• East Asian mathematical journal
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• v.21 no.2
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• pp.163-170
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• 2005

We have proved that a finite BCI-algebra(X, *, 0) is a KL-product if and only if for any subset I of X such that $I{\times}X{\subseteq}I$ the cardinality of $0{\times}X$ divides the cardinality of I.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.155-163
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• 2021

For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. Connected graphs of order n with connected double geodetic number 2 or n are characterized. For integers n, a and b with 2 ≤ a < b ≤ n, there exists a connected graph G of order n such that dg(G) = a and dgc(G) = b. It is shown that for positive integers r, d and k ≥ 5 with r < d ≤ 2r and k - d - 3 ≥ 0, there exists a connected graph G of radius r, diameter d and connected double geodetic number k.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.33 no.3
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• pp.427-435
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• 2023

Cardinality estimation is used in wide range of applications and a fundamental problem processing a large range of data. While the internet moves into the era of big data, the function addressing cardinality estimation use only on-chip cache memory. To use memory efficiently, there have been various methods proposed. However, because of the noises between estimator, which is data structure per flow, loss of accuracy occurs in these algorithms. In this paper, we focus on minimizing noises. We propose multiple data structure that each estimator has the number of estimated value as many as the number of structures and choose the minimum value, which is one with minimum noises, We discover that the proposed algorithm achieves better performance than the best existing work using the same tight memory, such as 1 bit per flow, through experiment.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.3
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• pp.720-737
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• 2024

Private set intersection cardinality (PSI-CA) is a typical problem in the field of secure multi-party computation, which enables two parties calculate the cardinality of intersection securely without revealing any information about their sets. And it is suitable for private data protection scenarios where only the cardinality of the set intersection needs to be calculated. However, most of the currently available PSI-CA protocols only meet the security under the semi-honest model and can't resist the malicious behaviors of participants. To solve the problems above, by the application of the variant of Elgamal cryptography and Bloom filter, we propose an efficient PSI-CA protocol with high security. We also present two new operations on Bloom filter called IBF and BIBF, which could further enhance the safety of private data. Using zero-knowledge proof to ensure the safety under malicious adversary model. Moreover, in order to minimize the error in the results caused by the false positive problem, we use Garbled Bloom Filter and key-value pair packing creatively and present an improved PSI-CA protocol. Through experimental comparison with several existing representative protocols, our protocol runs with linear time complexity and more excellent characters, which is more suitable for practical application scenarios.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.4
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• pp.64-71
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• 2015

In this paper, we present a multi-period 0-1 knapsack problem which has the cardinality constraints. Theoretically, the presented problem can be regarded as an extension of the multi-period 0-1 knapsack problem. In the multi-period 0-1 knapsack problem, there are n jobs to be performed during m periods. Each job has the execution time and its completion gives profit. All the n jobs are partitioned into m periods, and the jobs belong to i-th period may be performed not later than in the i-th period, i = 1, ${\cdots}$, m. The total production time for periods from 1 to i is given by $b_i$ for each i = 1, ${\cdots}$, m, and the objective is to maximize the total profit. In the extended problem, we can select a specified number of jobs from each of periods associated with the corresponding cardinality constraints. As the extended problem is NP-hard, the branch and bound method is preferable to solve it, and therefore it is important to have efficient procedures for solving its linear programming relaxed problem. So we intensively explore the LP relaxed problem and suggest a polynomial time algorithm. We first decompose the LP relaxed problem into m subproblems associated with each cardinality constraints. Then we identify some new properties based on the parametric analysis. Finally by exploiting the special structure of the LP relaxed problem, we develop an efficient algorithm for the LP relaxed problem. The developed algorithm has a worst case computational complexity of order max[$O(n^2logn)$, $O(mn^2)$] where m is the number of periods and n is the total number of jobs. We illustrate a numerical example.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.323-333
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• 2015

Let X be a compact metric space and let |A| denote the cardinality of a set A. We prove that if $f:X{\rightarrow}X$ is a homeomorphism and ${\mid}X{\mid}={\infty}$, then for all ${\delta}$ > 0 there is $A{\subset}X$ such that |A| = 4 and for all $k{\in}\mathbb{Z}$ there are $x,y{\in}f^k(A)$, $x{\neq}y$, such that dist(x, y) < ${\delta}$. An observer that can only distinguish two points if their distance is grater than ${\delta}$, for sure will say that A has at most 3 points even knowing every iterate of A and that f is a homeomorphism. We show that for hyperexpansive homeomorphisms the same ${\delta}$-observer will not fail about the cardinality of A if we start with |A| = 3 instead of 4. Generalizations of this problem are considered via what we call (m, n)-expansiveness.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.2
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• pp.115-118
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• 2001

본 논문에서는 L-R 퍼지수의 집합-이론적 연산의 개념을 정의하고, 이들 개념의 성질들을 조사한다. 이들 연산들의 결과들을 이용하여 제2형 퍼지집합의 기수개념에 관하여 연구한다.

• Journal of Internet Computing and Services
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• v.20 no.3
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• pp.77-84
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• 2019

Workflow management system is a system that manages the workflow model which defines the process of work in reality. We can define the workflow process by sequencing jobs which is performed by the performers. Using the workflow management system, we can also analyze the flow of the process and revise it more efficiently. Many researches are focused on how to make the workflow process model more efficiently and manage it more easily. Recently, many researches use the workflow log files which are the execution history of the workflow process model performed by the workflow management system. Ourresearch group has many interests in making useful knowledge from the workflow event logs. In this paper we use XES log files because there are many data using this format. This papersuggests what are the cardinalities of the temporal workcases and how to get them from the workflow event logs. Cardinalities of the temporal workcases are the occurrence pattern of critical elements in the workflow process. We discover instance cardinalities, activity cardinalities and organizational resource cardinalities from several XES-based workflow event logs and visualize them. The instance cardinality defines the occurrence of the workflow process instances, the activity cardinality defines the occurrence of the activities and the organizational cardinality defines the occurrence of the organizational resources. From them, we expect to get many useful knowledge such as a patterns of the control flow of the process, frequently executed events, frequently working performer and etc. In further, we even expect to predict the original process model by only using the workflow event logs.

• Journal of KIISE:Software and Applications
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• v.35 no.2
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• pp.81-90
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• 2008

BCC(Boolean Cardinality Constraint) is to select one boolean variable from n different variables. It is widely used in many areas including software engineering. Thus, many efficient encoding techniques of BCC into CNF have been studied extensively In this paper we analyze some representative encodings with respect to flexibility as well as efficiency. In addition we use a visualization tool to draw the CNF clauses generated from each encodings. Visualizing the clauses exposes a hidden structure in encodings and makes to compare each encodings on the structure level, which is one of the prominent achievement in our work compared to other works. And we apply our analysis on the pigeon-hole problems to have confidence. In our experimental settings, the commander encoding shows the best performance.