It is not too late to update the BloomFIlter interface to have the merge
return a boolean. The incorrect Shape would still throw an exception, so
the return value would only come into play if the bits could not be set.
thoughts?
On Mon, Mar 2, 2020 at 7:56 AM Claude Warren <cla...@xenei.com> wrote:
> for the remove(), add(), and subtract() methods I agree that void is not
> correct and it should be boolean and be the same as the value you would get
> from calling isValid().
>
> You are correct the getCounts() should return an iterator of some type on
> int[], I don't know why I thought long[]. I am happy with a plain
> Iterator<int[]> as the return.
>
> Claude
>
>
>
> On Mon, Mar 2, 2020 at 1:02 AM Alex Herbert <alex.d.herb...@gmail.com>
> wrote:
>
>>
>>
>> > On 1 Mar 2020, at 15:39, Claude Warren <cla...@xenei.com> wrote:
>> >
>> > I think the CountingBloomFilter interface needs to extend BloomFilter.
>>
>> I said that but did not write it, sorry.
>>
>> >
>> > I think I am confused.
>> >
>> > I would expect CountingBloomFilter to have
>> >
>> > interface CountingBloomFilter extends BloomFilter {
>> > // these 2 methods are the reverse of merge()
>> > void remove( BloomFilter );
>> > void remove( Hasher );
>>
>> Fine. Same intention but different method names. But why void? It forces
>> you to check if the remove was valid with a second call. On the plus side
>> it matches the void merge(…) methods and in most cases a user would not
>> care to check anyway. If they are controlling the filter then leave it to
>> them to make sure they do not remove something they did not add.
>>
>> >
>> > // these 2 methods are the addition/subtraction of counts
>> > void add( CountingBloomFilter )
>> > void subtract( CountingBloomFilter );
>>
>> Fine. But same comment as above with the void return.
>>
>> >
>> > // 2 methods to retrieve data
>> > Stream<long[]> getCounts();
>>
>> I don’t like this use of long[]. In my previous post I argued that if you
>> were to ever want to store more than max integer items in a filter then the
>> Bloom filter would have more bit indices than max integer. So we never have
>> to support long counts. A filter that exceeds max integer for a count is
>> highly likely to be saturated and no use as a filter anyway.
>>
>> For most backing implementations the object type of the stream will be
>> different so you will have to write a Spliterator<T> implementation or wrap
>> some iterator anyway. So why not return the Spliterator:
>>
>> Spliterator<int[]> getCounts();
>>
>> Since the backing implementation will likely not store int[] pairs then
>> this will have a lot of object creation and garbage collection overhead to
>> go through the counts. This does not seem to be a big concern here if the
>> purpose is the same as for the BloomFilter for long[] getBits(), i.e. to
>> get a canonical representation for storage.
>>
>> Note: The Spliterator may not have a known size (number of non zero bits)
>> at creation, for example if the counts are stored in a fixed size array.
>> Thus efficient parallel traversal by binary tree splitting is limited by
>> how evenly the counts are distributed. For a backing implementation using a
>> collection then the size should be known. In this case a Spliterator would
>> be of more use than a plain Iterator. You can convert one to the other
>> using:
>>
>> java.util.Spliterators:
>> public static<T> Iterator<T> iterator(Spliterator<? extends T>
>> spliterator)
>> public static <T> Spliterator<T> spliterator(Iterator<? extends T>
>> iterator,
>> long size,
>> int characteristics)
>>
>> So which to choose for the API?
>>
>> The Hasher currently uses an Iterator:
>>
>> PrimitiveIterator.OfInt getBits(Shape shape);
>>
>> In the case of a StaticHasher this could return a spliterator. But the
>> DynamicHasher needs a reworking of the internal Iterator class. It could be
>> a Spliterator to use the new IntConsumer API but in most (all) cases
>> splitting would not be possible for dynamic hashing as the parts are
>> produced in order. It is likely that they will be consumed sequentially too.
>>
>> I would suggest that Spliterator is the more modern implementation,
>> despite not always being applicable to parallelisation in a stream.
>> Currently the iterator from the Hasher is used in forEachRemaining() and
>> while loop is approximately equal measure. The while loops are for a fast
>> exit and would be uglier if rewritten for a
>> Spliterator.tryAdvance(IntConsumer) syntax.
>>
>> There is a use of the IteratorChain in HasherBloomFilter that would need
>> a rethink for spliterators.
>>
>> The path of least resistance is to use Iterator<int[]> for the API of
>> CountingBloomFilter to be consistent with Hasher’s use of Iterator.
>>
>> WDYT?
>>
>>
>> > boolean isValid()
>>
>> Fine. Allows some level of feedback that the counts are corrupt.
>>
>> > }
>> >
>> > Claude
>> >
>> >
>> > On Sun, Mar 1, 2020 at 2:48 PM Alex Herbert <alex.d.herb...@gmail.com
>> <mailto:alex.d.herb...@gmail.com>>
>> > wrote:
>> >
>> >>
>> >>
>> >>> On 1 Mar 2020, at 09:28, Claude Warren <cla...@xenei.com> wrote:
>> >>>
>> >>> The idea of a backing array is fine and the only problem I see with
>> it is
>> >>> in very large filters (on the order of 10^8 bits and larger) but
>> document
>> >>> the size calculation and let the developer worry about it.
