In this paper, we give evidence for the problems Disjoint Cycles and Disjoint Paths that they cannot be preprocessed in polynomial time such that resulting instances always have a size bounded by a polynomial in a specified parameter (or, in short: do not have a polynomial kernel); these results are assuming the validity of certain complexity theoretic assumptions. We build upon recent results ...

A new set of wavelet filter families has been added to the systematized collection of Daubechies wavelets. This new set includes complex and real, orthogonal and biorthogonal, least and most disjoint families defined using constraints derived from the principle of separably disjoint root sets in the complex z-domain. All of the new families are considered to be constraint selected without a sea...

In previous work, we have successfully used an ideal joint sparseness assumption: W-Disjoint Orthogonality (WDO). This assumption, that the time-frequency representations of the sources have disjoint support, is satisfied in an approximate sense by many signals of practical interest, including speech. Here we discuss results derived from a stochastic model of speech signals that justify the WDO...

Disjoint-Set forests, consisting of Union-Find trees are data structures having a widespread practical application due to their efficiency. Despite them being well-known, no exact structural characterization of these trees is known (such a characterization exists for Union trees which are constructed without using path compression). In this paper we provide such a characterization and show that...

The well-known Disjoint Paths problem is to decide if a graph contains k pairwise disjoint paths, each connecting different terminal pair from set of distinct vertex pairs. We determine, with an exception two cases, the complexity for H -free graphs. If fixed, we obtain -Disjoint problem, which known be polynomial-time solvable on class all graphs every ? 1 . latter does no longer hold need con...