Fault-tolerant path embedding in folded hypercubes with both node and edge faults

Authors:
Che-Nan Kuo;Hsin-Hung Chou;Nai-Wen Chang;Sun-Yuan Hsieh
Affiliations:
Department of Digital Content Design and Management, Toko University, No. 51, Sec. 2, Syuefu Rd., Puzih City, Chiayi County 61363, Taiwan;Department of Information Management, Chang Jung Christian University, No. 396, Sec. 1, Changrong Rd., Gueiren Dist., Tainan City 71101, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan City 701, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan City 701, Taiwan
Venue:
Theoretical Computer Science
Year:
2013

Citing 10
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Abstract

The folded hypercube FQ"n is a well-known variation of the hypercube structure. FQ"n is superior to Q"n in many measurements, such as diameter, fault diameter, connectivity, and so on. Let V@?(FQ"n) (resp. E@?(FQ"n)) denote the set of faulty nodes (resp. faulty edges) in FQ"n. In the case that all nodes in FQ"n are fault-free, it has been shown that FQ"n contains a fault-free path of length 2^n-1 (resp. 2^n-2) between any two nodes of odd (resp. even) distance if |E@?(FQ"n)|@?n-1, where n=1 is odd; and FQ"n contains a fault-free path of length 2^n-1 between any two nodes if |E@?(FQ"n)|@?n-2, where n=2 is even. In this paper, we extend the above result to obtain two further properties, which consider both node and edge faults, as follows: 1.FQ"n contains a fault-free path of length at least 2^n-2|V@?(FQ"n)|-1 (resp. 2^n-2|V@?(FQ"n)|-2) between any two fault-free nodes of odd (resp. even) distance if |V@?(FQ"n)|+|E@?(FQ"n)|@?n-1, where n=1 is odd. 2.FQ"n contains a fault-free path of length at least 2^n-2|V@?(FQ"n)|-1 between any two fault-free nodes if |V@?(FQ"n)|+|E@?(FQ"n)|@?n-2, where n=2 is even.