provides an effective stream event heterogeneous solution for IoT-enabled datasets in spark clusters.

scholarly journals Scaling Algorithms for Weighted Matching in General Graphs

2018 ◽  
Vol 14 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Ran Duan ◽  
Seth Pettie ◽  
Hsin-Hao Su
Keyword(s):  
Weighted Matching ◽  
Scaling Algorithms ◽  
General Graphs

Risk identification and modeling for blockchain-enabled container shipping

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Son Nguyen ◽  
Peggy Shu-Ling Chen ◽  
Yuquan Du
Keyword(s):  
Design Methodology ◽  
Directed Acyclic Graph ◽  
Risk Identification ◽  
Container Shipping ◽  
Content Type ◽  
Acyclic Graph ◽  
Operational Risks ◽  
Systems Security ◽  
Event Risk ◽  
Potential Risks

PurposeAlthough being considered for adoption by stakeholders in container shipping, application of blockchain is hindered by different factors. This paper investigates the potential operational risks of blockchain-integrated container shipping systems as one of such barriers.Design/methodology/approachLiterature review is employed as the method of risk identification. Scientific articles, special institutional reports and publications of blockchain solution providers were included in an inclusive qualitative analysis. A directed acyclic graph (DAG) was constructed and analyzed based on network topological metrics.FindingsTwenty-eight potential risks and 47 connections were identified in three groups of initiative, transitional and sequel. The DAG analysis results reflect a relatively well-connected network of identified hazardous events (HEs), suggesting the pervasiveness of information risks and various multiple-event risk scenarios. The criticality of the connected systems' security and information accuracy are also indicated.Originality/valueThis paper indicates the changes of container shipping operational risk in the process of blockchain integration by using updated data. It creates awareness of the emerging risks, provides their insights and establishes the basis for further research.

Distributed garbage collection for general graphs

2018 ◽  
Vol 53 (5) ◽  
pp. 29-44
Author(s):  
Steven R. Brandt ◽  
Hari Krishnan ◽  
Costas Busch ◽  
Gokarna Sharma
Keyword(s):  
Garbage Collection ◽  
Distributed Garbage Collection ◽  
General Graphs

scholarly journals The Age of Old Galactic Populations

1998 ◽  
Vol 11 (1) ◽  
pp. 560-561
Author(s):  
M. Grenon
Keyword(s):  
High Velocity ◽  
Radial Velocities ◽  
Thick Disk ◽  
Early Evolution ◽  
Galactic Bulge ◽  
Colour Class ◽  
The Galaxy ◽  
Nearby Stars

As a preparation to the HIPPARCOS mission, a large observing programme on NLTT stars (propermotion > 0.18 ″/yr) was started in Genevaphotometry. The original programme consists of 10047 stars brighter than mR = 11.5, or mR = 12.5 if of colour class m. Among them, 7813 targets could be included in the HIPPARCOS programme, selected according to their observability and internal priorities in favour of large parallaxe stars (photometric distances < 100 pc) and high-velocity stars. The bulk of new nearby, halo, mild-metal poor and SMR stars in the HIP Catalogue originates from this proposal (N° 139). No less than 208 new nearby stars with π ≥ 40 mas were discovered south of δ +10°, the closest has π(HIP)= 182 mas. Radial velocities were obtained with CORAVEL at OHP and ESO. Most aspects of the early evolution of the Galaxy may be addressed with this sample. Here we discuss, as examples, the ages of the thick disk and of the galactic bulge.

scholarly journals Secure the IoT Networks as Epidemic Containment Game

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 156
Author(s):  
Juntao Zhu ◽  
Hong Ding ◽  
Yuchen Tao ◽  
Zhen Wang ◽  
Lanping Yu
Keyword(s):  
Heuristic Algorithms ◽  
Heuristic Method ◽  
Exact Algorithms ◽  
Epidemic Threshold ◽  
Solution Quality ◽  
Sis Model ◽  
Linear Programming Formulation ◽  
Iot Devices ◽  
General Graphs ◽  
The Internet Of Things

The spread of a computer virus among the Internet of Things (IoT) devices can be modeled as an Epidemic Containment (EC) game, where each owner decides the strategy, e.g., installing anti-virus software, to maximize his utility against the susceptible-infected-susceptible (SIS) model of the epidemics on graphs. The EC game’s canonical solution concepts are the Minimum/Maximum Nash Equilibria (MinNE/MaxNE). However, computing the exact MinNE/MaxNE is NP-hard, and only several heuristic algorithms are proposed to approximate the MinNE/MaxNE. To calculate the exact MinNE/MaxNE, we provide a thorough analysis of some special graphs and propose scalable and exact algorithms for general graphs. Especially, our contributions are four-fold. First, we analytically give the MinNE/MaxNE for EC on special graphs based on spectral radius. Second, we provide an integer linear programming formulation (ILP) to determine MinNE/MaxNE for the general graphs with the small epidemic threshold. Third, we propose a branch-and-bound (BnB) framework to compute the exact MinNE/MaxNE in the general graphs with several heuristic methods to branch the variables. Fourth, we adopt NetShiled (NetS) method to approximate the MinNE to improve the scalability. Extensive experiments demonstrate that our BnB algorithm can outperform the naive enumeration method in scalability, and the NetS can improve the scalability significantly and outperform the previous heuristic method in solution quality.

Strong Equitable Vertex Arboricity in Cartesian Product Networks

2021 ◽  
pp. 2150010
Author(s):  
Zhiwei Guo ◽  
Yaping Mao ◽  
Nan Jia ◽  
He Li
Keyword(s):  
Maximum Degree ◽  
Cartesian Product ◽  
Color Class ◽  
Vertex Arboricity

An equitable [Formula: see text]-tree-coloring of a graph [Formula: see text] is defined as a [Formula: see text]-coloring of vertices of [Formula: see text] such that each component of the subgraph induced by each color class is a tree of maximum degree at most [Formula: see text], and the sizes of any two color classes differ by at most one. The strong equitable vertex [Formula: see text]-arboricity of a graph [Formula: see text] refers to the smallest integer [Formula: see text] such that [Formula: see text] has an equitable [Formula: see text]-tree-coloring for every [Formula: see text]. In this paper, we investigate the Cartesian product with respect to the strong equitable vertex [Formula: see text]-arboricity, and demonstrate the usefulness of the proposed constructions by applying them to some instances of product networks.

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