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[theory-seminar] Theory Lunch 10/6: Josh Wang on Triangle Finding Algorithms

Greg Bodwin greg.bodwin at gmail.com
Thu Nov 6 11:24:08 PST 2014


Reminder: in ~1 hour!

On Wed, Nov 5, 2014 at 12:46 PM, Greg Bodwin <greg.bodwin at gmail.com> wrote:

> Hey all,
>
> As usual, we'll have Theory Lunch this Thursday.  Food at 12:15, talk at
> 12:30.  Gates 4b wing lobby.  Speaker details below.
>
> Best,
> Greg
>
> ---------------------------
>
> We present new algorithms for finding induced four-node subgraphs in a
> given graph, which run in time roughly that of detecting a clique on
> three nodes.
>
> The best known algorithms for triangle finding in an n-node graph take
> O(n^w) time, where w < 2.373 is the matrix multiplication exponent. We
> give a general randomized technique for finding any induced four-node
> subgraph, except for the clique or independent set on 4 nodes, in
> Õ(n^w) time with high probability. The algorithm can be derandomized
> in some cases.
>
> For sparse graphs with m edges, the best known triangle finding
> algorithm runs in O(m^(2w/(w+1))) <= O(m^1.41) time. We give a
> randomized Õ(m^(2w/(w+1))) time algorithm for finding any induced
> four-node subgraph other than C_4, K_4 and their complements. Some
> cases can be derandomized. For C_4 or its complement, we get slightly
> slower algorithms.
>
> Joint work with Virginia Vassilevska Williams, Ryan Williams, and Huacheng
> Yu.
>
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