Dear Martin,
Glad MASON team solved your problem. Let me step back and provide you
with two lines of effort which address the scalability problem from
different perspectives.
First, there are solutions which allow you to perform search for exact
or approximate shortest paths on large graphs by transforming the
problem either by spatial embedding of graphs or by making the problem
multi-resolution (so called landmark / backbone or center piece
routing). Check the following three examples:
http://www.cs.ucsb.edu/~bowlin/pdf/orion-wosn10.pdf (for social
networks example)
http://matsim.org/uploads/Garbald07_Balmer.pdf (for routing in dynamic
transport network)
http://research.yahoo.com/files/paper_7.pdf (a combination for
recommendation networks)
These approaches usually require precomputing some auxiliary
datastructures, but size of those can be adjusted and later quickly
amortized if queries are repeated, compared to default cached
Dijkstra. Additionally, frameworks like Matsim who is JAVA,
open-sourced, might be partially using JUNG, provide code which is
easy to hack.
Second, you stated that your actual problem is to find mean shortest
path metric, not to route. One might consider statistical approach:
sampling of the large graph and computing this statistic of the
sample. Of course, for a statistic like characteristic path length one
needs to apply a smart sampling (snowball, traceroute) to get unbiased
and consistent estimates. You might want to skim through the following
set of slides to get intuition behind those ideas:
http://vw.indiana.edu/netsci06/ws-slides/eric_kolaczyk.pdf
Lastly, if you a few bucks to spare for some cloud service this might be fun:
http://www.math.cmu.edu/~ctsourak/tkdd10.pdf
Regards
Maciek
On Mon, Nov 15, 2010 at 7:44 PM, Martin Pokropp
<[log in to unmask]> wrote:
> Dear Maciej,
>
> thankyou for your email concerning the problems I experienced with finding
> the mean shortest path of my simulated networks and sorry for my late
> response.
> Meanwhile, after Sean Luke had forwarded me a conversation he had with
> Gabriel Balan, I decided to customize the code in the socialnets package for
> my purposes and for my machine, which is limited to only 2GB. It still takes
> an eternity to get the mean shortest path, but at least I do no longer
> experience any heap space problems. For my purposes, this is sufficient,
> because I don't really need the SP for my simulations. I only need it as an
> additional information about the properties of my networks. Therefore I
> think that considering to use JUNG is no longer necessary for my purposes,
> although I found it very interesting to read about your approach!
>
> Thankyou and best regards
>
> Martin
>
>
>
> 2010/11/12 Maciej M. Latek <[log in to unmask]>
>>
>> Dear Martin,
>>
>> Sorry for delayed response, past two weeks were filled with
>> conferences and presentations. Let me share my experiences with large
>> scale routing on JUNG networks with you.
>>
>> The biggest network we routed was 33000 nodes, 70000 edges
>> transportation graph. 16GB machine was able to handle JUNG's Dijkstra
>> and service repeated calls for paths with reasonable speed. As most of
>> paths were "local", I would expect that in general cache necessary to
>> handle such a graph would be larger.
>>
>> One thing we experimented with was to switch to truncated
>> breadth-first search and caching of only requested paths. I attach a
>> sample modification of JUNG's code we played around. This approach
>> sacrifices sophistication for better control over speed / memory
>> trade-off.
>>
>> We assume that your SimState can provide horizon for the
>> TruncatedDistanceLabeller. The code for TruncatedShortestPath
>> implements truncated breadth-first search, but as far as I see it does
>> not implement the limited caching. Let me know if such a solution
>> would be of interest to you.
>>
>> Best regards
>>
>> Maciej
>>
>>
>>
>> On Mon, Nov 8, 2010 at 12:30 PM, Martin Pokropp
>> <[log in to unmask]> wrote:
>> > Dear Sean, Dear Mr. Balan, Mr. Panait and Mr. Latek,
>> >
>> > increasing the stack size does the job for the task of finding the
>> > components of the network with
>> >
>> >
>> > sim.field.network.stats.ConnectivityStatistics.getConnectedComponents(network)
>> >
>> > But the biggest component (size about 29000 nodes) now seems to be too
>> > big
>> > for the shortest path algorithms in
>> >
>> >
>> > sim.field.network.stats.NetworkStatistics.getMeanShortestPath(giantComponent,
>> > metric)
>> >
>> > I tried out very high heap sizes (2000M). The task goes on for minutes,
>> > then a "java.lang.OutOfMemoryError: java heap space" is thrown.