>> >>
>> >> Let us look at the use case where we max out the array. Using the Bloom
>> >> filter calculator:
>> >>
>> >> n = 149,363,281
>> >> p = 0.001000025 (1 in 1000)
>> >> m = 2147483647 (256MiB)
>> >> k = 10
>> >>
>> >> n = 74,681,641
>> >> p = 0.000001 (1 in 999950)
>> >> m = 2147483647 (256MiB)
>> >> k = 20
>> >>
>> >> n = 49,787,761
>> >> p = 0.000000001 (1 in 999924899)
>> >> m = 2147483647 (256MiB)
>> >> k = 30
>> >>
>> >> So you will be able to put somewhere in the order of 10^8 or 10^7 items
>> >> into the filter. I would say that anyone putting more than that into
>> the
>> >> filter has an unusual use case. The CountingBloomFilter can throw an
>> >> exception if m is too large and will throw an OutOfMemoryError if you
>> >> cannot allocate an array large enough.
>> >>
>> >> One clear point here is that you cannot use a short as a 16-bit count
>> >> would easily overflow. So you have to use an integer array for the
>> counts.
>> >>
>> >> A maximum length int[] is roughly 8GB.
>> >>
>> >> What would another implementation cost in terms of memory? The
>> >> TreeMap<Integer, Integer> was the most space efficient. In the previous
>> >> e-mail the saturation of a Bloom filter bits was approximately 50%
>> when at
>> >> the intended capacity. So we have to estimate the size of a TreeMap
>> >> containing Integer.MAX_VALUE/2 indices ~ 2^30. The memory test shows
>> the
>> >> TreeMap memory scales linearly with entries:
>> >>
>> >> 32768 / 65536 (0.500) : TreeMap<Integer, Integer> = 1834061
>> bytes
>> >> 65536 / 131072 (0.500) : TreeMap<Integer, Integer> = 3669080
>> bytes
>> >> 131072 / 262144 (0.500) : TreeMap<Integer, Integer> = 7339090
>> bytes
>> >>
>> >> So what is the memory for a TreeMap with 2^30 indices. I make it about:
>> >>
>> >> (2^30 / 131,072) * 7,339,090 bytes ~ 6e10 bytes = 55.99 GB
>> >>
>> >> I would say that this amount of RAM is unusual. It is definitely not as
>> >> efficient as using an array. So very large counting Bloom filters are
>> going
>> >> to require some thought as to the hardware they run on. This may not
>> be the
>> >> case in 10 years time.
>> >>
>> >> I would say that we try an int[] backing array for the storage
>> >> implementation and document it’s limitations. A different
>> implementation
>> >> could be provided in future if required.
>> >>
>> >> This could be done by making CountingBloomFilter an interface that
>> extends
>> >> BloomFilter with the methods:
>> >>
>> >> subtract(BloomFilter filter)
>> >> subtract(Hasher filter)
>> >>
>> >> These will negate the effect of the corresponding merge(BloomFilter)
>> >> operation.
>> >>
>> >> Do we also need access to the counts and add/subtract of another
>> >> CountingBloomFilter?:
>> >>
>> >> add(CountingBloomFilter filter);
>> >> subtract(CountingBloomFilter filter);
>> >>
>> >> Iterator<int[]> getCounts();
>> >> int getSize(); // Number of items added
>> >>
>> >> The CountingBloomFilter is then an interface that defines how to
>> reverse
>> >> the merge of some bits into the filter.
>> >>
>> >> My concern is the inefficiency of the creation of objects in any method
>> >> that provides access to the counts (e.g. above using an iterator as for
>> >> Hasher.getBits()). I presume this method would be to allow some type of
>> >> storage/serialisation of the filter akin to the long[] getBits()
>> method of
>> >> BloomFilter. So it may be better done using a method:
>> >>
>> >> int getCount(int index);
>> >>
>> >> The caller can then use long[] getBits() to get the indices set in the
>> >> filter and then for each non-zero bit index call getCount(index). Or
>> just
>> >> not include the method as the counts are only of concern when storing
>> the
>> >> filter. This functionality is cleaner pushed into an implementation.
>> >>
>> >> In a previous post we discussed whether to throw an exception on
>> >> overflow/underflow or raise in an invalid flag. Using the invalid flag
>> idea
>> >> the interface would be:
>> >>
>> >> interface CountingBloomFilter {
>> >> int add(CountingBloomFilter filter);
>> >> int subtract(BloomFilter filter);
>> >> int subtract(Hasher filter);
>> >> int subtract(CountingBloomFilter filter);
>> >> int getStatus();
>> >>
>> >> // Maybe
>> >> int getSize();
>> >> int getCount(int index);
>> >> }
>> >>
>> >> The status would be negative if any operation overflowed/underflowed,
>> or
>> >> zero if OK. The current status is returned by the add/subtract methods.
