An efficient parallel strategy for the perfect domination problem on distance-hereditary graphs

For a simple graph G=(V,E) with no isolated vertices, a total Roman {3}-dominating function(TR3DF) on G is a function f:V(G)→{0,1,2,3} having the property that (i) ∑w∈N(v)f(w)≥3 if f(v)=0; (ii) ∑w∈N(v)f(w)≥2 if f(v)=1; and (iii) every vertex v with f(v)≠0 has a neighbor u with f(u)≠0 for every vertex v∈V(G). The weight of a TR3DF f is the sum f(V)=∑v∈V(G)f(v) and the minimum weight of a total Roman {3}-dominating function on G is called the total Roman {3}-domination number denoted by γt{R3}(G). In this paper, we show that the total Roman {3}-domination problem is NP-complete for planar graphs and chordal bipartite graphs. Finally, we present a linear-time algorithm to compute the value of γt{R3} for trees.

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Automatic generation method of parallel strategy for dispatching instructions in distribution network based on clustering and layering

10.1117/12.2618453 ◽

2021 ◽

Author(s):

Yuxing Chen ◽

Zili Yin ◽

Junyan Gao ◽

Gonglin Zhang ◽

JunQuan Zhang ◽

...

Keyword(s):

Distribution Network ◽

Automatic Generation ◽

Parallel Strategy

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k-Efficient domination: Algorithmic perspective

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830922500513 ◽

2022 ◽

Author(s):

Mohsen Alambardar Meybodi

Keyword(s):

Decision Problem ◽

Dominating Set ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Chordal Graphs ◽

Sparse Graphs ◽

Fpt Algorithm ◽

Domination Problem ◽

Efficient Dominating Set ◽

Np Complete

A set [Formula: see text] of a graph [Formula: see text] is called an efficient dominating set of [Formula: see text] if every vertex [Formula: see text] has exactly one neighbor in [Formula: see text], in other words, the vertex set [Formula: see text] is partitioned to some circles with radius one such that the vertices in [Formula: see text] are the centers of partitions. A generalization of this concept, introduced by Chellali et al. [k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122], is called [Formula: see text]-efficient dominating set that briefly partitions the vertices of graph with different radiuses. It leads to a partition set [Formula: see text] such that each [Formula: see text] consists a center vertex [Formula: see text] and all the vertices in distance [Formula: see text], where [Formula: see text]. In other words, there exist the dominators with various dominating powers. The problem of finding minimum set [Formula: see text] is called the minimum [Formula: see text]-efficient domination problem. Given a positive integer [Formula: see text] and a graph [Formula: see text], the [Formula: see text]-efficient Domination Decision problem is to decide whether [Formula: see text] has a [Formula: see text]-efficient dominating set of cardinality at most [Formula: see text]. The [Formula: see text]-efficient Domination Decision problem is known to be NP-complete even for bipartite graphs [M. Chellali, T. W. Haynes and S. Hedetniemi, k-Efficient partitions of graphs, Commun. Comb. Optim. 4 (2019) 109–122]. Clearly, every graph has a [Formula: see text]-efficient dominating set but it is not correct for efficient dominating set. In this paper, we study the following: [Formula: see text]-efficient domination problem set is NP-complete even in chordal graphs. A polynomial-time algorithm for [Formula: see text]-efficient domination in trees. [Formula: see text]-efficient domination on sparse graphs from the parametrized complexity perspective. In particular, we show that it is [Formula: see text]-hard on d-degenerate graphs while the original dominating set has Fixed Parameter Tractable (FPT) algorithm on d-degenerate graphs. [Formula: see text]-efficient domination on nowhere-dense graphs is FPT.

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Application of a Novel ‘Make and Test in Parallel’ Strategy to Investigate the Effect of Formulation on the Pharmacokinetics of GDC-0810 in Healthy Subjects

Pharmaceutical Research ◽

10.1007/s11095-018-2516-0 ◽

2018 ◽

Vol 35 (12) ◽

Cited By ~ 3

Author(s):

Sravanthi Cheeti ◽

Hao Helen Hou ◽

Eric Nelson ◽

Helen Walker ◽

Buyun Chen ◽

...

Keyword(s):

Healthy Subjects ◽

Parallel Strategy

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Linear-Time Algorithm for the Paired-Domination Problem in Convex Bipartite Graphs

Theory of Computing Systems ◽

10.1007/s00224-011-9378-8 ◽

2011 ◽

Vol 50 (4) ◽

pp. 721-738 ◽

Cited By ~ 8

Author(s):

Ruo-Wei Hung

Keyword(s):

Linear Time ◽

Time Algorithm ◽

Bipartite Graphs ◽

Linear Time Algorithm ◽

Domination Problem ◽

Paired Domination ◽

Convex Bipartite Graphs

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Parallel strategy for multiple scan operations with data replication

World Wide Web ◽

10.1007/s11280-018-0625-7 ◽

2018 ◽

Vol 22 (6) ◽

pp. 2561-2587

Author(s):

Xing Wei ◽

Huiqi Hu ◽

Huichao Duan ◽

Weining Qian ◽

Aoying Zhou

Keyword(s):

Data Replication ◽

Multiple Scan ◽

Parallel Strategy

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Parallel Strategy to Factorize Fermat Numbers with Implementation in Maple Software

Journal of Software ◽

10.17706/jsw.16.4.167-173 ◽

2021 ◽

pp. 167-173

Author(s):

Jianhui Li ◽

◽

Manlan Liu

Keyword(s):

Parallel Computing ◽

Parallel Algorithm ◽

Computational Efficiency ◽

Sequential Algorithm ◽

Parallel Processes ◽

Fermat Numbers ◽

Fermat Number ◽

Parallel Strategy

In accordance with the traits of parallel computing, the paper proposes a parallel algorithm to factorize the Fermat numbers through parallelization of a sequential algorithm. The kernel work to parallelize a sequential algorithm is presented by subdividing the computing interval into subintervals that are assigned to the parallel processes to perform the parallel computing. Maple experiments show that the parallelization increases the computational efficiency of factoring the Fermat numbers, especially to the Fermat number with big divisors.

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