// n: expected insertions
  // b: m/n, bits per insertion
  // p: expected false positive probability
  //
  // 1) Optimal k = b * ln2
  // 2) p = (1 - e ^ (-kn/m))^k
  // 3) For optimal k: p = 2 ^ (-k) ~= 0.6185^b
  // 4) For optimal k: m = -nlnp / ((ln2) ^ 2)

  /**
   * Computes the optimal number of hash functions (k) for a given false positive probability (p).
   *

### Expanding existing distributed setup

MinIO supports expanding distributed erasure coded clusters by specifying new set of clusters on the command-line as shown below:

```sh

alias kv-pairify='yq ".configuration[]" | jq ".[]" | jq -r ".name + \"=\" + .value"'
```

Let's take for example a set of 12 compute nodes with an aggregate memory of _1.2TiB_, we need to do following settings for optimal results. Add the following optimal entries for _core-site.xml_ to configure _s3a_ with **MinIO**. Most important options here are

```
cat ${HADOOP_CONF_DIR}/core-site.xml | kv-pairify | grep "mapred"

	maxPartsCount             = 10000
	maxPartSize               = 1024 * 1024 * 1024 * 5
	minPartSize               = 1024 * 1024 * 128 // chosen by us to be optimal for HDDs
)

// optimalPartInfo - calculate the optimal part info for a given
// object size.
//
// NOTE: Assumption here is that for any object to be uploaded to any S3 compatible
// object storage it will have the following parameters as constants.

final class SingletonImmutableSet<E> extends ImmutableSet<E> {
  // We deliberately avoid caching the asList and hashCode here, to ensure that with
  // compressed oops, a SingletonImmutableSet packs all the way down to the optimal 16 bytes.

  final transient E element;

  SingletonImmutableSet(E element) {
    this.element = Preconditions.checkNotNull(element);
  }

  @Override
  public int size() {
    return 1;
  }

# MinIO Server Limits Per Tenant

For optimal production setup MinIO recommends Linux kernel version 4.x and later.

## Erasure Code (Multiple Drives / Servers)

| Item                                                            | Specification |
|:----------------------------------------------------------------|:--------------|
| Maximum number of servers per cluster                           | no-limit      |

final class SingletonImmutableSet<E> extends ImmutableSet<E> {
  // We deliberately avoid caching the asList and hashCode here, to ensure that with
  // compressed oops, a SingletonImmutableSet packs all the way down to the optimal 16 bytes.

  final transient E element;

  SingletonImmutableSet(E element) {
    this.element = Preconditions.checkNotNull(element);
  }

  @Override
  public int size() {
    return 1;
  }

---

Für dieses Beispiel verwenden wir jedoch ein sehr einfaches HTML-Dokument mit etwas JavaScript, alles in einem langen String.

Das ist natürlich nicht optimal und man würde das nicht in der Produktion machen.

In der Produktion hätten Sie eine der oben genannten Optionen.

list_quorum                     (string)    set the acceptable quorum expected for list operations e.g. "optimal", "reduced", "disk", "strict", "auto" (default: 'strict')
replication_priority            (string)    set replication priority (default: 'auto')

      return o != null && unsafeBinarySearch(o) >= 0;
    } catch (ClassCastException e) {
      return false;
    }
  }

  @Override
  public boolean containsAll(Collection<?> targets) {
    // TODO(jlevy): For optimal performance, use a binary search when
    // targets.size() < size() / log(size())
    // TODO(kevinb): see if we can share code with OrderedIterator after it
    // graduates from labs.
    if (targets instanceof Multiset) {