Publication 1999 Issue No. 10 - October Abstract - Unicast in Hypercubes with Large Number of Faulty Nodes
Unicast in Hypercubes with Large Number of Faulty Nodes
October 1999 (vol. 10 no. 10)
pp. 964-975
 ASCII Text x Qian-Ping Gu, Shietung Peng, "Unicast in Hypercubes with Large Number of Faulty Nodes," IEEE Transactions on Parallel and Distributed Systems, vol. 10, no. 10, pp. 964-975, October, 1999.
 BibTex x @article{ 10.1109/71.808128,author = {Qian-Ping Gu and Shietung Peng},title = {Unicast in Hypercubes with Large Number of Faulty Nodes},journal ={IEEE Transactions on Parallel and Distributed Systems},volume = {10},number = {10},issn = {1045-9219},year = {1999},pages = {964-975},doi = {http://doi.ieeecomputersociety.org/10.1109/71.808128},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Parallel and Distributed SystemsTI - Unicast in Hypercubes with Large Number of Faulty NodesIS - 10SN - 1045-9219SP964EP975EPD - 964-975A1 - Qian-Ping Gu, A1 - Shietung Peng, PY - 1999KW - Fault toleranceKW - interconnection networkKW - off-line routing algorithmKW - unicastKW - hypercubes.VL - 10JA - IEEE Transactions on Parallel and Distributed SystemsER -

Abstract—Unicast in computer/communication networks is a one-to-one communication between a source node $s$ and a destination node $t$. We propose three algorithms which find a nonfaulty routing path between $s$ and $t$ for unicast in the hypercube with a large number of faulty nodes. Given the $n$-dimensional hypercube $H_n$ and a set $F$ of faulty nodes, node $u\in H_n$ is called $k$-safe if $u$ has at least $k$ nonfaulty neighbors. The $H_n$ is called $k$-safe if every node of $H_n$ is $k$-safe. It has been known that for $0\leq k\leq n/2$, a $k$-safe $H_n$ is connected if $|F|\leq 2^k(n-k)-1$. Our first algorithm finds a nonfaulty path of length at most $d(s,t)+4$ in $O(n)$ time for unicast between 1-safe $s$ and $t$ in the $H_n$ with $|F|\leq 2n-3$, where $d(s,t)$ is the distance between $s$ and $t$. The second algorithm finds a nonfaulty path of length at most $d(s,t)+6$ in $O(n)$ time for unicast in the $2$-safe $H_n$ with $|F|\leq 4n-9$. The third algorithm finds a nonfaulty path of length at most $d(s,t)+O(k^2)$ in time $O(|F|+n)$ for unicast in the $k$-safe $H_n$ with $|F|\leq 2^k(n-k)-1$ ($0\leq k\leq n/2$). The time complexities of the algorithms are optimal. We show that in the worst case, the length of the nonfaulty path between $s$ and $t$ in a $k$-safe $H_n$ with $|F|\leq 2^k(n-k)-1$ is at least $d(s,t)+ 2(k+1)$ for $0\leq k\leq n/2$. This implies that the path lengths found by the algorithms for unicast in the 1-safe and 2-safe hypercubes are optimal.

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Index Terms:
Fault tolerance, interconnection network, off-line routing algorithm, unicast, hypercubes.
Citation:
Qian-Ping Gu, Shietung Peng, "Unicast in Hypercubes with Large Number of Faulty Nodes," IEEE Transactions on Parallel and Distributed Systems, vol. 10, no. 10, pp. 964-975, Oct. 1999, doi:10.1109/71.808128