Hamiltonian Cycle Embeddings in Faulty Hypercubes Under the Forbidden Faulty Set Model

2021 ◽  
pp. 1-20
Author(s):  
Chunfang Li ◽  
Shangwei Lin ◽  
Shengjia Li
Keyword(s):  
Hamiltonian Cycle ◽  
Fault Tolerant ◽  
Hamiltonian Property ◽  
Free Edges

In this paper, we study the fault-tolerant capability of hypercubes with respect to the hamiltonian property based on the concept of forbidden faulty sets. We show, with the assumption that each vertex is incident with at least three fault-free edges, that an [Formula: see text]-dimensional hypercube contains a fault-free hamiltonian cycle, even if there are up to [Formula: see text] edge faults. Moreover, we give an example to show that the result is optimal with respect to the number of edge faults tolerated.

scholarly journals Hierarchical Hexagon: A New Fault-Tolerant Interconnection Network for Parallel Systems

2021 ◽  
Vol 21 (1) ◽  
pp. 32-49
Author(s):  
Laxminath Tripathy ◽  
Chita Ranjan Tripathy
Keyword(s):  
Fault Tolerance ◽  
Hamiltonian Cycle ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Parallel Systems ◽  
Node Degree ◽  
Topological Parameters ◽  
Massively Parallel Systems ◽  
Network Cost ◽  
Hypercube Networks

Abstract A new interconnection network topology called Hierarchical Hexagon HH(n) is proposed for massively parallel systems. The new network uses a hexagon as the primary building block and grows hierarchically. Our proposed network is shown to be superior to the star based and the hypercube networks, with respect to node degree, diameter, network cost, and fault tolerance. We thoroughly analyze different topological parameters of the proposed topology including fault tolerance routing and embedding Hamiltonian cycle.

scholarly journals Extending Perfect Matchings to Hamiltonian Cycles in Line Graphs

10.37236/9143 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Marién Abreu ◽  
John Baptist Gauci ◽  
Domenico Labbate ◽  
Giuseppe Mazzuoccolo ◽  
Jean Paul Zerafa
Keyword(s):  
Hamiltonian Cycle ◽  
Perfect Matching ◽  
Complete Bipartite Graph ◽  
Line Graph ◽  
Sufficient Conditions ◽  
Perfect Matchings ◽  
Hamiltonian Cycles ◽  
Hamiltonian Graph ◽  
Open Problems ◽  
Hamiltonian Property

A graph admitting a perfect matching has the Perfect–Matching–Hamiltonian property (for short the PMH–property) if each of its perfect matchings can be extended to a hamiltonian cycle. In this paper we establish some sufficient conditions for a graph $G$ in order to guarantee that its line graph $L(G)$ has the PMH–property. In particular, we prove that this happens when $G$ is (i) a Hamiltonian graph with maximum degree at most 3, (ii) a complete graph, (iii) a balanced complete bipartite graph with at least 100 vertices, or (iv) an arbitrarily traceable graph. Further related questions and open problems are proposed along the paper.

Fault-Free Hamiltonian Cycles in Balanced Hypercubes with Conditional Edge Faults

2019 ◽  
Vol 30 (05) ◽  
pp. 693-717 ◽  
Author(s):  
Pingshan Li ◽  
Min Xu
Keyword(s):  
Hamiltonian Cycle ◽  
Free Edge ◽  
Hamiltonian Cycles ◽  
Interesting Problem ◽  
Balanced Hypercube ◽  
Free Edges

The balanced hypercube, [Formula: see text], is a variant of hypercube [Formula: see text]. Zhou et al. [Inform. Sci. 300 (2015) 20–27] proposed an interesting problem that whether there is a fault-free Hamiltonian cycle in [Formula: see text] with each vertex incident to at least two fault-free edges. In this paper, we consider this problem and show that each fault-free edge lies on a fault-free Hamiltonian cycle in [Formula: see text] after no more than [Formula: see text] faulty edges occur if each vertex is incident with at least two fault-free edges for all [Formula: see text]. Our result is optimal with respect to the maximum number of tolerated edge faults.

