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Furthermore, we show how similar modelling techniques enable an enhanced polynomial size formulation to be derived for the shortest elementary path.
A principally elementary path in N is an elementary path in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_0 N $$\end{document }T 0 (N ).
For instance, in the elementary path EP4, GenopageCDS is mapped with the abstract entity CDS and GenopageProtein with Protein.
An elementary path is constructed from v 1 to v |p|since Suff (vi, k − 1) = Pref (v i+1, k − 1), for 1 ≤ i < |p|.
Alternative paths can be computed for each elementary path in two phases (Fig. 4): (1) abstraction of the elementary paths and (2) computation of all the corresponding alternative paths.
The DAG N H (i, j ) is obtained by removing from N the arc (u, v) and collapsing the resulting elementary path with intermediate node v into a single arc (Fig. 7).
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Three design methods for generating smooth reference trajectories are discussed: circle-segments, generalised elementary paths, and bi-elementary paths.
First, only elementary paths (not involving cycles) are considered as possible explanations for edges.
Albeit a negative effect in B might be observed transiently, we generally consider non-elementary paths containing a negative cycle as not sufficient for explaining an edge; only elementary paths with appropriate sign and weight are accepted.
To delineate elementary paths, we distinguish in the initial query some entities that play a special role.
Such elementary queries are represented by elementary paths in the mixed query graph, where each vertex has at the most two adjacent vertices.
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