16.1. Calculating the shortest-path tree for an area

This calculation yields the set of intra-area routes associated with an area (called hereafter Area A). A router calculates the shortest-path tree using itself as the root.[21] The formation of the shortest path tree is done here in two stages. In the first stage, only links between routers and transit networks are considered. Using the Dijkstra algorithm, a tree is formed from this subset of the link state database. In the second stage, leaves are added to the tree by considering the links to stub networks.

The procedure will be explained using the graph terminology that was introduced in Section 2. The area's link state database is represented as a directed graph. The graph's vertices are routers, transit networks and stub networks. The first stage of the procedure concerns only the transit vertices (routers and transit networks) and their connecting links. Throughout the shortest path calculation, the following data is also associated with each transit vertex:

Vertex (node) ID

A 32-bit number uniquely identifying the vertex. For router vertices this is the router's OSPF Router ID. For network vertices, this is the IP address of the network's Designated Router.

A link state advertisement

Each transit vertex has an associated link state advertisement. For router vertices, this is a router links advertisement. For transit networks, this is a network links advertisement (which is actually originated by the network's Designated Router). In any case, the advertisement's Link State ID is always equal to the above Vertex ID.

List of next hops

The list of next hops for the current set of shortest paths from the root to this vertex. There can be multiple shortest paths due to the equal-cost multipath capability. Each next hop indicates the outgoing router interface to use when forwarding traffic to the destination. On multi-access networks, the next hop also includes the IP address of the next router (if any) in the path towards the destination.

Distance from root

The link state cost of the current set of shortest paths from the root to the vertex. The link state cost of a path is calculated as the sum of the costs of the path's constituent links (as advertised in router links and network links advertisements). One path is said to be "shorter" than another if it has a smaller link state cost.

The first stage of the procedure (i.e., the Dijkstra algorithm) can now be summarized as follows. At each iteration of the algorithm, there is a list of candidate vertices. Paths from the root to these vertices have been found, but not necessarily the shortest ones. However, the paths to the candidate vertex that is closest to the root are guaranteed to be shortest; this vertex is added to the shortest-path tree, removed from the candidate list, and its adjacent vertices are examined for possible addition to/modification of the candidate list. The 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 link state advertisement 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 links advertisement, and bit V of the router links advertisement (see Section A.4.2) is set, set Area A's TransitCapability to TRUE. In any case, each link described by the advertisement gives the cost to an adjacent vertex. For each described link, (say it joins vertex V to vertex W):
   1. If this is a link to a stub network, examine the next link in V's advertisement. Links to stub networks will be considered in the second stage of the shortest path calculation.

   2. Otherwise, W is a transit vertex (router or transit network). Look up the vertex W's link state advertisement (router links or network links) in Area A's link state database. If the advertisement 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 advertisement.[22]

   3. If vertex W is already on the shortest-path tree, examine the next link in the advertisement.

   4. 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:
      • Greater than the value that already appears for vertex W on the candidate list, then examine the next link.

      • 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.

      • 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 (call it ABR), a routing table entry is added whose destination type is "area border router". The Options field found in the associated router links advertisement is copied into the routing table entry's Optional capabilities field. If in addition ABR is the endpoint of one of the calculating router's configured virtual links that uses Area A as its 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 ABR, and the virtual neighbor's IP address is set to the ABR interface address (contained in ABR's router links advertisement) that points back to the root of the shortest-path tree; equivalently, this is the interface that points back to ABR's parent vertex on the shortest-path tree (similar to the calculation in Section 16.1.1).

   If the newly added vertex is an AS boundary router, the routing table entry of type "AS boundary router" for the destination is located. Since routers can belong to more than one area, it is possible that several sets of intra- area paths exist to the AS boundary router, each set using a different area. However, the AS boundary router's routing table entry must indicate a set of paths which utilize a single area. The area leading to the routing table entry is selected as follows: The area providing the shortest path is always chosen; if more than one area provides paths with the same minimum cost, the area with the largest OSPF Area ID (when considered as an unsigned 32-bit integer) is chosen. Note that whenever an AS boundary router's routing table entry is added/modified, the Options found in the associated router links advertisement is copied into the routing table entry's Optional capabilities field.

   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 links advertisement). 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' link state advertisement.

   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' link state advertisement.

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 links advertisement is found in the link state database. Each stub network link appearing in the advertisement 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 advertisement.

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 links advertisement whose Link State ID is smaller than V's Router ID, reset the Link State Origin to V's router links advertisement.

   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 links advertisement. 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 links 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 ordered 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 [BBN].

• 16.1.1. The next hop calculation