• Title/Summary/Keyword: 강한 해밀톤 성질

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Strongly Hamiltonian Laceability of Mesh Networks (메쉬 연결망의 강한 해밀톤 laceability)

  • Park Kyoung-Wook;Lim Hyeong-Seok
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.8
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    • pp.393-398
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    • 2005
  • In interconnection networks, a Hamiltonian path has been utilized in many applications such as the implementation of linear array and multicasting. In this paper, we consider the Hamiltonian properties of mesh networks which are used as the topology of parallel machines. If a network is strongly Hamiltonian laceable, the network has the longest path joining arbitrary two nodes. We show that a two-dimensional mesh M(m, n) is strongly Hamiltonian laceabie, if $m{\geq}4,\;n{\geq}4(m{\geq}3,\;n{\geq}3\;respectively)$, and the number of nodes is even(odd respectively). A mesh is a spanning subgraph of many interconnection networks such as tori, hypercubes, k-ary n-cubes, and recursive circulants. Thus, our result can be applied to discover the fault-hamiltonicity of such networks.

Fault Hamiltonicity of Meshes with Two Wraparound Edges (두 개의 랩어라운드 에지를 갖는 메쉬의 고장 해밀톤 성질)

  • 박경욱;이형옥;임형석
    • Journal of KIISE:Computer Systems and Theory
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    • v.30 no.7_8
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    • pp.434-444
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    • 2003
  • In this paper, we consider the hamiltonian properties of m$\times$n (m$\geq$2, n$\geq$3) mesh networks with two wraparound edges on the first row and last row, called M$_2$(m, n), in the presence of a faulty node or link. We prove that M$_2$(m, n) with odd n is hamiltonian-connected and 1-fault hamiltonian. In addition, we prove that M$_2$(m, n) with even n is strongly hamiltonian laceable and 1-vertex fault tolerant strongly hamiltonian laceable.

Edge Fault Hamiltonian Properties of Mesh Networks with Two Additional Links (메쉬에 두 개의 링크를 추가한 연결망의 에지 고장 해밀톤 성질)

  • Park, Kyoung-Wook;Lim, Hyeong-Seok
    • The KIPS Transactions:PartA
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    • v.11A no.3
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    • pp.189-198
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    • 2004
  • We consider the fault hamiltonian properties of m ${\times}$ n meshes with two wraparound links on the first row and the last row, denoted by M$_2$(m,n), (m$\geq$2, n$\geq$3). M$_2$(m,n), which is bipartite, with a single faulty link has a fault-free path of length mn-l(mn-2) between arbitrary two nodes if they both belong to the different(same) partite set. Compared with the previous works of P$_{m}$ ${\times}$C$_{n}$ , it also has these hamiltonian properties. Our result show that two additional wraparound links are sufficient for an m${\times}$n mesh to have such properties rather than m wraparound links. Also, M$_2$(m,n) is a spanning subgraph of many interconnection networks such as multidimensional meshes, recursive circulants, hypercubes, double loop networks, and k-ary n-cubcs. Thus, our results can be applied to discover fault-hamiltonicity of such interconnection networks. By applying hamiltonian properties of M$_2$(m,n) to 3-dimensional meshes, recursive circulants, and hypercubes, we obtain fault hamiltonian properties of these networks.

Strong Hamiltonicity of Recursive Circulants (재귀원형군의 강한 해밀톤 성질)

  • Park, Jeong-Heum
    • Journal of KIISE:Computer Systems and Theory
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    • v.28 no.8
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    • pp.399-405
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    • 2001
  • 이 논문은 재귀원형군 G(2$^{m}$ , 2$^{k}$ )의 강한 해밀톤 성질을 그래프 이론적 관점에서 고찰한다. 재귀원형군은 [9]에서 제안된 다중 컴퓨터의 연결망 구조이다. G(2$^{m}$ , 2$^{k}$ )가 임의의 정점 쌍 ν, $\omega$를 잇는 길이 ι인 경로를 가지는가 하는 문제를 고려하여, (a) G(2$^{m}$ , 2$^{k}$ )는 ι$\geq$d(ν, $\omega$)을 만족하는 모든 ι에 대해서 길이 ι인 경로를 가지며, (b) G(2$^{m}$ , 4)는 ι$\geq$d(ν, $\omega$)+2인 모든 길이의 경로를 가지며, (c)G(2$^{m}$ , 2$^{k}$ ), k$\geq$3은 길이 d(ν, $\omega$)+2$^{k}$ -3인 경로를 가지지 않는 정점 쌍이 있음을 보인다. 여기서, d(ν, $\omega$)는 ν와 $\omega$ 사이의 거리이다.

