pbg at cs.berkeley.edu
Wed Feb 18 21:09:33 CST 2009
> On Wed, 18 Feb 2009 22:12:02 GMT, Rod Beck said:
>> From the fine article:
> "In greedy routing, a node passes information to the neighboring
> node that is
> closest to the final destination in an abstract space called hidden
> Sounds suspiciously like "throw the packet at the router that's got
> the shortest
> AS path to the destination" doesn't it? You don't need to know the
> topology to know router X is 2 AS's closer to the dest than router
> Y once
> X and Y have been loaded with the "hidden metric space" known as a
> BGP update ;)
No, it's quite different from BGP.
The high level point is that BGP needs to know a lot of information
about the network in order to route, while greedy routing (when it
works) requires very little state.
To make it concrete: You're right that BGP doesn't need to know the
entire topology, but it comes quite close, in terms of the total
amount of information it has. To throw the packet at the router
that's got the shortest AS path to the destination, you need to have
information from every neighbor about every destination. A BGP
router in general needs one FIB entry for every destination (IP
prefix) in the Internet, i.e., about 300,000 entries, and in the RIB
it has potentially 300K from every BGP neighbor.... potentially,
millions of entries.
In contrast, greedy routing would require probably less than a dozen
entries for the average router. This is because the router only
needs to know its own "identifier", and those of its immediate
neighbors. The routing algorithm has some "distance function" dist
(ID1, ID2). A packet comes with some destination identifier D, and
the router compares the distance dist(N, D) for each neighbor N, and
forwards the packet to the neighbor with smallest distance. For
example, suppose you know the topology is a two-dimensional grid.
Then the "identifier" is the router's (X,Y) coordinates and the
distance function can be Euclidean distance.
The main catch is of course that most networks don't have such nice
regular structure like the grid. Essentially, greedy routing tries
to "summarize" the structure of the network using a very small amount
of information. And there are topologies whose pattern of links is
"too complicated" (in a certain sense) for greedy routing to be able
to summarize it.
Therefore it is interesting when you find a network in which greedy
routing works, especially if that network is vaguely realistic. The
most well-known example is Jon Kleinberg's work on small world
networks (http://tinyurl.com/dye7ub), which gives some theoretical
backing to Milgram's "six degrees of separation" experiment from the
1960s (which basically used a kind of greedy routing). This physorg
paper seems to be very much in the same style, showing that greedy
routing works on an Internet-like graph. (Disclaimer: I have only
read the above article, not the paper.)
Of course there are plenty of reasons you would not use this in
practice, e.g., it gives the router little control over routing
policy, traffic engineering, etc.
> I'm not sure this article is actually telling us anything we didn't
> know. Now if there was a way to compute those distance metrics without
> global knowledge - if there was only an algorithm that
> only cared about what was "upstream" from a locally connected link
> and whether
> it was connected. Say, we could call it a link-state routing
> Now if they were able to actually develop a link-state protocol
> that involved
> *only* local adjacency announcements and not flooded announcements,
> would be something... But what I see here is "if somebody
> developed that,
> we'd be able to route more efficiently".
This is essentially what they are doing. The distance is computed
based on only local knowledge, not global knowledge. Each router
needs to know only local adjacencies. Caveat: I haven't read the
paper and don't know how they assign the router identifiers, so I am
answering only about greedy routing in general.
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