## An -size fault-tolerant sorting network (1996)

Venue: | In Proceedings of the 28th Annual ACM Symposium on the Theory of Computing |

Citations: | 1 - 0 self |

### BibTeX

@INPROCEEDINGS{Ma96an-size,

author = {Yuan Ma},

title = {An -size fault-tolerant sorting network},

booktitle = {In Proceedings of the 28th Annual ACM Symposium on the Theory of Computing},

year = {1996},

pages = {266--275}

}

### OpenURL

### Abstract

Abstract This thesis studies sorting circuits, networks, and PRAM algorithms that are tolerant to faults. We consider both worst-case and random fault models, although we mainly focus on the more challenging problem of random faults. In the random fault model, the circuit, network, or algorithm is required to sort all n-input permutations with probability at least 1 \Gamma 1n even if the result of each comparison is independently faulty with probability upper bounded by a fixed constant. In particular, ffl we construct a passive-fault-tolerant sorting circuit with O(n log n log log n) comparators, thereby answering an open question posed by Yao and Yao in 1985, ffl we construct a reversal-fault-tolerant sorting network with O(n loglog2 3 n) comparators, thereby answering an open question posed by Assaf and Upfal in 1990, ffl we design an optimal O(log n)-step O(n)-processor deterministic EREW PRAM fault-tolerant sorting algorithm, thereby answering an open question posed by Feige, Peleg, Raghavan, and Upfal in 1990, and ffl we prove a tight lower bound of \Omega (n log2 n) on the number of comparators needed for any destructive-fault-tolerant sorting or merging network, thereby answering an open question posed by Assaf and Upfal in 1990.