Istituto di Scienza e Tecnologie
dell’Informazione “A. Faedo”

The shortest path tour problem (SPTP) consists of finding a shortest path from a given origin node s to a given destination node d in a directed graph with nonnegative arc lengths with the constraint that the optimal path P should successively and sequentially pass through at least one node from given disjoint node subsets. In this talk, it will proved that the SPTP belongs to the complexity class P and several alternative techniques will be presented to solve it. Furthermore, some variants of the SPTP will be discussed and proved to be special facility location problems.

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I will presents new observational tests of the LCDM paradigm. In particular I will focus on the following questions: are there universal dark matter profiles? is there dark matter substructure? What is the equation of state of dark energy? I will discuss the crucial need to uderstand the interplay between baryons and dark matter as part of the paradigm.