A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint p... more A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint paths joining distinct source-sink pairs in which each vertex of the graph is covered by a path. A two-dimensional × torus is a graph defined as the product of two cycles and of length and , respectively. In this paper, we deal with an × bipartite torus, even ≥ , with a single faulty vertex, and present a necessary and sufficient condition for the torus to have a paired many-to-many 2-DPC connecting given two source-sink pairs as follows: Out of the four sources and sinks, exactly one of them has the same color as the faulty vertex. 1. 서 론 상호 연결망(interconnection networks)에서 노드들 사이의 라우팅이나 선형 배열의 임베딩 등과 관련하여 다루는 중요한 문제 중의 하나는 노드가 서로소인 경로 (node-disjoint paths)를 찾는 것이다. 노드가 서로소인 경로는 노드들 사이에 효율적인 데이터 라우팅을 위한 병렬 경로로 사용될 수 있다. 또한 노드가 서로소인 경 로에서 각 경로는 파이프라인 계산에 이용될 수 있다. 상호연결망은 자주 그래프로 모델 되는데, 정점과 에지 는 각각 노드와 통신 링크에 대응한다. 이 논문에서는 노드가 서로소인 경로를 간단히 서로소인 경로라고 부 르기로 한다. 서로...
Journal of KIISE:Computer Systems and Theory, 2009
A paired many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joi... more A paired 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. A two-dimensional torus is a graph defined as a product of two cycles and of length m and n, respectively. In this paper, we show that an torus with and odd has a 2-DPC joining any two source-sink pairs of vertices. This result is optimal in a sense that an torus does not always have a 3-DPC and that the graph with one faulty vertex or edge does not always have a 2-DPC.
Journal of KIISE:Computer Systems and Theory, 2012
A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint p... more A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint paths joining distinct source-sink pairs in which each vertex of the graph is covered by a path. A two-dimensional × torus is a graph defined as the product of two cycles and of length and , respectively. In this paper, we deal with an × bipartite torus, even ≥ , with a single faulty vertex, and present a necessary and sufficient condition for the torus to have a paired many-to-many 2-DPC connecting given two source-sink pairs as follows: Out of the four sources and sinks, exactly one of them has the same color as the faulty vertex.
보통 상호연결망의 신뢰도(reliability) 혹은 고장 감내 도(fault tolerance)에 대한 척도는, 고장이 없는 노드들 사이에 통신을 두절시키지 않고 고장이 발... more 보통 상호연결망의 신뢰도(reliability) 혹은 고장 감내 도(fault tolerance)에 대한 척도는, 고장이 없는 노드들 사이에 통신을 두절시키지 않고 고장이 발생할 수 있는 최대 노드수로 주어진다. 상호연결망의 연결도 (connectivity)는 노드 고장에 대한 신뢰도에 대응한다. 그래프 의 연결도가 서로소인 경로라는 개념으로 특성 을 밝힐 수 있음은 널리 알려져 있다. Menger의 정리에 따르면 그래프 가 -연결될( -connected) 필요충분조건은 임의의 소스와 싱크의 쌍 , 에 대하여 그것을 잇는 일대일 유형의 서로소인 경 로가 개 존재한다는 것이다. 또한 소위 Fan Lemma가 말하는 그래프 가 -연결될 필요충분조건은 단일 소 스 와 서로 다른 개의 싱크 ... 를 잇는 일대다 유형의 서로소인 경로가 개 존재한다는 것이다[1]. 더 구나 그래프 가 -연결될 필요충분조건은 개의 서로 다른 소스 ...와 개의 서로 다른 싱크
Journal of KIISE:Computer Systems and Theory, 2000
In this paper, we consider hamiltonian properties of a double loop network with edge and/or verte... more In this paper, we consider hamiltonian properties of a double loop network with edge and/or vertex faults. A double loop network G(mn;1,m) is a 4-regular graph obtained by adding some edges to an m×n rectangular grid graph. We show that a double loop network G(mn;1,m) with even m and n has a hamiltonian path joining every pair of vertices if the number of faulty elements is 1 or less, and has a hamiltonian cycle if the number of faulty elements is 2 or less.
Journal of KIISE:Computer Systems and Theory, 2007
In this Paper, we investigate conditions for proper interval graphs to have k-disjoint path cover... more 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 , 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 , a Proper interval graph is (paired) many-to-many k-disjoint path coverable if and only if the graph is 2k-1-connected.
Journal of KIISE:Computer Systems and Theory, 2001
In this paper, we investigate strong hamiltonian properties of recursive circulant G(2m,2k) from ... more In this paper, we investigate strong hamiltonian properties of recursive circulant G(2m,2k) from the graph theory point of view. Recursive circulant is an interconnection structure for multicomputer networks proposed in [9]. We consider the problem whether G(2m,2k) has a path of length l joining a pair of vortices v and H, and show that (a) G(2m,2) has a path of length l forany l≥d(w,w), (b) G(2m,4) has a path of length l for any l≥d(v,w) + 2, (c) for some pair of vertices in G(2m,2k), k≥3, there is no path of length d(v, w) + 2k-3, where d(v, w) is the distance from v to w.
Journal of KIISE:Computer Systems and Theory, 2006
An unpaired many-to-many k-disjoint nth cover (k-DPC) of a graph G is a set of k disjoint paths j... more 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, , with f or less faulty elements (vertices and/or edges) has an unpaired many-to-many k-DPC for any .
