• 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.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.1-11
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• 2010

The conditional covering problem is an important variation of well studied set covering problem. In the set covering problem, the problem is to find a minimum cardinality vertex set which will cover all the given demand points. The conditional covering problem asks to find a minimum cardinality vertex set that will cover not only the given demand points but also one another. This problem is NP-complete for general graphs. In this paper, we present an efficient algorithm to solve the conditional covering problem on interval graphs with n vertices which runs in O(n)time.

• Journal of the Korean Operations Research and Management Science Society
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• v.15 no.2
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• pp.97-104
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• 1990

The problem is a variation of the weighted set-covering problem (SCP) which requires the minimum-cost cover to be self-covering. It is shown that direct extension of the well-known greedy heuristic for SCP can have an arbitrarily large error in the worst case. It remains an open question whther these exists a greedy heuristic with a finite error bound.

• 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.

• International Journal of Reliability and Applications
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• v.5 no.4
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• pp.147-154
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• 2004

This work developed and algorithm for a set covering model when the reliability of covers is a concern. This model extended the usage of the set covering model.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.12
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• pp.5643-5656
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• 2016

The detection accuracy of steganalysis depends on many factors, including the embedding algorithm, the payload size, the steganalysis feature space and the properties of the cover source. In practice, the cover source mismatch (CSM) problem has been recognized as the single most important factor negatively affecting the performance. To address this problem, we propose a new framework for blind, universal steganalysis which uses traditional steganalyst features. Firstly, cover images with the same statistical properties are searched from a reference image database as aided samples. The test image and its aided samples form a whole test set. Then, by assuming that most of the aided samples are innocent, we conduct outlier detection on the test set to judge the test image as cover or stego. In this way, the framework has removed the need for training. Hence, it does not suffer from cover source mismatch. Because it performs anomaly detection rather than classification, this method is totally unsupervised. The results in our study show that this framework works superior than one-class support vector machine and the outlier detector without considering the image retrieval process.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10a
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• pp.857-862
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• 1987

Given a network with k specified vertices bi called centers, a cardinality constrained cover is a family {Bi} of k subsets covering the vertex set of a network, such that each subset Bi corresponds to and contains center bi, and satisfies a given cardinality constraint. A set of cardinality constrained overlapping territories is a cardinality constrained cover such that the total sum of T(B$_{i}$) for all subsets is minimum among all cardinality constrained covers, where T(B$_{i}$) is the summation of the shortest path lengths from center bi to every vertex in B$_{I}$. This paper considers a problem of finding a set of cardinality constrained overlapping territories. and proposes an algorithm for the Problem which has the time and space complexities are O(k$^{3}$$\mid$V$\mid$$^{2}$) and O(k$\mid$V$\mid$+$\mid$E$\mid$), respectively, where V and E are the sets of vertices and edges of a given network, respectively. The concept of overlapping territories has a possibility to be applied to a job assignment problem.oblem.