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Routers `A` and `D` exchange distance vectors with increasing costs until these costs reach :math:`\infty`. This problem may occur in other scenarios than the one depicted in the above figure. In fact, distance vector routing may suffer from count to infinity problems as soon as there is a cycle in the network. Unfortunately, cycles are widely used in networks since they provide the required redundancy to deal with link and router failures. To mitigate the impact of counting to infinity, some distance vector protocols consider that :math:`16=\infty`. Unfortunately, this limits the metrics that network operators can use and the diameter of the networks using distance vectors.
This count to infinity problem occurs because router `A` advertises to router `D` a route that it has learned via router `D`. A possible solution to avoid this problem could be to change how a router creates its distance vector. Instead of computing one distance vector and sending it to all its neighbors, a router could create a distance vector that is specific to each neighbor and only contains the routes that have not been learned via this neighbor. This could be implemented by the following pseudocode.
This technique is called `split-horizon`. With this technique, the count to infinity problem would not have happened in the above scenario, as router `A` would have advertised :math:`[A=0]` after the failure, since it learned all its other routes via router `D`. Another variant called `split-horizon with poison reverse` is also possible. Routers using this variant advertise a cost of :math:`\infty` for the destinations that they reach via the router to which they send the distance vector. This can be implemented by using the pseudo-code below.
Unfortunately, split-horizon is not sufficient to avoid all count to infinity problems with distance vector routing. Consider the failure of link `A-B` in the four routers network shown below.
After having detected the failure, router `B` sends its distance vectors:
:math:`[A=\infty,B=0,C=\infty,E=1]` to router `C`
:math:`[A=\infty,B=0,C=1,E=\infty]` to router `E`
If, unfortunately, the distance vector sent to router `C` is lost due to a transmission error or because router `C` is overloaded, a new count to infinity problem can occur. If router `C` sends its distance vector :math:`[A=2,B=1,C=0,E=\infty]` to router `E`, this router installs a route of distance `3` to reach `A` via `C`. Router `E` sends its distance vectors :math:`[A=3,B=\infty,C=1,E=1]` to router `B` and :math:`[A=\infty,B=1,C=\infty,E=0]` to router `C`. This distance vector allows `B` to recover a route of distance `4` to reach `A`.
Forwarding tables versus routing tables
Routers usually maintain at least two data structures that contain information about the reachable destinations. The first data structure is the `routing table`. The `routing table` is a data structure that associates a destination to an outgoing interface or a nexthop router and a set of additional attributes. Different routing protocols can associate different attributes for each destination. Distance vector routing protocols will store the cost to reach the destination along the shortest path. Other routing protocols may store information about the number of hops of the best path, its lifetime or the number of sub paths. A `routing table` may store different paths towards a given destination and flag one of them as the best one.
The `routing table` is a software data structure which is updated by (one or more) routing protocols. The `routing table` is usually not directly used when forwarding packets. Packet forwarding relies on a more compact data structure which is the `forwarding table`. On high-end routers, the `forwarding table` is implemented directly in hardware while lower performance routers will use a software implementation. A `forwarding table` contains a subset of the information found in the `routing table`. It only contains the nexthops towards each destination that are used to forward packets and no attributes. A `forwarding table` will typically associate each destination to one or more outgoing interface or nexthop router.
Link state routing
Link state routing is the second family of routing protocols. While distance vector routers use a distributed algorithm to compute their routing tables, link-state routers exchange messages to allow each router to learn the entire network topology. Based on this learned topology, each router is then able to compute its routing table by using a shortest path computation such as Dijkstra's algorithm [Dijkstra1959]_. A detailed description of this shortest path algorithm may be found in [Wikipedia:Dijkstra]_.
For link-state routing, a network is modeled as a `directed weighted graph`. Each router is a node, and the links between routers are the edges in the graph. A positive weight is associated to each directed edge and routers use the shortest path to reach each destination. In practice, different types of weights can be associated to each directed edge :
unit weight. If all links have a unit weight, shortest path routing prefers the paths with the least number of intermediate routers.
weight proportional to the propagation delay on the link. If all link weights are configured this way, shortest path routing uses the paths with the smallest propagation delay.
