Fault-tolerant routing in burnt pancake graphs

Node-to-Set Disjoint Paths Problem in Burnt Pancake Graphs

A burnt pancake graph is a variant of Cayley graphs and its topology is suitable for massively parallel systems. However, for a burnt pancake graph, there is much room for further research. Hence, in this study, we focus on n-burnt pancake graphs and propose an algorithm to obtain n disjoint paths from a source node to n destination nodes in polynomial order time of n, n being the degree of the...

Hamiltonian Paths and Cycles in Faulty Burnt Pancake Graphs

Recently, research on parallel processing systems is very active, and many complex topologies have been proposed. A burnt pancake graph is one such topology. In this paper, we prove that a faulty burnt pancake graph with degree n has a fault-free Hamiltonian cycle if the number of faulty elements is no more than n − 2, and it has a fault-free Hamiltonian path between any pair of non-faulty node...

Cluster Fault-tolerant Routing in Pancake Graphs

In this paper, we propose an O(n) algorithm that finds a fault-free path between any pair of non-faulty nodes in an n-pancake graph with n−2 faulty clusters whose diameters are at most 2. The lengths of the paths obtained by our algorithm are at most d◦(Pn)+7 where d◦(Pn) = b5(n+1)/3c represents the upper bound of the diameter of Pn given by Gates and Papadimitriou. According to the computer ex...

Strong matching preclusion of burnt pancake graphs

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The burnt pancake graph is a more complex variant of the pancake graph. In this talk, we examine the properties ...

Fault Tolerant Routing in the Star and Pancake Interconnection Networks