Deadlock-free multicast wormhole routing in multicomputer networks
ISCA '91 Proceedings of the 18th annual international symposium on Computer architecture
A Variation on the Hypercube with Lower Diameter
IEEE Transactions on Computers
Existence and Construction of Edge-Disjoint Pathson Expander Graphs
SIAM Journal on Computing
Topological properties of the crossed cube architecture
Parallel Computing
Connectivity of the crossed cube
Information Processing Letters
Resource Deadlocks and Performance of Wormhole Multicast Routing Algorithms
IEEE Transactions on Parallel and Distributed Systems
Fault-Free Hamiltonian Cycles in Faulty Arrangement Graphs
IEEE Transactions on Parallel and Distributed Systems
Diagnosability of the Möbius Cubes
IEEE Transactions on Parallel and Distributed Systems
Unicast in Hypercubes with Large Number of Faulty Nodes
IEEE Transactions on Parallel and Distributed Systems
Edge Congestion and Topological Properties of Crossed Cubes
IEEE Transactions on Parallel and Distributed Systems
Area-Efficient VLSI Layouts for Binary Hypercubes
IEEE Transactions on Computers
The congestion of n-cube layout on a rectangular grid
Discrete Mathematics - Special issue on Selected Topics in Discrete Mathematics conferences
Longest fault-free paths in star graphs with vertex faults
Theoretical Computer Science
Longest Fault-Free Paths in Star Graphs with Edge Faults
IEEE Transactions on Computers
Embedding of Rings and Meshes onto Faulty Hypercubes Using Free Dimensions
IEEE Transactions on Computers
Embedding Graphs onto the Supercube
IEEE Transactions on Computers
Embedding Binary Trees into Crossed Cubes
IEEE Transactions on Computers
Embedding Hamiltonian Paths in Faulty Arrangement Graphs with the Backtracking Method
IEEE Transactions on Parallel and Distributed Systems
The Crossed Cube Architecture for Parallel Computation
IEEE Transactions on Parallel and Distributed Systems
Fault-Tolerant Embedding of Complete Binary Trees in Hypercubes
IEEE Transactions on Parallel and Distributed Systems
Deadlock-Free Multicast Wormhole Routing in 2-D Mesh Multicomputers
IEEE Transactions on Parallel and Distributed Systems
Fault-Tolerant Ring Embedding in a Star Graph with Both Link and Node Failures
IEEE Transactions on Parallel and Distributed Systems
Diagnosability of Crossed Cubes under the Comparison Diagnosis Model
IEEE Transactions on Parallel and Distributed Systems
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Fault-tolerant cycle embedding in the hypercube
Parallel Computing
Fault Hamiltonicity and Fault Hamiltonian Connectivity of the Arrangement Graphs
IEEE Transactions on Computers
Fault-tolerant cycle-emebedding of crossed cubes
Information Processing Letters
The t/k-Diagnosability of the BC Graphs
IEEE Transactions on Computers
Node-pancyclicity and edge-pancyclicity of crossed cubes
Information Processing Letters
Edge disjoint Hamiltonian cycles in k-ary n-cubes and hypercubes
IEEE Transactions on Computers
Optimal fault-tolerant embedding of paths in twisted cubes
Journal of Parallel and Distributed Computing
Embedding meshes into crossed cubes
Information Sciences: an International Journal
Optimal Embeddings of Paths with Various Lengths in Twisted Cubes
IEEE Transactions on Parallel and Distributed Systems
Fault-free Hamiltonian cycles in crossed cubes with conditional link faults
Information Sciences: an International Journal
Edge-pancyclicity and path-embeddability of bijective connection graphs
Information Sciences: an International Journal
Embedding a family of disjoint 3D meshes into a crossed cube
Information Sciences: an International Journal
Embedding hamiltonian paths in hypercubes with a required vertex in a fixed position
Information Processing Letters
Embedding a family of disjoint multi-dimensional meshes into a crossed cube
Information Processing Letters
A note about some properties of BC graphs
Information Processing Letters
Fault-tolerant embedding of paths in crossed cubes
Theoretical Computer Science
Conditional fault diameter of crossed cubes
Journal of Parallel and Distributed Computing
Embedding a family of 2D meshes into Möbius cubes
WSEAS Transactions on Mathematics
Long paths in hypercubes with conditional node-faults
Information Sciences: an International Journal
Constructing the nearly shortest path in crossed cubes
Information Sciences: an International Journal
Embedding Hamiltonian paths in augmented cubes with a required vertex in a fixed position
Computers & Mathematics with Applications
Path embeddings in faulty 3-ary n-cubes
Information Sciences: an International Journal
Embedding meshes/tori in faulty crossed cubes
Information Processing Letters
Embedding meshes into locally twisted cubes
Information Sciences: an International Journal
Bipanconnectivity of balanced hypercubes
Computers & Mathematics with Applications
A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube
Information Sciences: an International Journal
Panconnectivity and edge-pancyclicity of k-ary n-cubes with faulty elements
Discrete Applied Mathematics
Efficient unicast in bijective connection networks with the restricted faulty node set
Information Sciences: an International Journal
Theoretical Computer Science
Edge-pancyclicity of twisted cubes
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Complete path embeddings in crossed cubes
Information Sciences: an International Journal
Panconnectivity of n-dimensional torus networks with faulty vertices and edges
Discrete Applied Mathematics
Dimension-adjacent trees and parallel construction of independent spanning trees on crossed cubes
Journal of Parallel and Distributed Computing
DVcube: A novel compound architecture of disc-ring graph and hypercube-like graph
Theoretical Computer Science
Fault-tolerant cycle embedding in the faulty hypercubes
Information Sciences: an International Journal
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The crossed cube is an important variant of the hypercube. The n{\hbox{-}}{\rm{dimensional}} crossed cube has only about half diameter, wide diameter, and fault diameter of those of the n{\hbox{-}}{\rm{dimensional}} hypercube. Embeddings of trees, cycles, shortest paths, and Hamiltonian paths in crossed cubes have been studied in literature. Little work has been done on the embedding of paths except shortest paths, and Hamiltonian paths in crossed cubes. In this paper, we study optimal embedding of paths of different lengths between any two nodes in crossed cubes. We prove that paths of all lengths between \lceil{\frac{n+1}{2}}\rceil +1 and 2^n-1 can be embedded between any two distinct nodes with a dilation of 1 in the n{\hbox{-}}{\rm{dimensional}} crossed cube. The embedding of paths is optimal in the sense that the dilation of the embedding is 1. We also prove that \lceil{\frac{n+1}{2}}\rceil+1 is the shortest possible length that can be embedded between arbitrary two distinct nodes with dilation 1 in the n{\hbox{-}}{\rm{dimensional}} crossed cube.