A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint p... more A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint paths joining distinct source-sink pairs in which each vertex of the graph is covered by a path. A two-dimensional × torus is a graph defined as the product of two cycles and of length and , respectively. In this paper, we deal with an × bipartite torus, even ≥ , with a single faulty vertex, and present a necessary and sufficient condition for the torus to have a paired many-to-many 2-DPC connecting given two source-sink pairs as follows: Out of the four sources and sinks, exactly one of them has the same color as the faulty vertex. 1. 서 론 상호 연결망(interconnection networks)에서 노드들 사이의 라우팅이나 선형 배열의 임베딩 등과 관련하여 다루는 중요한 문제 중의 하나는 노드가 서로소인 경로 (node-disjoint paths)를 찾는 것이다. 노드가 서로소인 경로는 노드들 사이에 효율적인 데이터 라우팅을 위한 병렬 경로로 사용될 수 있다. 또한 노드가 서로소인 경 로에서 각 경로는 파이프라인 계산에 이용될 수 있다. 상호연결망은 자주 그래프로 모델 되는데, 정점과 에지 는 각각 노드와 통신 링크에 대응한다. 이 논문에서는 노드가 서로소인 경로를 간단히 서로소인 경로라고 부 르기로 한다. 서로...
Journal of KIISE:Computer Systems and Theory, 2009
A paired many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joi... more A paired 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. A two-dimensional torus is a graph defined as a product of two cycles and of length m and n, respectively. In this paper, we show that an torus with and odd has a 2-DPC joining any two source-sink pairs of vertices. This result is optimal in a sense that an torus does not always have a 3-DPC and that the graph with one faulty vertex or edge does not always have a 2-DPC.
Journal of KIISE:Computer Systems and Theory, 2012
A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint p... more A paired many-to-many -disjoint path cover (-DPC for short) of a graph is a set of disjoint paths joining distinct source-sink pairs in which each vertex of the graph is covered by a path. A two-dimensional × torus is a graph defined as the product of two cycles and of length and , respectively. In this paper, we deal with an × bipartite torus, even ≥ , with a single faulty vertex, and present a necessary and sufficient condition for the torus to have a paired many-to-many 2-DPC connecting given two source-sink pairs as follows: Out of the four sources and sinks, exactly one of them has the same color as the faulty vertex.
보통 상호연결망의 신뢰도(reliability) 혹은 고장 감내 도(fault tolerance)에 대한 척도는, 고장이 없는 노드들 사이에 통신을 두절시키지 않고 고장이 발... more 보통 상호연결망의 신뢰도(reliability) 혹은 고장 감내 도(fault tolerance)에 대한 척도는, 고장이 없는 노드들 사이에 통신을 두절시키지 않고 고장이 발생할 수 있는 최대 노드수로 주어진다. 상호연결망의 연결도 (connectivity)는 노드 고장에 대한 신뢰도에 대응한다. 그래프 의 연결도가 서로소인 경로라는 개념으로 특성 을 밝힐 수 있음은 널리 알려져 있다. Menger의 정리에 따르면 그래프 가 -연결될( -connected) 필요충분조건은 임의의 소스와 싱크의 쌍 , 에 대하여 그것을 잇는 일대일 유형의 서로소인 경 로가 개 존재한다는 것이다. 또한 소위 Fan Lemma가 말하는 그래프 가 -연결될 필요충분조건은 단일 소 스 와 서로 다른 개의 싱크 ... 를 잇는 일대다 유형의 서로소인 경로가 개 존재한다는 것이다[1]. 더 구나 그래프 가 -연결될 필요충분조건은 개의 서로 다른 소스 ...와 개의 서로 다른 싱크
Journal of KIISE:Computer Systems and Theory, 2000
In this paper, we consider hamiltonian properties of a double loop network with edge and/or verte... more In this paper, we consider hamiltonian properties of a double loop network with edge and/or vertex faults. A double loop network G(mn;1,m) is a 4-regular graph obtained by adding some edges to an m×n rectangular grid graph. We show that a double loop network G(mn;1,m) with even m and n has a hamiltonian path joining every pair of vertices if the number of faulty elements is 1 or less, and has a hamiltonian cycle if the number of faulty elements is 2 or less.
Journal of KIISE:Computer Systems and Theory, 2007
In this Paper, we investigate conditions for proper interval graphs to have k-disjoint path cover... more 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 , 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 , a Proper interval graph is (paired) many-to-many k-disjoint path coverable if and only if the graph is 2k-1-connected.
Journal of KIISE:Computer Systems and Theory, 2001
In this paper, we investigate strong hamiltonian properties of recursive circulant G(2m,2k) from ... more In this paper, we investigate strong hamiltonian properties of recursive circulant G(2m,2k) from the graph theory point of view. Recursive circulant is an interconnection structure for multicomputer networks proposed in [9]. We consider the problem whether G(2m,2k) has a path of length l joining a pair of vortices v and H, and show that (a) G(2m,2) has a path of length l forany l≥d(w,w), (b) G(2m,4) has a path of length l for any l≥d(v,w) + 2, (c) for some pair of vertices in G(2m,2k), k≥3, there is no path of length d(v, w) + 2k-3, where d(v, w) is the distance from v to w.
Journal of KIISE:Computer Systems and Theory, 2006
An unpaired many-to-many k-disjoint nth cover (k-DPC) of a graph G is a set of k disjoint paths j... more 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, , with f or less faulty elements (vertices and/or edges) has an unpaired many-to-many k-DPC for any .
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