scholarly journals A complexidade do reconhecimento de grafos k-fino próprio de precedência

2020 ◽  
Author(s):  
Flavia Bonomo-Braberman ◽  
Fabiano Oliveira ◽  
Moysés Sampaio Jr. ◽  
Jayme Szwarcfiter
Keyword(s):  
Threshold Graphs ◽  
Complexity Status ◽  
Np Complete

The class of precedence proper k-thin graphs is a subclass of proper k-thin graphs. The complexity status of recognizing proper k-thin graphs is unknown for any fixed k ≥ 2. In this work, we prove that, when k is part of the input, the problem of recognizing precedence proper k-thin graphs is NP-complete, and we present a characterization for them based on threshold graphs.

COMPLEXITY OF SEMIGROUP IDENTITY CHECKING

2004 ◽  
Vol 14 (04) ◽  
pp. 455-464 ◽  
Author(s):  
ANDRZEJ KISIELEWICZ
Keyword(s):  
Computational Complexity ◽  
General Formula ◽  
Commutative Semigroup ◽  
Simple Proof ◽  
Finite Semigroup ◽  
Structure Theory ◽  
Semigroup Identity ◽  
Commutative Semigroups ◽  
Complexity Status ◽  
Np Complete

We consider the [Formula: see text] problem, whose instance is a finite semigroup S and an identity I, and the question is whether I is satisfied in S. We show that the question concerning computational complexity of this problem is much harder, when restricted to commutative semigroups. We provide a relatively simple proof that in general the problem is co-NP-complete, and demonstrate, using some structure theory, that for a fixed commutative semigroup the problem can be solved in polynomial time. The complexity status of the general [Formula: see text] problem remains open.

scholarly journals Proper Orientations of Chordal Graphs

2020 ◽  
Author(s):  
Julio Araujo ◽  
Alexandre Cezar ◽  
Carlos Vinícius Gomes Costa Lima ◽  
Vinicius Fernandes Dos Santos ◽  
Ana Shirley Ferreira Silva
Keyword(s):  
Upper Bound ◽  
Linear Time ◽  
Time Algorithm ◽  
Chordal Graphs ◽  
Linear Time Algorithm ◽  
Threshold Graphs ◽  
Minimum Integer ◽  
Split Graphs ◽  
Np Complete ◽  
Proper Orientation

An orientation D of a graph G = (V, E) is a digraph obtained from G by replacing each edge by exactly one of the two possible arcs with the same end vertices. For each v ∈ V(G), the indegree of v in D, denoted by dD−(v), is the number of arcs with head v in D. An orientation D of G is proper if dD−(u) ≠ dD−(v), for all uv ∈ E(G). An orientation with maximum indegree at most k is called a k-orientation. The proper orientation number of G, denoted by χ→(G), is the minimum integer k such that G admits a proper k-orientation. We prove that determining whether χ→(G) ≤ k is NP-complete for chordal graphs of bounded diameter. We also present a tight upper bound for χ→(G) on split graphs and a linear-time algorithm for quasi-threshold graphs.

scholarly journals Discovering the maximum k-clique on social networks using bat optimization algorithm

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Akram Khodadadi ◽  
Shahram Saeidi
Keyword(s):  
Genetic Algorithm ◽  
Social Networks ◽  
Social Network ◽  
Coding Theory ◽  
Evaluation Criteria ◽  
Convergence Speed ◽  
Optimization Approach ◽  
Computational Results ◽  
Complete Subgraph ◽  
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.

scholarly journals Popular Matching in Roommates Setting Is NP-hard

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.

scholarly journals Shellability is NP-complete

2019 ◽  
Vol 66 (3) ◽  
pp. 1-18
Author(s):  
Xavier Goaoc ◽  
Pavel Paták ◽  
Zuzana Patáková ◽  
Martin Tancer ◽  
Uli Wagner
Keyword(s):  
Np Complete

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

Mathematics ◽  
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.

On 3-colorings of bipartitep-threshold graphs

1987 ◽  
Vol 11 (3) ◽  
pp. 327-338 ◽  
Author(s):  
Ioan Tomescu
Keyword(s):  
Threshold Graphs

Reconstructing a Graph from its Neighborhood Lists

1993 ◽  
Vol 2 (2) ◽  
pp. 103-113 ◽  
Author(s):  
Martin Aigner ◽  
Eberhard Triesch
Keyword(s):  
Decision Problem ◽  
Graph Isomorphism ◽  
Bipartite Graphs ◽  
Labeled Graph ◽  
Np Complete

Associate to a finite labeled graph G(V, E) its multiset of neighborhoods (G) = {N(υ): υ ∈ V}. We discuss the question of when a list is realizable by a graph, and to what extent G is determined by (G). The main results are: the decision problem is NP-complete; for bipartite graphs the decision problem is polynomially equivalent to Graph Isomorphism; forests G are determined up to isomorphism by (G); and if G is connected bipartite and (H) = (G), then H is completely described.

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