slow with redundancy removal

[Brian Cohn]

I'm trying to remove redundancies on matricies with 500-1500 constraints, and a similar number of variables. I want to remove redundancy prior to running hit-and-run on the space.

h_representation.RDS.zip

h <- readRDS("h_representation.RDS")
redundancy_result <- rcdd::redundant(h)

> dim(h)
[1] 173  72

I've read that the computational complexity is at worst an O(nn), where the major computation time is taken up by nn linear programs. For my case, I would expect each linear programming call to take less than 1ms, so the n*n time should be 173^2=29,929 milliseconds = ~ 30 seconds. But with rcdd's redundant function it takes 166 seconds. How is redundancy implemented in dd_MatrixCanonicalize? Or am I calculating this incorrectly? Is there a way to parallelize redundancy removal?

Thanks you!

References:

Ray shooting: https://www.inf.ethz.ch/personal/fukudak/lect/pclect/notes2014/PolyComp2014.pdf
8.2 H Redundancy Removal: https://www.inf.ethz.ch/personal/fukudak/lect/pclect/notes2014/PolyComp2014.pdf

[Charles J. Geyer]

Cddlib doesn't do threads. There is also the issue that this problem is not embarrassingly parallel. If you do each of these linear programs in parallel, they are not easily combined into a solution. But I'm not an expert on computational geometry.

…

On Tue, Jul 3, 2018, 3:23 AM Brian Cohn ***@***.***> wrote: I'm trying to remove redundancies on matricies with 500-1500 constraints, and a similar number of variables. I want to remove redundancy prior to running hit-and-run on the space. h_representation.RDS.zip <https://github.com/cjgeyer/rcdd/files/2158263/h_representation.RDS.zip> h <- readRDS("h_representation.RDS") redundancy_result <- rcdd::redundant(h) > dim(h) [1] 173 72 I've read that the computational complexity is at worst an O(n*n), where the major computation time is taken up by n*n linear programs. For my case, I would expect each linear programming call to take less than 1ms, so the n*n time should be 173^2=29,929 milliseconds = ~ 30 seconds. But with rcdd's redundant function it takes 166 seconds. How is redundancy implemented in dd_MatrixCanonicalize? Or am I calculating this incorrectly? Is there a way to parallelize redundancy removal? Thanks you! References: Ray shooting: https://www.inf.ethz.ch/personal/fukudak/lect/pclect/notes2014/PolyComp2014.pdf 8.2 H Redundancy Removal: https://www.inf.ethz.ch/personal/fukudak/lect/pclect/notes2014/PolyComp2014.pdf [image: image] <https://user-images.githubusercontent.com/13772726/42207750-8827ccac-7e5f-11e8-82a9-9a82c4c2f6f9.png> — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#1>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AAcdwEFCRX1sAh22BobcYA2u-k7Fb_RXks5uCyoKgaJpZM4VAgB2> .