• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.10
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• pp.1531-1536
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• 2022

This paper considers a problem to find a set of intervals containing all the points for the given n points and m intervals on a line, This is a special case of the set cover problem, well known as an NP-hard problem. As optimization criteria of the problem, there are minimizing the number of intervals to cover the points, maximizing the number of points each of which is covered by exactly one interval, and so on. In this paper, the intervals have weights and the sum of weights of intervals to cover a point is defined as a membership of the point. We will study the problem to find an interval cover minimizing the maximum of memberships of points. Using the dynamic programming method, we provide an O(m²)-time algorithm to improve the time complexity O(nm log n) given in the previous work.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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• pp.2658-2679
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• 2018

This paper proposes a novel Random Scheduling Algorithm based on Subregion Coverage (RSASC), to solve the SET K-cover problem (an NP-complete problem). SET K-cover problem distributes the set of sensors into the maximum number of mutually exclusive subsets (MESSs) in such a way that each of them can be scheduled for lifetime extension of WSN. Sensor coverage divides the target region into different subregions. RSASC first sorts the subregions in the ascending order concerning their sensor coverage. Then, it forms the subregion groups according to their similar sensor coverage. Lastly, RSASC ensures the K-coverage of each subregion from every group by randomly scheduling the sensors. We consider the target-coverage and area-coverage applications of WSN to analyze the usefulness of our proposed RSASC algorithm. The distinct quality of RSASC is that it utilizes less number of deployed sensors (33% less) to form the optimum number of MESSs with the higher computational speed (saves more than 93% of the time) as compared to the existing three algorithms.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.4
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• pp.165-170
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• 2023

This paper proposes an algorithm that can obtain a solution with linear time for a set cover problem(SCP) in which there is no polynomial time algorithm as an NP-complete problem so far. Until now, only heuristic greed algorithms are known to select sets that can be covered to the maximum. On the other hand, the proposed algorithm is a competitive algorithm that applies an inclusion-exclusion principle rule to N nodes up to 2nd or 3rd in the maximum number of elements to obtain a set covering all k nodes, and selects the minimum cover set among them. The proposed algorithm compensated for the disadvantage that the greedy algorithm does not obtain the optimal solution. As a result of applying the proposed algorithm to various application cases, an optimal solution was obtained with a polynomial time of O(kn²).

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.2
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• pp.185-191
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• 2023

To the exact cover problem that remains NP-complete to which no polynomial time algorithm is made available, this paper proposes a linear time algorithm that yields an optimal solution. The proposed algorithm makes use of the set cover problem's major feature which states that "no identical element shall be included in more than one covering set". To satisfy this criterion, the proposed algorithm initially selects a subset with the minimum cardinality and deletes those that contain the cardinality identical to that of the selected subset. This process is repeatedly performed on remaining subsets until the final solution is obtained. Provided that the solution is unattainable, it selects subsets with the maximum cardinality and repeats the same process. The proposed algorithm has not only obtained the optimal solution with ease but also proved its wide applicability on N-queens problems, hence disproving the NP-completeness of the exact cover problem.

• Journal of Korea Multimedia Society
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• v.12 no.5
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• pp.728-736
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• 2009

We propose a method using the genetic algorithm to solve the maximum set cover problem. It is needed for scheduling the power of sensor nodes in extending the lifetime of the wireless sensor network with variable sensing range. The existing Greedy Heuristic method calculates the power scheduling of sensor nodes repeatedly in the process of operation, and so the communication traffic of sensor nodes is increased. The proposed method reduces the amount of communication traffic of sensor nodes, and so the energies of nodes are saved, and the lifetime of network can be extended. The effectiveness of this method was verified through computer simulation, and considering the energy losses of communication operations about 10% in the network lifetime is improved.

