| 摘要: |
| 随机算法由于其简洁和高效的特点正在计算中占据越来越重要的位置.但有时随机算法的优良性能并不要求用完全独立的随机变量作为它的输入.仅用成对独立的随机变量作为输入，得到了一个关于估计并集的基的问题的随机算法.这一方法可以减少随机算法中使用的随机位.对于固定的精确度ε和确信度δ,此算法需要O(t1/2)的随机位，比标准的随机算法所使用的随机位数O(tlogtM)要少得多.而算法的执行时间并没有显著地增加O(t2logM). |
| 关键词: 随机算法 成对独立性 并集 随机位 k-独立性 |
| DOI： |
| 分类号: |
| 基金项目:This project is suppported by the National Natural Science Foundation of China under Grant No.69673038 (国家自然科学基金). |
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| A Randomized Algorithm for the Union of Sets Problem |
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ZHANG Li-yu,ZHU Hong,ZHANG Pi-xing
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| Abstract: |
| Randomized algorithms are playing a more and more important role in computation because of their simplicity and fastness. But sometimes the good performance of randomized algorithms does not require completely independent random variables as their input. In this paper, a new random algorithm is introduced for the classical problem of estimating the cardinality of a union of sets, which only needs pair-wise independent random input. This approach helps to reduce the random bits used in the algorithm. For fixed accuracy parameter ε and confidence parameter δ, the algorithm needs O(t1/2) random bits, much fewer than those of a standard randomized algorithm O(tlogtM). And the running time bounds of the algorithm do not increase essentially O(t2logM), where t is the number of sets and M is the maximal cardinality of an individual set). |
| Key words: randomized algorithm, pair-wise independence, union of sets, random bit, k-wise independence. |
