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Bisection Widths of Transposition Graphs
 Discrete Applied Mathematics
, 1998
"... Introduction Several interconnection networks of parallel computers based on permutations have appeared recently, e.g. bubblesort and star graph, alternating group graphs ..., see a survey paper of Lakshmivarahan et al. [8]. Leighton [10] introduced the n\Gammadimensional complete transposition grap ..."
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graph interconnection network. Especially, he asked what the bisection width of the complete transposition graph is (problem (R) 3.356). The bisection width is the size of the smallest edge cut of a graph which divides it into two equal parts. This graph invariant is a fundamental concept in the theory of
A proof for bisection width of grids
 International Journal of Mathematical and Computer Sciences
"... Abstract—The optimal bisection width of rdimensional N× · · · × N grid is known to be Nr−1 when N is even, but when N is odd, only approximate values are available. This paper shows that the exact bisection width of grid is N ..."
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Abstract—The optimal bisection width of rdimensional N× · · · × N grid is known to be Nr−1 when N is even, but when N is odd, only approximate values are available. This paper shows that the exact bisection width of grid is N
Bisection Widths of Transposition Graphs and Their Applications
, 1998
"... We prove lower and upper bounds on bisection widths of the transposition graphs. This class of graphs contains several frequently studied interconnection networks including star graphs and hypercubes. In particular, we prove that the bisection width of the complete transposition graph is of order \T ..."
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We prove lower and upper bounds on bisection widths of the transposition graphs. This class of graphs contains several frequently studied interconnection networks including star graphs and hypercubes. In particular, we prove that the bisection width of the complete transposition graph is of order
The Bisection Width and the Isoperimetric Number of Arrays
 DISCRETE APPL. MATH
, 2000
"... We prove that the bisection width, bw(A d ), of a ddimensional array A d = P k1 P k2 P k d where k 1 k 2 k d , is given by bw(A d ) = P d i=e K i where e is the largest index for which k e is even (if it exists, e = 1 otherwise) and K i = k i 1 k i 2 k 1 . We also show th ..."
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We prove that the bisection width, bw(A d ), of a ddimensional array A d = P k1 P k2 P k d where k 1 k 2 k d , is given by bw(A d ) = P d i=e K i where e is the largest index for which k e is even (if it exists, e = 1 otherwise) and K i = k i 1 k i 2 k 1 . We also show
Computation of the Bisection Width for Random dRegular Graphs
"... In this paper we provide an explicit way to compute asymptotically almost sure upper bounds on the bisection width of random d regular graphs, for any value of d. We provide the bounds for 5 d 12. ..."
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In this paper we provide an explicit way to compute asymptotically almost sure upper bounds on the bisection width of random d regular graphs, for any value of d. We provide the bounds for 5 d 12.
The Isoperimetric Number and The Bisection Width of Generalized Cylinders
, 2002
"... A d{dimensional generalized cylinder is the Cartesian product of d graphs each of which is either a path graph or a cycle graph. In this paper, we use a simple embedding technique to nd exact formulae for the edge{isoperimetric number and the bisection width of a cylinder in certain cases, e.g. when ..."
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A d{dimensional generalized cylinder is the Cartesian product of d graphs each of which is either a path graph or a cycle graph. In this paper, we use a simple embedding technique to nd exact formulae for the edge{isoperimetric number and the bisection width of a cylinder in certain cases, e
New Spectral Lower Bounds on the Bisection Width of Graphs
, 2000
"... The communication overhead is a major bottleneck for the execution of a process graph on a parallel computer system. In the case of two processors, the minimization of the communication can be modeled by the graph bisection problem. The spectral lower bound of 2 jV j 4 for the bisection width of a g ..."
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Cited by 8 (2 self)
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The communication overhead is a major bottleneck for the execution of a process graph on a parallel computer system. In the case of two processors, the minimization of the communication can be modeled by the graph bisection problem. The spectral lower bound of 2 jV j 4 for the bisection width of a
Upper Bounds on the Bisection Width of 3 and 4regular Graphs
 in Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science (MFCS 2001
, 2001
"... We derive new upper bounds on the bisection width of graphs which have a regular vertex degree. We show that the bisection width of large 3regular graphs with V vertices is at most 1/6 V. For the bisection width of large 4regular graphs we show an upper bound of 2/5 V. ..."
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We derive new upper bounds on the bisection width of graphs which have a regular vertex degree. We show that the bisection width of large 3regular graphs with V vertices is at most 1/6 V. For the bisection width of large 4regular graphs we show an upper bound of 2/5 V.
Brief Contributions________________________________________________________________________________ An Upper Bound for the Bisection Width of a Diagonal Mesh
"... Abstract—Recently, it was correctly pointed out by Jha that there is an error in our earlier paper on diagonal mesh networks. In response to Jha’s critique, we now provide an upper bound on the bisection width of a diagonal mesh. The proof is a constructive one and an algorithm is provided to divide ..."
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Abstract—Recently, it was correctly pointed out by Jha that there is an error in our earlier paper on diagonal mesh networks. In response to Jha’s critique, we now provide an upper bound on the bisection width of a diagonal mesh. The proof is a constructive one and an algorithm is provided
Results 1  10
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