The goal is to find a minimum weight spanning tree that uses at most K distinct labels.
We present constant factor approximation algorithms for the following two problems: First, given a connected graph G="(V,E) with non-negative edge weights, find a minimum weight spanning tree that respects prescribed upper bounds on the vertex degrees.
This result improves on a previous result of Fischer [T. Fischer, Optimizing the degree of minimum weight spanning trees. Technical Report 14853, Dept. of Computer Science, Cornell University, Ithaca, NY, 1993] that finds an MST of degree at most optbΔ(G +logbn, for any b>1.
To tackle this issue, we compute the so-called maximum weight spanning tree (MWST).
We then build the minimum weight spanning tree between connected components.
This variety characterized by morphological traits like fruit size and seed weight spans a genetic continuum between 'wild' and 'domesticated' forms of the crop.
Finally, we replace all of the edges of the minimum weight spanning tree by linear chains of k mutational steps by inserting unobserved haplotypes.
This problem can be efficiently solved by calculating a maximum weight spanning tree from a fully connected indirected graph, where vertices are the developmental stages (1,…, L) and the weight of an edge (u, v) is equal to the mutual information between the corresponding variables (X u, X v ) (Chow and Liu, 1968).
21 Possibly, the most powerful arguments against rapid postnatal weight gain come from animal studies of low birth weight spanning five decades, which demonstrate that postnatal dietary interventions to slow growth increase longevity and protect against the risks posed by a high carbohydrate, high fat diet in later life.
First, connectivity weights span nearly 6 orders of magnitude.
