• Title, Summary, Keyword: order-preserving

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MAXIMAL PROPERTIES OF SOME SUBSEMIBANDS OF ORDER-PRESERVING FULL TRANSFORMATIONS

  • Zhao, Ping;Yang, Mei
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.2
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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.

GENERATING SETS OF STRICTLY ORDER-PRESERVING TRANSFORMATION SEMIGROUPS ON A FINITE SET

  • Ayik, Hayrullah;Bugay, Leyla
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.4
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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 $2{\leq}r{\leq}n-1$.

REGULARITY AND GREEN'S RELATIONS ON SEMIGROUPS OF TRANSFORMATION PRESERVING ORDER AND COMPRESSION

  • Zhao, Ping;Yang, Mei
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.5
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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 $CPO_n$.

A Comparative Study of Precedence-Preserving Genetic Operators in Sequential Ordering Problems and Job Shop Scheduling Problems (서열 순서화 문제와 Job Shop 문제에 대한 선행관계유지 유전 연산자의 비교)

  • Lee, Hye-Ree;Lee, Keon-Myung
    • Journal of the Korean Institute of Intelligent Systems
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    • v.14 no.5
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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.

CLASS-PRESERVING AUTOMORPHISMS OF GENERALIZED FREE PRODUCTS AMALGAMATING A CYCLIC NORMAL SUBGROUP

  • Zhou, Wei;Kim, Goan-Su
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.5
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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.

A NOTE ON BILATERAL SEMIDIRECT PRODUCT DECOMPOSITIONS OF SOME MONOIDS OF ORDER-PRESERVING PARTIAL PERMUTATIONS

  • Fernandes, Vitor H.;Quinteiro, Teresa M.
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.2
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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 $\mathcal{C}_2$.

COREGULARITY OF ORDER-PRESERVING SELF-MAPPING SEMIGROUPS OF FENCES

  • JENDANA, KETSARIN;SRITHUS, RATANA
    • Communications of the Korean Mathematical Society
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    • v.30 no.4
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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).

ON WEAKLY GRADED POSETS OF ORDER-PRESERVING MAPS UNDER THE NATURAL PARTIAL ORDER

  • Jitjankarn, Phichet
    • Communications of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.347-358
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    • 2020
  • In this paper, we simplify the natural partial ordering ≼ on the semigroup 𝒪([n]) under composition of all order-preserving maps on [n] = {1, …, n}, and describe its maximal elements. Also, we show that the poset (𝒪([n]), ≼) is weakly graded and determine when (𝒪([n]), ≼) has a structure of (i + 1)-avoidance.

New Construction of Order-Preserving Encryption Based on Order-Revealing Encryption

  • Kim, Kee Sung
    • Journal of Information Processing Systems
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    • v.15 no.5
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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.

Modified Mass-Preserving Sample Entropy

  • Kim, Chul-Eung;Park, Sang-Un
    • Communications for Statistical Applications and Methods
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    • v.9 no.1
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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.