Redundancy elimination in the estimation of multiple paths (Q2722583)

This paper considers approximating certain objects by source-to-sink graphs in a directed acyclic graph.NEWLINENEWLINENEWLINEThree distance measures are assumed to exist, a metric on the paths, an estimated distance from vertices to their closest objects, and a distance from vertices to specified objects. The latter two distance measures seem unrelated; both are extended to paths by taking maxima.NEWLINENEWLINENEWLINEThe author defines a certain subset \(S\) of all objects, and proves the following. If an object of \(S\) can be closely approximated by a path then it can be approximated by a path out of a set of well-separated paths in the graph.NEWLINENEWLINENEWLINEHowever, it remains open under what conditions the object set \(S\) is non-empty, or contains a meaningful portion of all objects given.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00036].