Feedback Node Sets in Pancake Graphs and Burnt Pancake Graphs

Abstract

A feedback node set (FNS) of a graph is a subset of the nodes of the graph whose deletion makes the residual graph acyclic. By finding an FNS in an interconnection network, we can set a check point at each node in it to avoid a livelock configuration. Hence, to find an FNS is a critical issue to enhance the dependability of a parallel computing system. In this paper, we propose a method to find FNS's in n-pancake graphs and n-burnt pancake graphs. By analyzing the types of cycles proposed in our method, we also give the number of the nodes in the FNS in an n-pancake graph, (n−2.875)(n−1)!+1.5(n−3)!, and that in an n-burnt pancake graph, 2 n−1 (n − 1)!(n − 3.5).