In this paper, the dimensional results of Moran-Sierpinski gasket are considered. Moran-Sierpinski gasket has the Moran structure, which is an extension of the Sierpinski gasket by the method of Moran set. By the tech...In this paper, the dimensional results of Moran-Sierpinski gasket are considered. Moran-Sierpinski gasket has the Moran structure, which is an extension of the Sierpinski gasket by the method of Moran set. By the technique of Moran set, the Hausdorff, packing, and upper box dimensions of the Moran-Sierpinski gasket are given. The dimensional results of the Sierpinski gasket can be seen as a special case of this paper.展开更多
The PARAMETERIZED SET PACKING problem asks, for an input consisting of a col- lection C of n finite sets with |c|≤m for any c∈C and a positive integer k, whether C contains at least k mutually disjoint sets. We give...The PARAMETERIZED SET PACKING problem asks, for an input consisting of a col- lection C of n finite sets with |c|≤m for any c∈C and a positive integer k, whether C contains at least k mutually disjoint sets. We give a fixed-parameter-tractable algorithm for this problem that runs in times O (f(k,m)+g(k,m)n), where where, bm is the minimal positive root of m-degree equation and e= =2.7182818. In particular, this gives an O (k4(5.7k)k+[k(5.7k)k+3]n) algorithm to construct mutually k disjoint sets if |c|≤3 for any c∈C.展开更多
基金Supported by the National Natural Science Foundation of China(10771082 and 10871180)
文摘In this paper, the dimensional results of Moran-Sierpinski gasket are considered. Moran-Sierpinski gasket has the Moran structure, which is an extension of the Sierpinski gasket by the method of Moran set. By the technique of Moran set, the Hausdorff, packing, and upper box dimensions of the Moran-Sierpinski gasket are given. The dimensional results of the Sierpinski gasket can be seen as a special case of this paper.
基金the Main Subject Foundation of the State Council's Office of OverseasChinese Affairs under Grant 93A109. Part of the work was
文摘The PARAMETERIZED SET PACKING problem asks, for an input consisting of a col- lection C of n finite sets with |c|≤m for any c∈C and a positive integer k, whether C contains at least k mutually disjoint sets. We give a fixed-parameter-tractable algorithm for this problem that runs in times O (f(k,m)+g(k,m)n), where where, bm is the minimal positive root of m-degree equation and e= =2.7182818. In particular, this gives an O (k4(5.7k)k+[k(5.7k)k+3]n) algorithm to construct mutually k disjoint sets if |c|≤3 for any c∈C.
