Recognition of probe proper interval graphs

In a partitioned probe graph the vertex set is partitioned into probes and non-probes, such that the set of non-probes is an independent set. A probe proper interval graph is the intersection graph of a set of intervals on the line such that every vertex is mapped to an interval, no interval contains another, and two vertices are adjacent if and only if the corresponding intervals intersect and at least one of them is a probe. We present the first linear-time algorithm that determines whether an input partitioned probe graph is a probe proper interval graph, and if the answer is positive then the algorithm constructs a corresponding set of intervals.