Multicast protection scheme based on Hamiltonian cycle in fault-tolerant optical mesh networks

2010 ◽  
Vol 16 (5) ◽  
pp. 292-298 ◽  
Author(s):  
Xingwei Wang ◽  
Lei Guo ◽  
Jiannong Cao ◽  
Jingjing Wu ◽  
Weigang Hou
Keyword(s):  
Hamiltonian Cycle ◽  
Mesh Networks ◽  
Fault Tolerant ◽  
Protection Scheme ◽  
Optical Mesh Networks

Local and global hamiltonian cycle protection algorithm based on abstracted virtual topology in fault-tolerant multi-domain optical networks

2010 ◽  
Vol 58 (3) ◽  
pp. 851-859 ◽  
Author(s):  
Lei Guo ◽  
Xingwei Wang ◽  
Jiannong Cao ◽  
Weigang Hou ◽  
Jingjing Wu ◽  
...  
Keyword(s):  
Optical Networks ◽  
Hamiltonian Cycle ◽  
Fault Tolerant ◽  
Virtual Topology

FAULT-TOLERANT RING EMBEDDING IN A HONEYCOMB TORUS WITH NODE FAILURES

1999 ◽  
Vol 09 (04) ◽  
pp. 551-561 ◽  
Author(s):  
G. M. MEGSON ◽  
XIAOPING LIU ◽  
XIAOFAN YANG
Keyword(s):  
Interconnection Networks ◽  
Hamiltonian Cycle ◽  
Fault Tolerant ◽  
Distributed Applications ◽  
Attractive Alternative ◽  
Single Fault ◽  
Torus Networks ◽  
Node Failures

Honeycomb torus networks have been recognised as an attractive alternative to existing torus interconnection networks in parallel and distributed applications. In this paper we establish that there exists a hamiltonian cycle in a honeycomb torus with two adjacent faulty nodes and that with a single fault a ring embedding with one less node than the fault free torus can be found.

The 3-Good Neighbor Edge-Fault-Tolerant Strong Menger Edge Connectivity on the Class of BC Networks

2021 ◽  
Author(s):  
Rong Liu ◽  
Pingshan Li
Keyword(s):  
Fault Tolerant ◽  
Minimum Degree ◽  
Disjoint Paths ◽  
Edge Connectivity ◽  
Restricted Condition ◽  
Good Neighbor ◽  
Twisted Cubes ◽  
Free Edges

A graph [Formula: see text] is called strongly Menger edge connected (SM-[Formula: see text] for short) if the number of disjoint paths between any two of its vertices equals the minimum degree of these two vertices. In this paper, we focus on the maximally edge-fault-tolerant of the class of BC-networks (contain hypercubes, twisted cubes, Möbius cubes, crossed cubes, etc.) concerning the SM-[Formula: see text] property. Under the restricted condition that each vertex is incident with at least three fault-free edges, we show that even if there are [Formula: see text] faulty edges, all BC-networks still have SM-[Formula: see text] property and the bound [Formula: see text] is sharp.

A Fault-Tolerant Router Algorithm Based on Hamiltonian Cycle in Wireless Sensor Network

2010 ◽  
Vol 44-47 ◽  
pp. 1641-1645
Author(s):  
Wei Peng Jing ◽  
Ya Qiu Liu ◽  
Qu Wu
Keyword(s):  
Wireless Sensor Network ◽  
Fault Tolerance ◽  
Sensor Network ◽  
Recovery Time ◽  
Hamiltonian Cycle ◽  
Fault Tolerant ◽  
Wireless Sensor ◽  
Single Node ◽  
Single Link ◽  
Utilization Ratio

In wireless sensor network, energy conservation is the primary goal, while throughput and fault tolerance are other important factor. In this paper, we propose a novel fault-tolerant link-based Hamiltonian Cycle (FLHC) scheme for tolerating the single-link or single-node failure. Theoretical analysis and simulations show that FLHC has better resources utilization ratio and faster recovery time. Thus the topology which uses the method to build has good fault tolerance and robustness.

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