As a generalization of the traditional path protection (PP) scheme in WDM
networks where a backup path is needed for each active path,
the partial path protection (PPP) scheme uses a collection of backup paths
to protect an active path, where each backup path in the collection
protects one or more links on the active path such that every link on the
active path is protected by one of the backup paths.
While there is no known polynomial time algorithm for computing an active path
and a corresponding backup path using the PP scheme for a given source
destination node pair,
we show that an active path and a corresponding collection of backup paths
using the PPP scheme can be computed in polynomial time,
whenever they exist, under each of the following four network models:
(a) dedicated protection in WDM networks without wavelength converters;
(b) shared protection in WDM networks without wavelength converters;
(c) dedicated protection in WDM networks with wavelength converters;
(d) shared protection in WDM networks with wavelength converters.
This is achieved by proving that that for any given source $s$ and
destination $d$ in the network, if one candidate active path connecting
$s$ and $d$ is protectable using PPP, then any candidate active path
connecting $s$ and $d$ is also protectable using PPP.
It is known that the existence of PP implies the existence of PPP while
the reverse is not true.
We demonstrate a similar result in the case of segmented path protection.
This fundamental property of the PPP scheme
is of great importance in the context of achieving further research advances
in the area of protection and restoration of WDM networks.
Mathematics Subject Classification: Primary: 68M10, 68M15; Secondary: 68Q25, 68W40.