Polynomial algorithms for partitioning a tree into single-center subtrees to minimize flat service costs

This paper deals with the following graph partitioning problem. Consider a connected graph with n nodes, p of which are centers, while the remaining ones are units. For each unit-center pair there is a fixed service cost and the goal is to find a partition into connected components such that each component contains only one center and the total service cost is minimum. This problem is known to be NP-hard on general graphs, and here we show that it remains such even if the service cost is monotone and the graph is bipartite. However, in this paper we derive some polynomial time algorithms for trees. For this class of graphs we provide several reformulations of the problem as integer linear programs proving the integrality of the corresponding polyhedra. As a consequence, the tree partitioning problem can be solved in polynomial time either by linear programming or by suitable convex nondifferentiable optimization algorithms. Moreover, we develop a dynamic programming algorithm, whose recursion is based on sequences of minimum weight closure problems, which solves the problem on trees in O(np) time

Adiabatic renormalization in theories with modified dispersion relations

We generalize the adiabatic renormalization to theories with dispersion relations modified at energies higher than a new scale $M_C$. We obtain explicit expressions for the mean value of the stress tensor in the adiabatic vacuum, up to the second adiabatic order. We show that for any dispersion relation the divergences can be absorbed into the bare gravitational constants of the theory. We also point out that, depending on the renormalization prescription, the renormalized stress tensor may contain finite trans-Planckian corrections even in the limit $M_C\to\infty$.Comment: Typos corrected; to appear in the Proceedings of IRGAC 06, Journal of Physics

Multiple genome relationships and a complex biogeographic history in the eastern range of Quercus suber L. (Fagaceae) implied by nuclear and chloroplast DNA variation

The complex evolutionary history of Quercus suber has been throughly investigated in many recent works, but the details of its differentiation processes are still largely unknown. In addition, the geographical and evolutionary roles of the eastern parts of the species range have gained much less attention compared to other southern European areas. In order to fill this gap, new insights to infer the species diversification and range establishment of the cork oak in the east-central Mediterranean are here provided by means of inter- and intra-specific plastid DNA and nuclear ribosomal ITS phylogeographic studies. We analyzed 95 natural cork oak populations; 6 closely related, sympatric oaks were included in the study and used for comparisons.Evidence for a clear phylogeographical structure was detected with PCR-RFLP at 5 chloroplast loci, while ITS sequence variation is apparently unrelated with the geographical distribution. Five chloroplast haplotypes and three ITS main lineages were identified. Three haplotypes and all ITS lineages occur in the Italian Peninsula, stressing the importance of these territories for the evolutionary history of the species. Two divergent "Italian" haplotypes are highly shared, and one ITS variant is basal to the ingroup, revealing sister relationships within Cerris taxonomic group. Hypotheses of hybridization, lineage sorting of ancient DNA polymorphisms and of reticulate evolution of the whole species group are presented and discussed

Caracterização química do óleo essencial dos frutos de Piper amalago e Piper hispidum.

Poster