Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Computing the diameter in multiple-loop networks
Journal of Algorithms
Extremal Problems in the Construction of Distributed Loop Networks
SIAM Journal on Discrete Mathematics
Distributed loop computer networks: a survey
Journal of Parallel and Distributed Computing
Optimal distributed algorithms in unlabeled tori and chordal rings
Journal of Parallel and Distributed Computing
A Combinatorial Problem Related to Multimodule Memory Organizations
Journal of the ACM (JACM)
A complementary survey on double-loop networks
Theoretical Computer Science
Monomial Ideals and Planar Graphs
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Making change and finding repfigits: balancing a knapsack
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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It is known that there exists a Minimum Distance Diagram (MDD) for circulant digraphs of degree two (or double-loop computer networks) which is an L-shape. Its description provides the graph's diameter and average distance on constant time. In this paper we clarify, justify and extend these diagrams to circulant digraphs of arbitrary degree by presenting monomial ideals as a natural tool. We obtain some properties of the ideals we are concerned. In particular, we prove that the corresponding MDD is also an L-shape in the affine r-dimensional space. We implement in PostScript language a graphic representation of MDDs for circulant digrahs with two or three jumps. Given the irredundant irreducible decomposition of the associated monomial ideal, we provide formulae to compute the diameter and the average distance. Finally, we present a new and attractive family (parametrized with the diameter d2) of circulant digraphs of degree three associated to an irreducible monomial ideal.