• Title/Summary/Keyword: Interval Graph

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NEW CONCEPTS OF REGULAR INTERVAL-VALUED FUZZY GRAPHS

  • TALEBI, A.A.;RASHMANLOU, HOSSEIN;DAVVAZ, BIJAN
    • Journal of applied mathematics & informatics
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    • v.35 no.1_2
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    • pp.95-111
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    • 2017
  • Recently, interval-valued fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in [0.1] rather than the crisp values between 0 and 1. In this paper, we introduce the concepts of regular and totally regular interval-valued fuzzy graphs and discusses some properties of the ${\mu}$-complement of interval-valued fuzzy graph. Self ${\mu}$-complementary interval-valued fuzzy graphs and self-weak ${\mu}$-complementary interval-valued fuzzy graphs are defined and a necessary condition for an interval valued fuzzy graph to be self ${\mu}$-complementary is discussed. We define busy vertices and free vertices in interval valued fuzzy graph and study their image under an isomorphism.

Notes On Inverse Interval Graph Coloring Problems

  • Chung, Yerim;Kim, Hak-Jin
    • Journal of the Korea Society of Computer and Information
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    • v.24 no.10
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    • pp.57-64
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    • 2019
  • In this paper, we study a polynomially solvable case of the inverse interval graph coloring problem. Given an interval graph associated with a specific interval system, the inverse interval graph coloring problem is defined with the assumption that there is no proper K-coloring for the given interval graph, where K is a fixed integer. The problem is to modify the system of intervals associated with the given interval graph by shifting some of the intervals in such a way that the resulting interval graph becomes K-colorable and the total modification is minimum with respect to a certain norm. In this paper, we focus on the case K = 1 where all intervals associated with the interval graph have length 1 or 2, and interval displacement is only allowed to the righthand side with respect to its original position. To solve this problem in polynomial time, we propose a two-phase algorithm which consists of the sorting and First Fit procedure.

Conditions for Disjoint Path Coverability in Proper Interval Graphs (진구간 그래프의 서로소인 경로 커버에 대한 조건)

  • Park, Jung-Heum
    • Journal of KIISE:Computer Systems and Theory
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    • v.34 no.10
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    • pp.539-554
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    • 2007
  • In this Paper, we investigate conditions for proper interval graphs to have k-disjoint path covers of three types each: one-to-one, one-to-many, and many-to-many. It was proved that for $k{\geq}2$, a proper interval graph is one-to-one k-disjoint path coverable if and only if the graph is k-connected, and is one-to-many k-disjoint path coverable if and only if the graph is k+1-connected. For $k{\geq}3$, a Proper interval graph is (paired) many-to-many k-disjoint path coverable if and only if the graph is 2k-1-connected.

Fully Dynamic Algorithm for the Vertex Connectivity of Interval Graphs (선분 그래프의 정점 연결성에 대한 완전 동적 알고리즘)

  • Kim, Jae-hoon
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.20 no.2
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    • pp.415-420
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    • 2016
  • A graph G=(V,E) is called an interval graph with a set V of vertices representing intervals on a line such that there is an edge $(i,j){\in}E$ if and only if intervals i and j intersect. In this paper, we are concerned in the vertex connectivity, one of various characteristics of the graph. Specifically, the vertex connectivity of an interval graph is represented by the overlapping of intervals. Also we propose an efficient algorithm to compute the vertex connectivity on the fully dynamic environment in which the vertices or the edges are inserted or deleted. Using a special kind of interval tree, we show how to compute the vertex connectivity and to maintain the tree in O(logn) time when a new interval is added or an existing interval is deleted.

A Scheduling Algorithm Using the Interval Graph (구간 그래프를 이용한 스케쥴링 알고리듬)

  • 김기현;정정화
    • Journal of the Korean Institute of Telematics and Electronics A
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    • v.31A no.1
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    • pp.84-92
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    • 1994
  • In this paper, we present a novel scheduling algorithm using the weighted interval graph. An interval graph is constructed, where an interval is a time frame of each operation. And for each operation type, we look for the maximum clique of the interval graph: the number of nodes of the maximum clique represents the number of operation that are executed concurrently. In order to minimize resource cost. we select the operation type to reduce the number of nodes of a maximum clique. For the selected operation type, an operation selected by selection rule is moved to decrease the number of nodes of a maximum clique. A selected operation among unscheduled operations is moved repeatly and assigned to a control step consequently. The proposed algorithm is applied to the pipeline and the nonpipeline data path synthesis. The experiment for examples shows the efficiency of the proposed scheduling algorithm.

