• Communications of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.183-191
• /
• 2017

We define a stratification and a partition of a finite topological space and define a partial order on the partition. Open subsets can be described completely in terms of this partially ordered partition. We associate a directed graph to the partially ordered partition of a finite topological space. This gives a one-to-one correspondence between finite topological spaces and a certain class of directed graphs.

• Kyungpook Mathematical Journal
• /
• v.56 no.3
• /
• pp.657-668
• /
• 2016

Given a partition ${\lambda}=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_l)$ of a positive integer n, let Tab(${\lambda}$, k) be the set of all tabloids of shape ${\lambda}$ whose weights range over the set of all k-compositions of n and ${\mathcal{OP}}^k_{\lambda}_{rev}$ the set of all ordered partitions into k blocks of the multiset $\{1^{{\lambda}_l}2^{{\lambda}_{l-1}}{\cdots}l^{{\lambda}_1}\}$. In [2], Butler introduced an inversion-like statistic on Tab(${\lambda}$, k) to show that the rank-selected $M{\ddot{o}}bius$ invariant arising from the subgroup lattice of a finite abelian p-group of type ${\lambda}$ has nonnegative coefficients as a polynomial in p. In this paper, we introduce an inversion-like statistic on the set of ordered partitions of a multiset and construct an inversion-preserving bijection between Tab(${\lambda}$, k) and ${\mathcal{OP}}^k_{\hat{\lambda}}$. When k = 2, we also introduce a major-like statistic on Tab(${\lambda}$, 2) and study its connection to the inversion statistic due to Butler.

• Proceedings of the KIEE Conference
• /
• 1988.07a
• /
• pp.557-560
• /
• 1988

In this paper, we present a new k-way partitioning algorithm for a graph of an electrical circuit wherein nodes and edges are regarded as cells (modules) and nets, respectively. In contrast to the previous work, our method is based upon a linearly ordered partition paradigm. We also claim that the maximum number of netcuts mostly governs the performance of k-way partitioning, thus having influence on the construction of a new cost function. In addition, our approach elaborates upon balancing the partition size. Our experiments show excellent results in comparison with previous k-way partitioning algorithms.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.22 no.4
• /
• pp.95-102
• /
• 2022

This paper proposed a linear time algorithm for a three-partition problem(TPP) in which a polynomial time algorithm is not known as NP-complete. This paper proposes a backtracking method that improves the problems of not being able to obtain a solution of the MM method using the sum of max-min values and third numbers, which are known polynomial algorithms in the past. In addition, the problem of MM applying the backtracking method was improved. The proposed algorithm partition the descending ordered set S into three and assigned to the forward, backward, and best-fit allocation method with maximum margin, and found an optimal solution for 50.00%, which is 5 out of 10 data in initial allocation phase. The remaining five data also showed performance to find the optimal solution by exchanging numbers between surplus boxes and shortage boxes at least once and up to seven times. The proposed algorithm that performs simple allocation and exchange optimization with less O(k) linear time performance complexity than the three-partition m=n/3 data, and it was shown that there could be a polynomial time algorithm in which TPP is a P-problem, not NP-complete.

• 한국공간정보시스템학회:학술대회논문집
• /
• 2005.11a
• /
• pp.61-66
• /
• 2005

Spatiotemporal data mining represents the confluence of several fields including spatiotemporal databases, machine loaming, statistics, geographic visualization, and information theory. Exploration of spatial data mining and temporal data mining has received much attention independently in knowledge discovery in databases and data mining research community. In this paper, we introduce an algorithm Max_MOP for discovering moving sequences in mobile environment. Max_MOP mines only maximal frequent moving patterns. We exploit the characteristic of the problem domain, which is the spatiotemporal proximity between activities, to partition the spatiotemporal space. The task of finding moving sequences is to consider all temporally ordered combination of associations, which requires an intensive computation. However, exploiting the spatiotemporal proximity characteristic makes this task more cornputationally feasible. Our proposed technique is applicable to location-based services such as traffic service, tourist service, and location-aware advertising service.