• Journal of the Korea Society of Computer and Information
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• v.16 no.7
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• pp.85-93
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• 2011

The Vertex Coloring Problem hasn't been solved in polynomial time, so this problem has been known as NP-complete. This paper suggests linear time algorithm for Vertex Coloring Problem (VCP). The proposed algorithm is based on assumption that we can't know a priori the minimum chromatic number ${\chi}(G)$=k for graph G=(V,E) This algorithm divides Vertices V of graph into two parts as independent sets $\overline{C}$ and cover set C, then assigns the color to $\overline{C}$. The element of independent sets $\overline{C}$ is a vertex ${\upsilon}$ that has minimum degree ${\delta}(G)$ and the elements of cover set C are the vertices ${\upsilon}$ that is adjacent to ${\upsilon}$. The reduced graph is divided into independent sets $\overline{C}$ and cover set C again until no edge is in a cover set C. As a result of experiments, this algorithm finds the ${\chi}(G)$=k perfectly for 26 Graphs that shows the number of selecting ${\upsilon}$ is less than the number of vertices n.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.3
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• pp.193-199
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• 2019

In this paper I propose an algorithm of linear time complexity for NP-complete Maximum Independent Set (MIS) problem. Based on the basic property of the MIS, which forbids mutually adjoining vertices, the proposed algorithm derives the solution by repeatedly selecting vertices in the ascending order of their degree, given that the degree remains constant when vertices ${\nu}$ of the minimum degree ${\delta}(G)$ are selected and incidental edges deleted in a graph of n vertices. When applied to 22 graphs, the proposed algorithm could obtain the MIS visually yet effortlessly. The proposed linear MIS algorithm of time complexity O(n) always executes ${\alpha}(G)$ times, the cardinality of the MIS, and thus could be applied as a general algorithm to the MIS problem.

• Journal of the Korea Society of Computer and Information
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• v.20 no.11
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• pp.69-75
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• 2015

This paper suggests heuristic polynomial time algorithm for crew scheduling problem that is a kind of optimization problems. This problem has been solved by linear programming, set cover problem, set partition problem, column generation, etc. But the optimal solution has not been obtained by these methods. This paper sorts transit costs $c_{ij}$ to ascending order, and the task i and j crew paths are merged in case of the sum of operation time ${\Sigma}o$ is less than day working time T. As a result, we can be obtain the minimum number of crews $_{min}K$ and minimum transit cost $z=_{min}c_{ij}$. For the transit cost of specific number of crews $K(K>_{min}K)$, we delete the maximum $c_{ij}$ as much as the number of $K-_{min}K$, and to partition a crew path. For the 5 benchmark data, this algorithm can be gets less transit cost than state-of-the-art algorithms, and gets the minimum number of crews.

• Journal of the Korea Society of Computer and Information
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• v.21 no.5
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• pp.73-77
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• 2016

This paper deals with the network reliability problem that decides the communication line between main two districts while the k districts were destroyed in military communication network that the n communication lines are connected in m districts. For this problem, there is only in used the mathematical approach as linear programming (LP) software package and has been unknown the polynomial time algorithm. In this paper we suggest the heuristic algorithm with O(n) linear time complexity to solve the optimal solution for this problem. This paper suggests the flow path algorithm (FPA) and level path algorithm (LPA). The FPA is to search the maximum number of distinct paths between two districts. The LPA is to construct the levels and delete the unnecessary nodes and edges. The proposed algorithm can be get the same optimal solution as LP for experimental data.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.435-440
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• 2006

Let G be a simple graph with vertex set V(G) and edge set E(G). A subset S of E(G) is called an edge cover of G if the subgraph induced by S is a spanning subgraph of G. The maximum number of edge covers which form a partition of E(G) is called edge covering chromatic number of G, denoted by X'c(G). It is known that for any graph G with minimum degree ${\delta},\;{\delta}-1{\le}X'c(G){\le}{\delta}$. If $X'c(G) ={\delta}$, then G is called a graph of CI class, otherwise G is called a graph of CII class. It is easy to prove that the problem of deciding whether a given graph is of CI class or CII class is NP-complete. In this paper, we consider the classification of nearly bipartite graph and give some sufficient conditions for a nearly bipartite graph to be of CI class.