Fast Algorithms for Parameterized Problems with Relaxed Disjointness Constraints
نویسندگان
چکیده
The notion of a q-representative set for a family of subsets has recently proven to be very useful in the design of parameterized and exact algorithms. We generalize this notion to families of multisets. We also give an efficient way to find a representative set for a family of multisets. As an application we give a deterministic algorithm for minimal weight r-SIMPLE k-PATH running in time O(r) for 1 < r ≤ k. This extends a result of Abasi et. al [1] that gave a randomized algorithm of similar running time for the non-weighted case. We derive other algorithms for problems that can be viewed as augmenting a parameterized problem with a ‘relaxation’ parameter. A corollary of our construction is an improved explicit construction of lopsided universal sets (cf. [8]) for a certain range of parameters.
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