:math:`weight=\frac{C}{bandwidth}` where `C` is a constant larger than the highest link bandwidth in the network. If all link weights are configured this way, shortest path routing prefers higher bandwidth paths over lower bandwidth paths.
Usually, the same weight is associated to the two directed edges that correspond to a physical link (i.e. :math:`R1 \rightarrow R2` and :math:`R2 \rightarrow R1`). However, nothing in the link state protocols requires this. For example, if the weight is set in function of the link bandwidth, then an asymmetric ADSL link could have a different weight for the upstream and downstream directions. Other variants are possible. Some networks use optimization algorithms to find the best set of weights to minimize congestion inside the network for a given traffic demand [FRT2002]_.
When a link-state router boots, it first needs to discover to which routers it is directly connected. For this, each router sends a HELLO message every `N` seconds on all its interfaces. This message contains the router's address. Each router has a unique address. As its neighboring routers also send HELLO messages, the router automatically discovers to which neighbors it is connected. These HELLO messages are only sent to neighbors that are directly connected to a router, and a router never forwards the HELLO messages that it receives. HELLO messages are also used to detect link and router failures. A link is considered to have failed if no HELLO message has been received from a neighboring router for a period of :math:`k \times N` seconds.
Once a router has discovered its neighbors, it must reliably distribute all its outgoing edges to all routers in the network to allow them to compute their local view of the network topology. For this, each router builds a `link-state packet` (LSP) containing the following information:
LSP.Router: identification (address) of the sender of the LSP
LSP.age: age or remaining lifetime of the LSP
LSP.seq: sequence number of the LSP
LSP.Links[]: links advertised in the LSP. Each directed link is represented with the following information:
LSP.Links[i].Id: identification of the neighbor
LSP.Links[i].cost: cost of the link
These LSPs must be reliably distributed inside the network without using the router's routing table since these tables can only be computed once the LSPs have been received. The `Flooding` algorithm is used to efficiently distribute the LSPs of all routers. Each router that implements `flooding` maintains a `link state database` (LSDB) containing the most recent LSP sent by each router. When a router receives a LSP, it first verifies whether this LSP is already stored inside its LSDB. If so, the router has already distributed the LSP earlier and it does not need to forward it. Otherwise, the router forwards the LSP on all its links except the link over which the LSP was received. Flooding can be implemented by using the following pseudo-code.
In this pseudo-code, `LSDB(r)` returns the most recent `LSP` originating from router `r` that is stored in the `LSDB`. `newer(lsp1, lsp2)` returns true if `lsp1` is more recent than `lsp2`. See the note below for a discussion on how `newer` can be implemented.
Which is the most recent LSP ?
A router that implements flooding must be able to detect whether a received LSP is newer than the stored LSP. This requires a comparison between the sequence number of the received LSP and the sequence number of the LSP stored in the link state database. The ARPANET routing protocol [MRR1979]_ used a 6 bits sequence number and implemented the comparison as follows :rfc:`789`
This comparison takes into account the modulo :math:`2^{6}` arithmetic used to increment the sequence numbers. Intuitively, the comparison divides the circle of all sequence numbers into two halves. Usually, the sequence number of the received LSP is equal to the sequence number of the stored LSP incremented by one, but sometimes the sequence numbers of two successive LSPs may differ, e.g. if one router has been disconnected for some time. The comparison above worked well until October 27, 1980. On this day, the ARPANET crashed completely. The crash was complex and involved several routers. At one point, LSP `40` and LSP `44` from one of the routers were stored in the LSDB of some routers in the ARPANET. As LSP `44` was the newest, it should have replaced LSP `40` on all routers. Unfortunately, one of the ARPANET routers suffered from a memory problem and sequence number `40` (`101000` in binary) was replaced by `8` (`001000` in binary) in the buggy router and flooded. Three LSPs were present in the network and `44` was newer than `40` which is newer than `8`, but unfortunately `8` was considered to be newer than `44`... All routers started to exchange these three link state packets forever and the only solution to recover from this problem was to shutdown the entire network :rfc:`789`.

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../../principles/linkstate.rst:16
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locale/pot/principles/network.pot, string 169