Trades, introduced by Hedayat, are two sets of blocks of elements which may be exchanged (traded) without altering the counts of certain subcollections of elements within their constituent blocks. They are of importance in applications where certain combinations of elements dynamically become prohibited from being placed in the same group of elements, since in this case one can trade the offending blocks with allowed ones. This is particularly the case in distributed storage systems, where due to privacy and other constraints, data of some groups of users cannot be stored together on the same server. We introduce a new class of balanced trades, important for access balancing of servers, and perturbation resilient balanced trades, important for studying the stability of server access frequencies with respect to changes in data popularity. The constructions and bounds on our new trade schemes rely on specialized selections of defining sets in minimal trades and number-theoretic analyses.
翻译:赫达亚特提出的贸易是两组要素,可以交换(交换),而不会改变各组成部分中某些要素的某些子集的计数,这些在各种应用中非常重要,在这些应用中,某些要素的动态组合被禁止放置在同一组要素中,因为在此情况下,我们可以用允许的元块进行交易,特别是在分布式储存系统中,由于隐私和其他限制,一些用户群体的数据无法在同一服务器上储存在一起。我们引入了一种新的平衡交易类别,对于服务器的存取平衡和扰动弹性平衡交易十分重要,对于研究服务器访问频率的稳定与数据流行性的变化十分重要。我们新的贸易计划的构建和界限依赖于在最小交易和数字理论分析中专门选择定义组。