• 정보과학회 논문지
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• 제43권5호
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• pp.509-515
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• 2016

순위패턴매칭문제는 텍스트 T와 패턴 P가 주어질 때, P와 각 문자들의 순위가 동일한 순서로 나타나는 T의 모든 부분문자열을 찾는 문제이다. 순위패턴매칭문제는 주가지수분석과 음악의 유사성분석과 같이 문자 자체를 비교하는 것보다 값의 변화순서가 중요한 분야에서 연구가 진행되었다. 순위다중패턴매칭문제는 텍스트 T와 여러 개의 패턴들로 이루어진 패턴집합 $\mathbb{P}$가 주어질 때, $\mathbb{P}$에 속한 패턴과 각 문자들의 순위가 동일한 순서로 나타나는 T의 모든 부분문자열을 찾는 문제이다. 본 논문에서는 순위다중패턴매칭문제를 해결하는 해싱기반 알고리즘을 제시한다.

• 대한수학회보
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• 제50권2호
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• pp.627-637
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• 2013

Let [$n$] = {1, 2, ${\ldots}$, $n$} be ordered in the standard way. The order-preserving full transformation semigroup ${\mathcal{O}}_n$ is the set of all order-preserving singular full transformations on [$n$] under composition. For this semigroup we describe maximal subsemibands, maximal regular subsemibands, locally maximal regular subsemibands, and completely obtain their classification.

• 대한수학회보
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• 제51권4호
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• pp.1055-1062
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• 2014

Let $O_n$ and $PO_n$ denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set $X_n=\{1,{\ldots},n\}$, respectively. Then the strictly partial order-preserving transformation semigroup $SPO_n$ on the set $X_n$, under its natural order, is defined by $SPO_n=PO_n{\setminus}O_n$. In this paper we find necessary and sufficient conditions for any subset of SPO(n, r) to be a (minimal) generating set of SPO(n, r) for $2{\leq}r{\leq}n-1$.

• 대한수학회보
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• 제49권5호
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• pp.949-959
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• 2012

In general, a class-preserving automorphism of generalized free products of nilpotent groups, amalgamating a cyclic normal subgroup of order 8, need not be an inner automorphism. We prove that every class-preserving automorphism of generalized free products of nitely generated nilpotent groups, amalgamating a cyclic normal subgroup of order less than 8, is inner.

• 한국지능시스템학회논문지
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• 제14권5호
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• pp.563-570
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• 2004

Genetic algorithms have been successfully applied to various optimization problems belonging to NP-hard problems. The sequential ordering problems(SOP) and the job shop scheduling problems(JSP) are well-known NP-hard problems with strong influence on industrial applications. Both problems share some common properties in that they have some imposed precedence constraints. When genetic algorithms are applied to this kind of problems, it is desirable for genetic operators to be designed to produce chromosomes satisfying the imposed precedence constraints. Several genetic operators applicable to such problems have been proposed. We call such genetic operators precedence-preserving genetic operators. This paper presents three existing precedence-preserving genetic operators: Precedence -Preserving Crossover(PPX), Precedence-preserving Order-based Crossover (POX), and Maximum Partial Order! Arbitrary Insertion (MPO/AI). In addition, it proposes two new operators named Precedence-Preserving Edge Recombination (PPER) and Multiple Selection Precedence-preserving Order-based Crossover (MSPOX) applicable to such problems. It compares the performance of these genetic operators for SOP and JSP in the perspective of their solution quality and execution time.

• 대한수학회보
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• 제53권2호
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• pp.495-506
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• 2016

In this note we consider the monoid $\mathcal{PODI}_n$ of all monotone partial permutations on $\{1,{\ldots},n\}$ and its submonoids $\mathcal{DP}_n$, $\mathcal{POI}_n$ and $\mathcal{ODP}_n$ of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids $\mathcal{POI}_n$ and $\mathcal{ODP}_n$ are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that $\mathcal{PODI}_n$ is a quotient of a semidirect product of $\mathcal{POI}_n$ and the group $\mathcal{C}_2$ of order two and, analogously, $\mathcal{DP}_n$ is a quotient of a semidirect product of $\mathcal{ODP}_n$ and $\mathcal{C}_2$.

• 대한수학회논문집
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• 제30권4호
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• pp.349-361
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• 2015

A fence is an ordered set that the order forms a path with alternating orientation. Let F = (F;${\leq}$) be a fence and let OT(F) be the semigroup of all order-preserving self-mappings of F. We prove that OT(F) is coregular if and only if ${\mid}F{\mid}{\leq}2$. We characterize all coregular elements in OT(F) when F is finite. For any subfence S of F, we show that the set COTS(F) of all order-preserving self-mappings in OT(F) having S as their range forms a coregular subsemigroup of OT(F). Under some conditions, we show that a union of COTS(F)'s forms a coregular subsemigroup of OT(F).

• 대한수학회보
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• 제49권5호
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• pp.1015-1025
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• 2012

Let $[n]=\{1,2,{\cdots},n\}$, and let $PO_n$ be the partial order-preserving transformation semigroup on [n]. Let $$CPO_n=\{{\alpha}{\in}PO_n:({\forall}x,y{\in}dom{\alpha}),\;|x{\alpha}-y{\alpha}|{\leq}|x-y|\}$$ Then $CPO_n$ is a subsemigroup of $PO_n$. In this paper, we characterize Green's relations and the regularity of elements for $CPO_n$.

• Journal of Information Processing Systems
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• 제15권5호
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• pp.1211-1217
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• 2019

Developing methods to search over an encrypted database (EDB) have received a lot of attention in the last few years. Among them, order-revealing encryption (OREnc) and order-preserving encryption (OPEnc) are the core parts in the case of range queries. Recently, some ideally-secure OPEnc schemes whose ciphertexts reveal no additional information beyond the order of the underlying plaintexts have been proposed. However, these schemes either require a large round complexity or a large persistent client-side storage of size O(n) where n denotes the number of encrypted items stored in EDB. In this work, we propose a new construction of an efficient OPEnc scheme based on an OREnc scheme. Security of our construction inherits the security of the underlying OREnc scheme. Moreover, we also show that the construction of a non-interactive ideally-secure OPEnc scheme with a constant client-side storage is theoretically possible from our construction.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.13-19
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• 2002

In nonparametric entropy estimation, both mass and mean-preserving maximum entropy distribution (Theil, 1980) and the underlying distribution of the sample entropy (Vasicek, 1976), the most widely used entropy estimator, consist of nb mass-preserving densities based on disjoint Intervals of the simple averages of two adjacent order statistics. In this paper, we notice that those nonparametric density functions do not actually keep the mass-preserving constraint, and propose a modified sample entropy by considering the generalized 0-statistics (Kaigh and Driscoll, 1987) in averaging two adjacent order statistics. We consider the proposed estimator in a goodness of fit test for normality and compare its performance with that of the sample entropy.