The Turan number of a graph H,denoted by ex(n,H),is the maximum number of edges in any graph on n vertices containing no H as a subgraph.Let P_(ι)denote the path onιvertices,S_(ι-1)denote the star onιvertices and ...The Turan number of a graph H,denoted by ex(n,H),is the maximum number of edges in any graph on n vertices containing no H as a subgraph.Let P_(ι)denote the path onιvertices,S_(ι-1)denote the star onιvertices and k_(1)P_(ι)∪k_(2)S_(ι-1)denote the path-star forest with disjoint union of k_(1)copies of P_(ι)and k_(2)copies of S_(ι-1).In 2022,[Graphs Combin.,2022,38(3):Paper No.84,16 pp.] raised a conjecture about the Turan number of k_(1)P_(2ι)∪k_(2)S_(2ι-1).In this paper,we determine the Turan numbers of P_(ι)∪kS_(ι-1)and k_(1)P_(2ι)∪k_(2)S_(2ι-1)for n appropriately large,which implies the above conjecture.The corresponding extremal graphs are also completely characterized.展开更多
基于本地化差分隐私多关系表示上的Star-JOIN查询已得到研究者广泛关注.现有基于OLH机制与层次树结构的Star-JOIN查询算法存在根节点泄露隐私风险、τ-截断机制没有给出如何选择合适τ值等问题.针对现有算法存在的不足,提出一种有效且...基于本地化差分隐私多关系表示上的Star-JOIN查询已得到研究者广泛关注.现有基于OLH机制与层次树结构的Star-JOIN查询算法存在根节点泄露隐私风险、τ-截断机制没有给出如何选择合适τ值等问题.针对现有算法存在的不足,提出一种有效且满足本地化差分隐私的Star-JOIN查询算法LPRR-JOIN(longitudinal path random response for join).该算法充分利用层次树的纵向路径结构与GRR机制,设计一种纵向本地扰动算法LPRR,该算法以所有属性纵向路径上的节点组合作为扰动值域.每个用户把自身元组映射到相应节点组合中,再利用GRR机制对映射后的元组进行本地扰动.为了避免事实表上存在的频率攻击,LPRR-JOIN算法允许每个用户利用阈值τ本地截断自身元组个数,大于τ条元组删减、小于τ条元组补充.为了寻找合适的τ值,LPRR-JOIN算法利用τ-截断带来的偏差与扰动方差构造总体误差函数,通过优化误差目标函数获得τ值;其次结合用户分组策略获得τ值的总体分布,再利用中位数获得合适的τ值.LPRR-JOIN算法与现有算法在3种多关系数据集上进行比较,实验结果表明其响应查询算法优于同类算法.展开更多
文摘The Turan number of a graph H,denoted by ex(n,H),is the maximum number of edges in any graph on n vertices containing no H as a subgraph.Let P_(ι)denote the path onιvertices,S_(ι-1)denote the star onιvertices and k_(1)P_(ι)∪k_(2)S_(ι-1)denote the path-star forest with disjoint union of k_(1)copies of P_(ι)and k_(2)copies of S_(ι-1).In 2022,[Graphs Combin.,2022,38(3):Paper No.84,16 pp.] raised a conjecture about the Turan number of k_(1)P_(2ι)∪k_(2)S_(2ι-1).In this paper,we determine the Turan numbers of P_(ι)∪kS_(ι-1)and k_(1)P_(2ι)∪k_(2)S_(2ι-1)for n appropriately large,which implies the above conjecture.The corresponding extremal graphs are also completely characterized.
文摘基于本地化差分隐私多关系表示上的Star-JOIN查询已得到研究者广泛关注.现有基于OLH机制与层次树结构的Star-JOIN查询算法存在根节点泄露隐私风险、τ-截断机制没有给出如何选择合适τ值等问题.针对现有算法存在的不足,提出一种有效且满足本地化差分隐私的Star-JOIN查询算法LPRR-JOIN(longitudinal path random response for join).该算法充分利用层次树的纵向路径结构与GRR机制,设计一种纵向本地扰动算法LPRR,该算法以所有属性纵向路径上的节点组合作为扰动值域.每个用户把自身元组映射到相应节点组合中,再利用GRR机制对映射后的元组进行本地扰动.为了避免事实表上存在的频率攻击,LPRR-JOIN算法允许每个用户利用阈值τ本地截断自身元组个数,大于τ条元组删减、小于τ条元组补充.为了寻找合适的τ值,LPRR-JOIN算法利用τ-截断带来的偏差与扰动方差构造总体误差函数,通过优化误差目标函数获得τ值;其次结合用户分组策略获得τ值的总体分布,再利用中位数获得合适的τ值.LPRR-JOIN算法与现有算法在3种多关系数据集上进行比较,实验结果表明其响应查询算法优于同类算法.
