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package netflix.ocelli.stats;
/*
Copyright 2012 Andrew Wang ([email protected])
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
import java.util.Arrays;
import java.util.LinkedList;
import java.util.ListIterator;
/**
* Implementation of the Cormode, Korn, Muthukrishnan, and Srivastava algorithm
* for streaming calculation of targeted high-percentile epsilon-approximate
* quantiles.
*
* This is a generalization of the earlier work by Greenwald and Khanna (GK),
* which essentially allows different error bounds on the targeted quantiles,
* which allows for far more efficient calculation of high-percentiles.
*
*
* See: Cormode, Korn, Muthukrishnan, and Srivastava
* "Effective Computation of Biased Quantiles over Data Streams" in ICDE 2005
*
* Greenwald and Khanna,
* "Space-efficient online computation of quantile summaries" in SIGMOD 2001
*
*/
public class CKMSQuantiles implements Quantiles {
/**
* Total number of items in stream.
*/
private int count = 0;
/**
* Used for tracking incremental compression.
*/
private int compressIdx = 0;
/**
* Current list of sampled items, maintained in sorted order with error
* bounds.
*/
protected LinkedList sample;
/**
* Buffers incoming items to be inserted in batch.
*/
private long[] buffer = new long[500];
private int bufferCount = 0;
/**
* Array of Quantiles that we care about, along with desired error.
*/
private final Quantile quantiles[];
public CKMSQuantiles(Quantile[] quantiles) {
this.quantiles = quantiles;
this.sample = new LinkedList();
}
/**
* Add a new value from the stream.
*
* @param value
*/
@Override
public synchronized void insert(int value) {
buffer[bufferCount] = value;
bufferCount++;
if (bufferCount == buffer.length) {
insertBatch();
compress();
}
}
/**
* Get the estimated value at the specified quantile.
*
* @param q
* Queried quantile, e.g. 0.50 or 0.99.
* @return Estimated value at that quantile.
*/
@Override
public synchronized int get(double q) {
// clear the buffer
insertBatch();
compress();
if (sample.size() == 0) {
return 0;
}
int rankMin = 0;
int desired = (int) (q * count);
ListIterator it = sample.listIterator();
Item prev, cur;
cur = it.next();
while (it.hasNext()) {
prev = cur;
cur = it.next();
rankMin += prev.g;
if (rankMin + cur.g + cur.delta > desired
+ (allowableError(desired) / 2)) {
return (int) prev.value;
}
}
// edge case of wanting max value
return (int) sample.getLast().value;
}
/**
* Specifies the allowable error for this rank, depending on which quantiles
* are being targeted.
*
* This is the f(r_i, n) function from the CKMS paper. It's basically how
* wide the range of this rank can be.
*
* @param rank
* the index in the list of samples
*/
private double allowableError(int rank) {
// NOTE: according to CKMS, this should be count, not size, but this
// leads
// to error larger than the error bounds. Leaving it like this is
// essentially a HACK, and blows up memory, but does "work".
// int size = count;
int size = sample.size();
double minError = size + 1;
for (Quantile q : quantiles) {
double error;
if (rank <= q.quantile * size) {
error = q.u * (size - rank);
} else {
error = q.v * rank;
}
if (error < minError) {
minError = error;
}
}
return minError;
}
private boolean insertBatch() {
if (bufferCount == 0) {
return false;
}
Arrays.sort(buffer, 0, bufferCount);
// Base case: no samples
int start = 0;
if (sample.size() == 0) {
Item newItem = new Item(buffer[0], 1, 0);
sample.add(newItem);
start++;
count++;
}
ListIterator it = sample.listIterator();
Item item = it.next();
for (int i = start; i < bufferCount; i++) {
long v = buffer[i];
while (it.nextIndex() < sample.size() && item.value < v) {
item = it.next();
}
// If we found that bigger item, back up so we insert ourselves
// before it
if (item.value > v) {
it.previous();
}
// We use different indexes for the edge comparisons, because of the
// above
// if statement that adjusts the iterator
int delta;
if (it.previousIndex() == 0 || it.nextIndex() == sample.size()) {
delta = 0;
}
else {
delta = ((int) Math.floor(allowableError(it.nextIndex()))) - 1;
}
Item newItem = new Item(v, 1, delta);
it.add(newItem);
count++;
item = newItem;
}
bufferCount = 0;
return true;
}
/**
* Try to remove extraneous items from the set of sampled items. This checks
* if an item is unnecessary based on the desired error bounds, and merges
* it with the adjacent item if it is.
*/
private void compress() {
if (sample.size() < 2) {
return;
}
ListIterator it = sample.listIterator();
int removed = 0;
Item prev = null;
Item next = it.next();
while (it.hasNext()) {
prev = next;
next = it.next();
if (prev.g + next.g + next.delta <= allowableError(it.previousIndex())) {
next.g += prev.g;
// Remove prev. it.remove() kills the last thing returned.
it.previous();
it.previous();
it.remove();
// it.next() is now equal to next, skip it back forward again
it.next();
removed++;
}
}
}
private class Item {
public final long value;
public int g;
public final int delta;
public Item(long value, int lower_delta, int delta) {
this.value = value;
this.g = lower_delta;
this.delta = delta;
}
@Override
public String toString() {
return String.format("%d, %d, %d", value, g, delta);
}
}
public static class Quantile {
public final double quantile;
public final double error;
public final double u;
public final double v;
public Quantile(double quantile, double error) {
this.quantile = quantile;
this.error = error;
u = 2.0 * error / (1.0 - quantile);
v = 2.0 * error / quantile;
}
@Override
public String toString() {
return String.format("Q{q=%.3f, eps=%.3f})", quantile, error);
}
}
}