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One-to-One Disjoint Path Covers in Recursive Circulants (재귀원형군의 일대일 서로소인 경로 커버)

  • 박정흠
    • Journal of KIISE:Computer Systems and Theory
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    • v.30 no.12
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    • pp.691-698
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    • 2003
  • In this paper, we propose a problem, called one-to-one disjoint path cover problem, whether or not there exist k disjoint paths joining a pair of vertices which pass through all the vertices other than the two exactly once. A graph which for an arbitrary k, has a one-to-one disjoint path cover between an arbitrary pair of vertices has a hamiltonian property stronger than hamiltonian-connectedness. We investigate this problem on recursive circulants and prove that for an arbitrary k $k(1{\leq}k{\leq}m)$$ G(2^m,4)$,$m{\geq}3$, has a one-to-one disjoint path cover consisting of k paths between an arbitrary pair of vortices.

Fault-hamiltonicity of Bipartite Double Loop Networks (이분 그래프인 이중 루프 네트워크의 고장 해밀톤 성질)

  • 박정흠
    • Journal of KIISE:Computer Systems and Theory
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    • v.31 no.1_2
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    • pp.19-26
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    • 2004
  • In this paper, we investigate the longest fault-free paths joining every pair of vertices in a double loop network with faulty vertices and/or edges, and show that a bipartite double loop network G(mn;1, m) is strongly hamiltonian-laceable when the number of faulty elements is two or less. G(mn;1, m) is bipartite if and only if m is odd and n is even.

Unpaired Many-to-Many Disjoint Path Covers in Hypercube-Like Interconnection Networks (하이퍼큐브형 상호연결망의 비쌍형 다대다 서로소인 경로 커버)

  • Park, Jung-Heum
    • Journal of KIISE:Computer Systems and Theory
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    • v.33 no.10
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    • pp.789-796
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    • 2006
  • An unpaired many-to-many k-disjoint nth cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct sources and sinks in which each vertex of G is covered by a path. Here, a source can be freely matched to a sink. In this paper, we investigate unpaired many-to-many DPC's in a subclass of hpercube-like interconnection networks, called restricted HL-graphs, and show that every n-dimensional restricted HL-graph, $(m{\geq}3)$, with f or less faulty elements (vertices and/or edges) has an unpaired many-to-many k-DPC for any $f{\geq}0\;and\;k{\geq}1\;with\;f+k{\leq}m-2$.

Paired Many-to-Many Disjoint Path Covers in Recursive Circulants and Tori (재귀원형군과 토러스에서 쌍형 다대다 서로소인 경로 커버)

  • Kim, Eu-Sang;Park, Jung-Heum
    • Journal of KIISE:Computer Systems and Theory
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    • v.36 no.1
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    • pp.40-51
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    • 2009
  • A paired many-to-many k-disjoint path cover (paired k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. In this paper, we investigate disjoint path covers in recursive circulants G($cd^m$,d) with $d{\geq}3$ and tori, and show that provided the number of faulty elements (vertices and/or edges) is f or less, every nonbipartite recursive circulant and torus of degree $\delta$ has a paired k-DPC for any f and $k{\geq}1$ with $f+2k{\leq}{\delta}-1$.

Many-to-Many Disjoint Path Covers in Double Loop Networks (이중 루프 네트워크의 다대다 서로소인 경로 커버)

  • Park Jung-Heum
    • Journal of KIISE:Computer Systems and Theory
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    • v.32 no.8
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    • pp.426-431
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    • 2005
  • A many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joining k distinct source-sink pairs in which each vertex of G is covered by a path. In this paper, we investigate many-to-many 2-DPC in a double loop network G(mn;1,m), and show that every nonbipartite G(mn;1,m), $m{\geq}3$, has 2-DPC joining any two source-sink pairs of vertices and that every bipartite G(mn;1,m) has 2-DPC joining any two source-sink pairs of black-white vertices and joining any Pairs of black-black and white-white vertices. G(mn;l,m) is bipartite if and only if n is odd and n is even.