Haplotype Inferring Via Galled-Tree Networks Is NP-Complete

AbstractThe k-clique problem is identifying the largest complete subgraph of size k on a network, and it has many applications in Social Network Analysis (SNA), coding theory, geometry, etc. Due to the NP-Complete nature of the problem, the meta-heuristic approaches have raised the interest of the researchers and some algorithms are developed. In this paper, a new algorithm based on the Bat optimization approach is developed for finding the maximum k-clique on a social network to increase the convergence speed and evaluation criteria such as Precision, Recall, and F1-score. The proposed algorithm is simulated in Matlab® software over Dolphin social network and DIMACS dataset for k = 3, 4, 5. The computational results show that the convergence speed on the former dataset is increased in comparison with the Genetic Algorithm (GA) and Ant Colony Optimization (ACO) approaches. Besides, the evaluation criteria are also modified on the latter dataset and the F1-score is obtained as 100% for k = 5.

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Popular Matching in Roommates Setting Is NP-hard

ACM Transactions on Computation Theory ◽

10.1145/3442354 ◽

2021 ◽

Vol 13 (2) ◽

pp. 1-20

Author(s):

Sushmita Gupta ◽

Pranabendu Misra ◽

Saket Saurabh ◽

Meirav Zehavi

Keyword(s):

Computational Complexity ◽

Np Hard ◽

Np Complete ◽

Open Question ◽

Popular Matching

An input to the P OPULAR M ATCHING problem, in the roommates setting (as opposed to the marriage setting), consists of a graph G (not necessarily bipartite) where each vertex ranks its neighbors in strict order, known as its preference. In the P OPULAR M ATCHING problem the objective is to test whether there exists a matching M * such that there is no matching M where more vertices prefer their matched status in M (in terms of their preferences) over their matched status in M *. In this article, we settle the computational complexity of the P OPULAR M ATCHING problem in the roommates setting by showing that the problem is NP-complete. Thus, we resolve an open question that has been repeatedly and explicitly asked over the last decade.

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Shellability is NP-complete

Journal of the ACM ◽

10.1145/3314024 ◽

2019 ◽

Vol 66 (3) ◽

pp. 1-18

Author(s):

Xavier Goaoc ◽

Pavel Paták ◽

Zuzana Patáková ◽

Martin Tancer ◽

Uli Wagner

Keyword(s):

Np Complete

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Learning Mesh Representations via Binary Space Partitioning Tree Networks

IEEE Transactions on Pattern Analysis and Machine Intelligence ◽

10.1109/tpami.2021.3093440 ◽

2021 ◽

pp. 1-1

Author(s):

Zhiqin Chen ◽

Andrea Tagliasacchi ◽

Hao Zhang

Keyword(s):

Space Partitioning ◽

Tree Networks ◽

Binary Space Partitioning

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Total Roman {3}-Domination: The Complexity and Linear-Time Algorithm for Trees

Mathematics ◽

10.3390/math9030293 ◽

2021 ◽

Vol 9 (3) ◽

pp. 293

Author(s):

Xinyue Liu ◽

Huiqin Jiang ◽

Pu Wu ◽

Zehui Shao

Keyword(s):

Linear Time ◽

Minimum Weight ◽

Domination Number ◽

Time Algorithm ◽

Simple Graph ◽

Linear Time Algorithm ◽

Domination Problem ◽

Np Complete ◽

Chordal Bipartite Graphs ◽

Dominating Function

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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