Details of Research Outputs

The PARAMETERIZED SET PACKING problem asks, for an input consisting of a collection 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 (Equation Presented) where, bm is the minimal positive root of m-degree equation (Equation Presented) and=2.7182818. In particular, this gives an O (k4(5.7k)k+[k(5.7k)k+3]n) algorithm to i=0 construct mutually fc disjoint sets if |c|≤3 for any c∈C.