• Journal of applied mathematics & informatics
• /
• v.37 no.5_6
• /
• pp.469-480
• /
• 2019

A generalized tiling is defined as a generalization of the properties of tiling a region of ${\mathbb{Z}}^2$ with dominoes, and comprises tiling with rhombus and any other tilings that admits height functions which can be ordered into a distributive lattice. By using properties of the distributive lattice, we prove that the Markov chain consisting of moving from one height function to the next by a flip is fast mixing and the mixing time ${\tau}({\epsilon})$ is given by ${\tau}({\epsilon}){\leq}(kmn)^3(mn\;{\ln}\;k+{\ln}\;{\epsilon}^{-1})$, where mn is the area of the grid ${\Gamma}$ that is a k-regular polycell. This result generalizes the result of the authors (T-tetromino tiling Markov chain is fast mixing, Theor. Comp. Sci. (2018)) and improves on the mixing time obtained by using coupling arguments by N. Destainville and by M. Luby, D. Randall, A. Sinclair.

• Kyungpook Mathematical Journal
• /
• v.58 no.4
• /
• pp.747-759
• /
• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• Journal of the Institute of Electronics Engineers of Korea SP
• /
• v.39 no.5
• /
• pp.486-493
• /
• 2002

In this paper, we proposed the effective multispectral image compression method using CIBP(classified interband bidrectional prediction) and extended SPIHT(set partition in hierarchical trees) in wavelet domain. We determine separately feature bands that have the highest correlation with other bands in the visible range and in the infrared range of wavelengths. Feature bands are coded to remove the spatial redundancy with SPIHT in the wavelet domain. Prediction bands that have high correlation with feature bands are wavelet transformed and they are classified into one of three classes considering reflection characteristics of the baseband. For Prediction bands, CIBP is performed to reduce the spectral redundancy. for the difference bands between prediction bands and the predicted bands, They are ordered to upgrade the compression efficiency of extended SPIHT with the largest error magnitude. The arranged bands are coded to compensate the prediction error with extended SPIHT. Experiments are carried out on the multispectral images. The results show that the proposed method reconstructs higher quality images than images reconstructed by the conventional methods at the same bit rate.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.10 no.12
• /
• pp.2132-2139
• /
• 2006

A parallel program including a nested parallelism has a complex execution aspects and tasks are executed concurrently. This concurrency is a main cause raising most of errors. In this paper, a new method for checking concurrency between two tasks is proposed. The existing techniques for checking the concurrency have their limits to represent a global structure. A new labeling technique that appropriate for image visualization is proposed. To show the global structure by imaging of execution aspects through region partition on 2D plane. On the basis of it, each of the tasks that can distinguish the ordered relation create an independent image. Image information generated by the result simplifies semantic analysis of the related task, and provides an outline of a global execution aspects structure of the program to user effectively.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.13 no.1
• /
• pp.143-152
• /
• 2013

Given weighted graph G=(V,E), n=|V|, m=|E|, the minimum cut problem is classified with source s and sink t or without s and t. Given undirected weighted graph without s and t, Stoer-Wagner algorithm is most popular. This algorithm fixes arbitrary vertex, and arranges maximum adjacency (MA)-ordering. In the last, the sum of weights of the incident edges for last ordered vertex is computed by cut value, and the last 2 vertices are merged. Therefore, this algorithm runs $\frac{n(n-1)}{2}$ times. Given graph with s and t, Ford-Fulkerson algorithm determines the bottleneck edges in the arbitrary augmenting path from s to t. If the augmenting path is no more exist, we determine the minimum cut value by combine the all of the bottleneck edges. This paper suggests minimum cut algorithm for undirected weighted graph with s and t. This algorithm suggests MA-merging and computes cut value simultaneously. This algorithm runs n-1 times and successfully divides V into disjoint S and V sets on the basis of minimum cut, but the Stoer-Wagner is fails sometimes. The proposed algorithm runs more than Ford-Fulkerson algorithm, but finds the minimum cut value within n-1 processing times.