>> >
>> > Do you think that the Jung package would do the job here, or is the task
>> > generally too complex (I'm using an ordinary desktop pc)?
>> >
>> > Regards,
>> >
>> > Martin
>> >
>> >
>> >
>> >
>> >
>> >
>> > 2010/11/8 Sean Luke <[log in to unmask]>
>> >>
>> >> Martin, the right person to look into this is Gabriel Balan, and to a
>> >> lesser extend Liviu Panait (whom I am cc:ing). They were the two who
>> >> put
>> >> this package together way back when. Gabriel is moving to New
>> >> Hampshire so
>> >> may be in radio silence right now however.
>> >>
>> >> In the meantime we need to nail down whether or not it's a recursion
>> >> bug
>> >> or a um, misfeature. Try increasing the stack size in Java. This is
>> >> done
>> >> with the -Xss parameter. The default value is probably 512K. Try
>> >> increasing it considerably, like
>> >>
>> >> java -Xss16392k ...
>> >>
>> >> You should also increase the heap I guess. I'd do something like:
>> >>
>> >> java -Xss16392k -Xmx500M -Xms500M ...
>> >>
>> >> If you can't find a stack size which will complete the task, then it's
>> >> possibly the case that we're seeing a recursion bug here rather than a
>> >> maximal graph limit.
>> >>
>> >> Your other option is to go with Jung. Now beware: I believe that Jung
>> >> isn't serializable, so you may be stuck unable to checkpoint out. I am
>> >> cc:ing Maciej Latek, who knows a lot about jerry-rigging MASON to Jung.
>> >>
>> >> Sean
>> >>
>> >>
>> >> On Nov 8, 2010, at 10:52 AM, Martin Pokropp wrote:
>> >>
>> >>> Dear Sean, Dear Mason Users,
>> >>>
>> >>>
>> >>> For my simulated undirected network I intend to use the additional
>> >>> socialnets package provided with Mason. My network has 30000 nodes and
>> >>> is
>> >>> sparse with about 6 edges per node.
>> >>>
>> >>> As there are isolated nodes, I cannot get the mean Shortest Path of
>> >>> the
>> >>> whole network. Instead, I'm trying to analyse the biggest connected
>> >>> component by using
>> >>>
>> >>>
>> >>>
>> >>> sim.field.network.stats.ConnectivityStatistics.getConnectedComponents(network)
>> >>>
>> >>> Unfortunately the VM throws multiple stack overflow errors:
>> >>>
>> >>>
>> >>> Exception in thread "main" java.lang.StackOverflowError
>> >>> at sim.field.network.Network.getNodeIndex(Network.java:618)
>> >>> at
>> >>>
>> >>> sim.field.network.stats.ConnectivityStatistics$ConnectedComponentFactory.exploreU(ConnectivityStatistics.java:220)
>> >>> at
>> >>>
>> >>> sim.field.network.stats.ConnectivityStatistics$ConnectedComponentFactory.exploreU(ConnectivityStatistics.java:222)
>> >>> at
>> >>>
>> >>> sim.field.network.stats.ConnectivityStatistics$ConnectedComponentFactory.exploreU(ConnectivityStatistics.java:222)
>> >>> at
>> >>>
>> >>> sim.field.network.stats.ConnectivityStatistics$ConnectedComponentFactory.exploreU(ConnectivityStatistics.java:222)
>> >>> at
>> >>>
>> >>> sim.field.network.stats.ConnectivityStatistics$ConnectedComponentFactory.exploreU(ConnectivityStatistics.java:222)
>> >>> at
>> >>>
>> >>> sim.field.network.stats.ConnectivityStatistics$ConnectedComponentFactory.exploreU(ConnectivityStatistics.java:222)
>> >>> at
>> >>>
>> >>> sim.field.network.stats.ConnectivityStatistics$ConnectedComponentFactory.exploreU(ConnectivityStatistics.java:222)
>> >>> at
>> >>>
>> >>> sim.field.network.stats.ConnectivityStatistics$ConnectedComponentFactory.exploreU(ConnectivityStatistics.java:222
>> >>> ...
>> >>>
>> >>> I guess that there are too many recursions and the
>> >>> getConnectedComponents
>> >>> method is not appropriate for networks such as mine?
>> >>>
>> >>> Best Regards,
>> >>>
>> >>> Martin
>> >>>
>> >>>
>> >>>
>> >>>
>> >>>
>> >
>> >
>
>
|
