  Interval graphs were used in the study of genomics by the famous molecular
biologist Benzer. Later on probe interval graphs were introduced by Zhang as a
generalization of interval graphs for the study of cosmid contig mapping of
DNA.
  A tagged probe interval graph (briefly, TPIG) is motivated by similar
applications to genomics, where the set of vertices is partitioned into two
sets, namely, probes and nonprobes and there is an interval on the real line
corresponding to each vertex. The graph has an edge between two probe vertices
if their corresponding intervals intersect, has an edge between a probe vertex
and a nonprobe vertex if the interval corresponding to a nonprobe vertex
contains at least one end point of the interval corresponding to a probe vertex
and the set of non-probe vertices is an independent set. This class of graphs
have been defined nearly two decades ago, but till today there is no known
recognition algorithm for it.
  In this paper, we consider a natural subclass of TPIG, namely, the class of
proper tagged probe interval graphs (in short PTPIG). We present
characterization and a linear time recognition algorithm for PTPIG. To obtain
this characterization theorem we introduce a new concept called canonical
sequence for proper interval graphs, which, we belief, has an independent
interest in the study of proper interval graphs. Also to obtain the recognition
algorithm for PTPIG, we introduce and solve a variation of consecutive $1$'s
problem, namely, oriented consecutive $1$'s problem and some variations of
PQ-tree algorithm. We also discuss the interrelations between the classes of
PTPIG and TPIG with probe interval graphs and probe proper interval graphs.
