algorithm then iterates again. It terminates when the candidate
list becomes empty.
The following steps describe the algorithm in detail. Remember
that we are computing the shortest path tree for Area A. All
references to link state database lookup below are from Area A's
database.
(1) Initialize the algorithm's data structures. Clear the list
of candidate vertices. Initialize the shortest-path tree to
only the root (which is the router doing the calculation).
Set Area A's TransitCapability to FALSE.
(2) Call the vertex just added to the tree vertex V. Examine
the LSA associated with vertex V. This is a lookup in the
Area A's link state database based on the Vertex ID. If
this is a router-LSA, and bit V of the router-LSA (see
Section A.4.2) is set, set Area A's TransitCapability to
TRUE. In any case, each link described by the LSA gives the
cost to an adjacent vertex. For each described link, (say
it joins vertex V to vertex W):
(a) If this is a link to a stub network, examine the next
link in V's LSA. Links to stub networks will be
considered in the second stage of the shortest path
calculation.
(b) Otherwise, W is a transit vertex (router or transit
network). Look up the vertex W's LSA (router-LSA or
network-LSA) in Area A's link state database. If the
LSA does not exist, or its LS age is equal to MaxAge, or
it does not have a link back to vertex V, examine the
next link in V's LSA.[23]
(c) If vertex W is already on the shortest-path tree,
examine the next link in the LSA.
(d) Calculate the link state cost D of the resulting path
from the root to vertex W. D is equal to the sum of the
link state cost of the (already calculated) shortest
path to vertex V and the advertised cost of the link
between vertices V and W. If D is:
o Greater than the value that already appears for
vertex W on the candidate list, then examine the
next link.
o Equal to the value that appears for vertex W on the
candidate list, calculate the set of next hops that
result from using the advertised link. Input to
this calculation is the destination (W), and its
parent (V). This calculation is shown in Section
16.1.1. This set of hops should be added to the
next hop values that appear for W on the candidate
list.
o Less than the value that appears for vertex W on the
candidate list, or if W does not yet appear on the
candidate list, then set the entry for W on the
candidate list to indicate a distance of D from the
root. Also calculate the list of next hops that
result from using the advertised link, setting the
next hop values for W accordingly. The next hop
calculation is described in Section 16.1.1; it takes
as input the destination (W) and its parent (V).
(3) If at this step the candidate list is empty, the shortest-
path tree (of transit vertices) has been completely built
and this stage of the procedure terminates. Otherwise,
choose the vertex belonging to the candidate list that is
closest to the root, and add it to the shortest-path tree
(removing it from the candidate list in the process). Note
that when there is a choice of vertices closest to the root,
network vertices must be chosen before router vertices in
order to necessarily find all equal-cost paths. This is
consistent with the tie-breakers that were introduced in the
modified Dijkstra algorithm used by OSPF's Multicast routing
extensions (MOSPF).
(4) Possibly modify the routing table. For those routing table
entries modified, the associated area will be set to Area A,
the path type will be set to intra-area, and the cost will
be set to the newly discovered shortest path's calculated
distance.
If the newly added vertex is an area border router or AS
boundary router, a routing table entry is added whose
destination type is "router". The Options field found in
the associated router-LSA is copied into the routing table
entry's Optional capabilities field. Call the newly added
vertex Router X. If Router X is the endpoint of one of the
calculating router's virtual links, and the virtual link
uses Area A as Transit area: the virtual link is declared
up, the IP address of the virtual interface is set to the IP
address of the outgoing interface calculated above for
Router X, and the virtual neighbor's IP address is set to
Router X's interface address (contained in Router X's
router-LSA) that points back to the root of the shortest-
path tree; equivalently, this is the interface that points
back to Router X's parent vertex on the shortest-path tree
(similar to the calculation in Section 16.1.1).
If the newly added vertex is a transit network, the routing
table entry for the network is located. The entry's
Destination ID is the IP network number, which can be
obtained by masking the Vertex ID (Link State ID) with its
associated subnet mask (found in the body of the associated
network-LSA). If the routing table entry already exists
(i.e., there is already an intra-area route to the
destination installed in the routing table), multiple
vertices have mapped to the same IP network. For example,
this can occur when a new Designated Router is being
established. In this case, the current routing table entry
should be overwritten if and only if the newly found path is
just as short and the current routing table entry's Link
State Origin has a smaller Link State ID than the newly
added vertex' LSA.
If there is no routing table entry for the network (the
usual case), a routing table entry for the IP network should
be added. The routing table entry's Link State Origin
should be set to the newly added vertex' LSA.
(5) Iterate the algorithm by returning to Step 2.
