Choosing table sizes for khmer

If you look at the documentation for the scripts (khmer’s command-line interface) you’ll see two mysterious parameters – -N and -x, or, more verbosely, -n_tables and --tablesize. What are these, and how do you specify them?

The really short version

There is no way (except for experience, rules of thumb, and intuition) to know what these parameters should be up front. So, make the product of these two parameters be the size of your available memory:

-N 4 -x 4e9

for a machine with 16 GB of free memory, for example. Also see the rules of thumb, below.

The short version

These parameters specify the maximum memory usage of the primary data structure in khmer, which is basically N big hash tables of size x. The product of the number of hash tables and the size of the hash tables specifies the total amount of memory used.

This table is used to track k-mers. If it is too small, khmer will fail in various ways (and should complain), but there is no harm in making it too large. So, the absolute safest thing to do is to specify as much memory as is available. Most scripts will inform you of the total memory usage, and (at the end) will complain if it’s too small.

For normalize-by-median, khmer uses one byte per hash entry, so: if you had 16 GB of available RAM, you should specify something like -N 4 -x 4e9, which multiplies out to about 16 GB.

For the graph partitioning stuff, khmer uses only 1 bit per k-mer, so you can multiple your available memory by 8: for 16 GB of RAM, you could use

-N 4 -x 32e9

which multiplies out to 128 Gbits of RAM, or 16 Gbytes.

Life is a bit more complicated than this, however, because some scripts – load-into-counting and load-graph – keep ancillary information that will consume memory beyond this table data structure. So if you run out of memory, decrease the table size.

Also see the rules of thumb, below.

The real full version

khmer’s scripts, at their heart, represents k-mers in a very memory efficient way by taking advantage of two data structures, Bloom filters and CountMin Sketches, that are both probabilistic and constant memory. The “probabilistic” part means that there are false positives: the less memory you use, the more likely it is that khmer will think that k-mers are present when they are not, in fact, present.

Digital normalization (normalize-by-median and filter-abund) uses the CountMin Sketch data structure.

Graph partitioning (load-graph etc.) uses the Bloom filter data structure.

The practical ramifications of this are pretty cool. For example, your digital normalization is guaranteed not to increase in memory utilization, and graph partitioning is estimated to be 10-20x more memory efficient than any other de Bruijn graph representation. And hash tables (which is what Bloom filters and CountMin Sketches use) are really fast and efficient. Moreover, the optimal memory size for these primary data structures is dependent on the number of k-mers, but not explicitly on the size of k itself, which is very unusual.

In exchange for this memory efficiency, however, you gain a certain type of parameter complexity. Unlike your more typical k-mer package (like the Velvet assembler, or Jellyfish or Meryl or Tallymer), you are either guaranteed not to run out of memory (for digital normalization) or much less likely to do so (for partitioning).

The biggest problem with khmer is that there is a minimum hash number and size that you need to specify for a given number of k-mers, and you cannot confidently predict what it is before actually loading in the data. This, by the way, is also true for de Bruijn graph assemblers and all the other k-mer-based software – the final memory usage depends on the total number of k-mers, which in turn depends on the true size of your underlying genomic variation (e.g. genome or transcriptome size), the number of errors, and the k-mer size you choose (the k parameter) [ see Conway & Bromage, 2011 ]. The number of reads or the size of your data set is only somewhat correlated with the total number of k-mers. Trimming protocols, sequencing depth, and polymorphism rates are all important factors that affect k-mer count.

The bad news is that we don’t have good ways to estimate total k-mer count a priori, although we can give you some rules of thumb, below. In fact, counting the total number of distinct k-mers is a somewhat annoying challenge. Frankly, we recommend just guessing instead of trying to be all scientific about it.

The good news is that you can never give khmer too much memory! k-mer counting and set membership simply gets more and more accurate as you feed it more memory. (Although there may be performance hits from memory I/O, e.g. see the NUMA architecture.) The other good news is that khmer can measure the false positive rate and detect dangerously low memory conditions. For partitioning, we actually know what a too-high false positive rate is – our k-mer percolation paper lays out the math. For digital normalization, we assume that a false positive rate of 10% is bad. In both cases the data-loading scripts will exit with an error-code.

Rules of thumb

Juse use -N 4, always, and vary the -x parameter.

For digital normalization, we recommend:

  • -x 2e9 for any amount of sequencing for a single microbial genome, MDA-amplified or single colony.
  • -x 4e9 for up to a billion mRNAseq reads from any organism. Past that, increase it.
  • -x 8e9 for most eukaryotic genome samples.
  • -x 8e9 will also handle most “simple” metagenomic samples (HMP on down)
  • For metagenomic samples that are more complex, such as soil or marine, start as high as possible. For example, we are using -x 64e9 for ~300 Gbp of soil reads.

For partitioning of complex metagenome samples, we recommend starting as high as you can – something like half your system memory. So if you have 256 GB of RAM, use -N 4 -x 256e9 which will use 4 x 256 / 8 = 128 GB of RAM for the basic graph storage, leaving other memory for the ancillary data structures.

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