[ https://issues.apache.org/jira/browse/MATH1169?page=com.atlassian.jira.plugin.system.issuetabpanels:alltabpanel
]
Adam Stelmaszczyk updated MATH1169:

Description:
Percentile class is now using Hoare selection algorithm (aka Quickselect) with median of 3
for choosing a pivot and caching pivots. Quickselect expected runtime is about 3.4N + O(N).
The constant can be improved to 1.5n by a bit complicated pivot strategy, yielding the Floyd–Rivest
algorithm, which has average complexity of 1.5N + O(N) for median, with other k being faster.
I implemented Floyd–Rivest algorithm without caching pivots following wikipedia and benchmarked
it with Caliper (https://code.google.com/p/caliper/).
Array size  runtime in seconds for FloydRivest  current Percentile  % faster
100000  6.907  7.083  2.5%
1000000  70.3  75.4  6.8%
10000000  708  868  18.4% (https://microbenchmarks.appspot.com/runs/c0f65e3544c0458eb6e0634b4e6fa68b#r:scenario.benchmarkSpec.methodName)
was:
Percentile class is now using Hoare selection algorithm (aka Quickselect) with median of 3
for choosing a pivot and caching pivots. Quickselect expected runtime is about 3.4N + o(N).
The constant can be improved to 1.5n by a bit complicated pivot strategy, yielding the Floyd–Rivest
algorithm, which has average complexity of 1.5N + O(N) for median, with other k being faster.
I implemented Floyd–Rivest algorithm without caching pivots following wikipedia and benchmarked
it with Caliper (https://code.google.com/p/caliper/).
Array size  runtime in seconds for FloydRivest  current Percentile  % faster
100000  6.907  7.083  2.5%
1000000  70.3  75.4  6.8%
10000000  708  868  18.4% (https://microbenchmarks.appspot.com/runs/c0f65e3544c0458eb6e0634b4e6fa68b#r:scenario.benchmarkSpec.methodName)
> Faster Percentile
> 
>
> Key: MATH1169
> URL: https://issues.apache.org/jira/browse/MATH1169
> Project: Commons Math
> Issue Type: Improvement
> Reporter: Adam Stelmaszczyk
> Priority: Minor
> Attachments: FloydRivest.java, Main.java, PercentileFloydRivest.java
>
>
> Percentile class is now using Hoare selection algorithm (aka Quickselect) with median
of 3 for choosing a pivot and caching pivots. Quickselect expected runtime is about 3.4N +
O(N).
> The constant can be improved to 1.5n by a bit complicated pivot strategy, yielding the
Floyd–Rivest algorithm, which has average complexity of 1.5N + O(N) for median, with other
k being faster.
> I implemented Floyd–Rivest algorithm without caching pivots following wikipedia and
benchmarked it with Caliper (https://code.google.com/p/caliper/).
> Array size  runtime in seconds for FloydRivest  current Percentile  % faster
> 100000  6.907  7.083  2.5%
> 1000000  70.3  75.4  6.8%
> 10000000  708  868  18.4% (https://microbenchmarks.appspot.com/runs/c0f65e3544c0458eb6e0634b4e6fa68b#r:scenario.benchmarkSpec.methodName)

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