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Interval prediction on the sum of binary random variables indexed by a graph

  • Park, Seongoh;Hahn, Kyu S.;Lim, Johan;Son, Won
    • Communications for Statistical Applications and Methods
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    • v.26 no.3
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    • pp.261-272
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    • 2019
  • In this paper, we propose a procedure to build a prediction interval of the sum of dependent binary random variables over a graph to account for the dependence among binary variables. Our main interest is to find a prediction interval of the weighted sum of dependent binary random variables indexed by a graph. This problem is motivated by the prediction problem of various elections including Korean National Assembly and US presidential election. Traditional and popular approaches to construct the prediction interval of the seats won by major parties are normal approximation by the CLT and Monte Carlo method by generating many independent Bernoulli random variables assuming that those binary random variables are independent and the success probabilities are known constants. However, in practice, the survey results (also the exit polls) on the election are random and hardly independent to each other. They are more often spatially correlated random variables. To take this into account, we suggest a spatial auto-regressive (AR) model for the surveyed success probabilities, and propose a residual based bootstrap procedure to construct the prediction interval of the sum of the binary outcomes. Finally, we apply the procedure to building the prediction intervals of the number of legislative seats won by each party from the exit poll data in the $19^{th}$ and $20^{th}$ Korea National Assembly elections.

Minimum Cost Range Assignment for the Vertex Connectivity of Graphs (그래프의 정점 연결성에 대한 최소 범위 할당)

  • Kim, Jae-Hoon
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.21 no.11
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    • pp.2103-2108
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    • 2017
  • For n points $p_i$ on the m-dimensional plane $R^m$ and a fixed range r, consider a set $T_i$ containing points the distances from $p_i$ of which are less than or equal to r. In case m=1, $T_i$ is an interval on a line, it is a circle on a plane when m=2. For the vertices corresponding to the sets $T_i$, there is an edge between the vertices if the two sets intersect. Then this graph is called an intersection graph G. For m=1 G is called a proper interval graph and for m=2, it is called an unit disk graph. In this paper, we are concerned in the intersection graph G(r) when r changes. In particular, we consider the problem to find the minimum r such that G(r)is connected. For this problem, we propose an O(n) algorithm for the proper interval graph and an $O(n^2{\log}\;n)$ algorithm for the unit disk graph. For the dynamic environment in which the points on a line are added or deleted, we give an O(log n) algorithm for the problem.

THE OPTIMAL SEQUENTIAL AND PARALLEL ALGORITHMS TO COMPUTE ALL HINGE VERTICES ON INTERVAL GRAPHS

  • Bera, Debashis;Pal, Madhumangal;Pal, Tapan K.
    • Journal of applied mathematics & informatics
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    • v.8 no.2
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    • pp.387-401
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    • 2001
  • If the distance between two vertices becomes longer after the removal of a vertex u, then u is called a hinge vertex. In this paper, a linear time sequential algorithm is presented to find all hinge vertices of an interval graph. Also, a parallel algorithm is presented which takes O(n/P + log n) time using P processors on an EREW PRAM.

A NOVEL DISCUSSION ON POWER FUZZY GRAPHS AND THEIR APPLICATION IN DECISION MAKING

  • T. BHARATHI;S. SHINY PAULIN;BIJAN DAVVAZ
    • Journal of applied mathematics & informatics
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    • v.42 no.1
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    • pp.123-137
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    • 2024
  • In this paper, Power fuzzy graphs is newly introduced by allotting fuzzy values on power graphs in such a way that the newly added edges, has the edge membership values between a closed interval which depends on vertex membership values and the length of the added edges. Power fuzzy subgraphs and total power fuzzy graphs are newly defined with properties and some special cases. It is observed that every power fuzzy graph is a fuzzy graph but the converse need not be true. Edges that are incident to vertices with the least vertex membership values are retained in the least power fuzzy subgraph. Further, the application of these concepts in real life time has been presented and discussed using power fuzzy graph model.