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172
Multicasting in the Hypercube, Chord and Binomial Graphs
, 2009
"... We discuss multicasting for the ncube network and its close variants, the Chord and the Binomial Graph (BNG) Network. We present simple transformations and proofs that establish that the spmulticast (shortest path) and Steiner tree problems for the ncube, Chord and the BNG network are NPComplete ..."
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We discuss multicasting for the ncube network and its close variants, the Chord and the Binomial Graph (BNG) Network. We present simple transformations and proofs that establish that the spmulticast (shortest path) and Steiner tree problems for the ncube, Chord and the BNG network are NP
BINOMIAL GRAPHS AND THEIR SPECTRA
, 1995
"... Pascal's triangle with entries reduced modulo 2 has been the object of a variety of investigations, including number theoretical questions on the parity of binomial coefficients [4] and geometrical explorations of the selfsimilarity of the Sierpinski triangle [7]. Graph theoiy has also entered ..."
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Pascal's triangle with entries reduced modulo 2 has been the object of a variety of investigations, including number theoretical questions on the parity of binomial coefficients [4] and geometrical explorations of the selfsimilarity of the Sierpinski triangle [7]. Graph theoiy has also
SelfHealing in Binomial Graph Networks
, 2007
"... The number of processors embedded in high performance computing platforms is growing daily to solve larger and more complex problems. However, as the number of components increases, so does the probability of failure. The logical network topologies must also support the faulttolerant capability in ..."
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Cited by 1 (1 self)
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in such dynamic environments. This paper presents a selfhealing mechanism to improve the faulttolerant capability of a Binomial graph (BMG) network. The selfhealing mechanism protects BMG from network bisection and helps maintain optimal routing even in failure circumstances. The experimental results show
Optimal Routing in Binomial Graph Networks
"... A circulant graph with n nodes and jumps j1,j2,...,jm is a graph in which each node i, 0 ≤ i ≤ n −1, is adjacent to all the vertices i ±jk mod n, where 1 ≤ k ≤ m. A binomial graph network (BMG) is a circulant graph where jk is the power of 2 that is less than or equal to n. This paper presents an op ..."
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Cited by 3 (2 self)
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A circulant graph with n nodes and jumps j1,j2,...,jm is a graph in which each node i, 0 ≤ i ≤ n −1, is adjacent to all the vertices i ±jk mod n, where 1 ≤ k ≤ m. A binomial graph network (BMG) is a circulant graph where jk is the power of 2 that is less than or equal to n. This paper presents
Binomial graph: A scalable and faulttolerant logical network topology
 In: ISPA07. Number 4742 in LNCS
, 2007
"... Abstract. The number of processors embedded in high performance computing platforms is growing daily to solve larger and more complex problems. The logical network topologies must also support the high degree of scalability in dynamic environments. This paper presents a scalable and fault tolerant t ..."
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Cited by 5 (3 self)
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topology called binomial graph (BMG). BMG provides desirable topological properties in terms of both scalability and faulttolerance for high performance computing such as reasonable degree, regular graph, low diameter, symmetric graph, low cost factor, low message traffic density, optimal connectivity
Fibonacci Heaps and Their Uses in Improved Network optimization algorithms
, 1987
"... In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated Fheaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. Fheaps support arbitrary deletion from an nitem heap in qlogn) amortized tim ..."
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Cited by 739 (18 self)
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In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated Fheaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. Fheaps support arbitrary deletion from an nitem heap in qlogn) amortized
Binomial edge ideals of graphs
, 2012
"... We characterize all graphs whose binomial edge ideals have a linear resolution. Indeed, we show that complete graphs are the only graphs with this property. We also compute some graded components of the first Betti number of the binomial edge ideal of a graph with respect to the graphical terms. Fin ..."
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Cited by 1 (0 self)
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We characterize all graphs whose binomial edge ideals have a linear resolution. Indeed, we show that complete graphs are the only graphs with this property. We also compute some graded components of the first Betti number of the binomial edge ideal of a graph with respect to the graphical terms
Binomial Ideals from Graphs
, 2000
"... This paper contains an examination of polynomial ideals associated to graphs and conjectures about them. We will describe how to obtain an ideal IG from a graph G. This ideal encodes the relations among all spanning trees of G. There are five conjectures we are concerned with. The first claims that ..."
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that IG is generated by quadratic binomials. We will discuss the relationships uncovered between different classes of graphs and their ideals. For instance, for any tree or onecircuit graph, IG = 0. Also, we can contract edges that are not part of any circuit. The number of circuits in a graph has a
INJECTIVE COLOURING OF BINOMIAL RANDOM GRAPHS
"... Abstract. The injective chromatic number of a graph G is the minimum number of colours needed to colour the vertices of G so that two vertices with a common neighbour receive distinct colours. In this paper, we investigate the injective chromatic number of the binomial random graph G(n, p) for a wid ..."
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Abstract. The injective chromatic number of a graph G is the minimum number of colours needed to colour the vertices of G so that two vertices with a common neighbour receive distinct colours. In this paper, we investigate the injective chromatic number of the binomial random graph G(n, p) for a
Results 1  10
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172