The stub networks are added to the tree in the procedure's
second stage. In this stage, all router vertices are again
examined. Those that have been determined to be unreachable in
the above first phase are discarded. For each reachable router
vertex (call it V), the associated router-LSA is found in the
link state database. Each stub network link appearing in the
LSA is then examined, and the following steps are executed:
(1) Calculate the distance D of stub network from the root. D
is equal to the distance from the root to the router vertex
(calculated in stage 1), plus the stub network link's
advertised cost. Compare this distance to the current best
cost to the stub network. This is done by looking up the
stub network's current routing table entry. If the
calculated distance D is larger, go on to examine the next
stub network link in the LSA.
(2) If this step is reached, the stub network's routing table
entry must be updated. Calculate the set of next hops that
would result from using the stub network link. This
calculation is shown in Section 16.1.1; input to this
calculation is the destination (the stub network) and the
parent vertex (the router vertex). If the distance D is the
same as the current routing table cost, simply add this set
of next hops to the routing table entry's list of next hops.
In this case, the routing table already has a Link State
Origin. If this Link State Origin is a router-LSA whose
Link State ID is smaller than V's Router ID, reset the Link
State Origin to V's router-LSA.
Otherwise D is smaller than the routing table cost.
Overwrite the current routing table entry by setting the
routing table entry's cost to D, and by setting the entry's
list of next hops to the newly calculated set. Set the
routing table entry's Link State Origin to V's router-LSA.
Then go on to examine the next stub network link.
For all routing table entries added/modified in the second
stage, the associated area will be set to Area A and the path
type will be set to intra-area. When the list of reachable
router-LSAs is exhausted, the second stage is completed. At
this time, all intra-area routes associated with Area A have
been determined.
The specification does not require that the above two stage
method be used to calculate the shortest path tree. However, if
another algorithm is used, an identical tree must be produced.
For this reason, it is important to note that links between
transit vertices must be bidirectional in order to be included
in the above tree. It should also be mentioned that more
efficient algorithms exist for calculating the tree; for
example, the incremental SPF algorithm described in [Ref1].
16.1.1. The next hop calculation
This section explains how to calculate the current set of
next hops to use for a destination. Each next hop consists
of the outgoing interface to use in forwarding packets to
the destination together with the IP address of the next hop
router (if any). The next hop calculation is invoked each
time a shorter path to the destination is discovered. This
can happen in either stage of the shortest-path tree
calculation (see Section 16.1). In stage 1 of the
shortest-path tree calculation a shorter path is found as
the destination is added to the candidate list, or when the
destination's entry on the candidate list is modified (Step
2d of Stage 1). In stage 2 a shorter path is discovered
each time the destination's routing table entry is modified
(Step 2 of Stage 2).
The set of next hops to use for the destination may be
recalculated several times during the shortest-path tree
calculation, as shorter and shorter paths are discovered.
In the end, the destination's routing table entry will
always reflect the next hops resulting from the absolute
shortest path(s).
Input to the next hop calculation is a) the destination and
b) its parent in the current shortest path between the root
(the calculating router) and the destination. The parent is
always a transit vertex (i.e., always a router or a transit
network).
If there is at least one intervening router in the current
shortest path between the destination and the root, the
destination simply inherits the set of next hops from the
parent. Otherwise, there are two cases. In the first case,
the parent vertex is the root (the calculating router
itself). This means that the destination is either a
directly connected network or directly connected router.
The outgoing interface in this case is simply the OSPF
interface connecting to the destination network/router. If
the destination is a router which connects to the
calculating router via a Point-to-MultiPoint network, the
destination's next hop IP address(es) can be determined by
examining the destination's router-LSA: each link pointing
back to the calculating router and having a Link Data field
belonging to the Point-to-MultiPoint network provides an IP
address of the next hop router. If the destination is a
directly connected network, or a router which connects to
the calculating router via a point-to-point interface, no
next hop IP address is required. If the destination is a
router connected to the calculating router via a virtual
link, the setting of the next hop should be deferred until
the calculation in Section 16.3.
In the second case, the parent vertex is a network that
directly connects the calculating router to the destination
router. The list of next hops is then determined by
examining the destination's router-LSA. For each link in
the router-LSA that points back to the parent network, the
link's Link Data field provides the IP address of a next hop
router. The outgoing interface to use can then be derived
from the next hop IP address (or it can be inherited from
the parent network).
16.2. Calculating the inter-area routes
The inter-area routes are calculated by examining summary-LSAs.
If the router has active attachments to multiple areas, only
backbone summary-LSAs are examined. Routers attached to a
single area examine that area's summary-LSAs. In either case,
the summary-LSAs examined below are all part of a single area's
link state database (call it Area A).