>> >>
>> >> However I note that overflow may not be a concern. The number of items
>> to
>> >> add to a filter to create overflow would be using a filter with a
>> number of
>> >> bits that is unrealistic to store in memory:
>> >>
>> >> n = 2147483647
>> >> p = 0.001000025 (1 in 1000)
>> >> m = 30875634182 (3.59GiB)
>> >> k = 10
>> >>
>> >> If you want to add 2 billion items (and overflow an integer count) then
>> >> your filter would be so big it would break the rest of the API that
>> uses a
>> >> 32-bit int for the bit index.
>> >>
>> >> Thus only underflow is a realistic concern. This could be documented as
>> >> handled in an implementation specific manner (i.e. throw or ignore).
>> The
>> >> API is then simplified to:
>> >>
>> >> interface CountingBloomFilter {
>> >> boolean add(CountingBloomFilter filter);
>> >> boolean subtract(BloomFilter filter);
>> >> boolean subtract(Hasher filter);
>> >> boolean subtract(CountingBloomFilter filter);
>> >> int getStatus();
>> >>
>> >> // Maybe
>> >> int getSize();
>> >> int getCount(int index);
>> >> }
>> >>
>> >> The boolean is used to state that add/subtract did not over/underflow.
>> >> Implementations can throw if they require it.
>> >>
>> >> The question then becomes what does getSize() represent if an
>> add/subtract
>> >> did not execute cleanly. Under this scheme it would be the number of
>> (add -
>> >> subtract) operations. The status flag would be used to indicate if the
>> size
>> >> is valid, or any of the counts from getCount(). The simpler API is to
>> not
>> >> allow access to counts/size or adding/subtracting counts:
>> >>
>> >> interface CountingBloomFilter {
>> >> boolean subtract(BloomFilter filter);
>> >> boolean subtract(Hasher filter);
>> >> int getStatus();
>> >> // Or something like ...
>> >> boolean isValid();
>> >> }
>> >>
>> >> This filter is then only concerned with reversing the merge of Bloom
>> >> filters with a valid status flag to indicate that the current state is
>> >> consistent (i.e. all filters have been cleanly merged/subtracted).
>> >>
>> >> WDYT?
>> >>
>> >>>
>> >>> As for the merge question. merge is a standard bloom filter
>> operation.
>> >> It
>> >>> is well defined in the literature. Merging a bloom filter into a
>> >> counting
>> >>> bloom filter means incrementing the bit counts. I think that
>> >> merge/remove
>> >>> should continue to operate as though the parameter were a standard
>> bloom
>> >>> filter.
>> >>>
>> >>
>> >> OK. So the count is to represent the number of filters that had a bit
>> set
>> >> at that index. This makes it more clear.
>> >>
>> >>> We had spoken of implementing and adding/deleting method pair that
>> would
>> >>> operate on CountingBloomFilters and would add/subtract the counts.
>> (e.g.
>> >>> add(CountingBloomFilter) and subtract(CountingBloomFilter))
>> >>>
>> >>> I disagree with your proposal for the merge(Hasher) implementation,
>> and I
>> >>> am not certain that an add(Hasher) makes sense. First consider that
>> the
>> >>> Hasher returns the bits that are to be enabled in the Bloom filter so
>> >>> collisions are expected. In the normal course of events a Hasher is
>> used
>> >>> to create a normal Bloom filter where all the duplicates are removed.
>> >> That
>> >>> filter is then merged into a CountingBloomFilter. So in some sense
>> the
>> >>> Hasher and the normal Bloom filter are the same. So I would expect
>> the
>> >>> merge of the Hasher and the merge of the normal Bloom filter created
>> from
>> >>> that hasher into a CountingBloomFilter to yield the same result. If
>> you
>> >>> wanted to add an add(Hasher)/delete(Hasher) pair of functions to a
>> >>> CountingBloomFilter you could implement with duplicate counting, but
>> I am
>> >>> not certain of the validity of such a count and I fear that it muddies
>> >> the
>> >>> waters with respect to what the CountingBloomFilter is counting.
>> >>
>> >> Agreed.
>> >>
>> >>>
>> >>> Claude
>> >>>
>> >>> On Sat, Feb 29, 2020 at 2:13 PM Alex Herbert <
>> alex.d.herb...@gmail.com
>> >> <mailto:alex.d.herb...@gmail.com <mailto:alex.d.herb...@gmail.com>>>
>> >>> wrote:
>> >>>
>> >>>>
>> >>>>
>> >>>>> On 29 Feb 2020, at 07:46, Claude Warren <cla...@xenei.com <mailto:
>> cla...@xenei.com> <mailto:
>> >> cla...@xenei.com <mailto:cla...@xenei.com>>> wrote:
>> >>>>>
>> >>>>> Alex would you take a look at pull request 131 [1]. it adds a new
>> >> hasher
>> >>>>> implementation and makes the HashFunctionValidator available for
>> public
>> >>>> use.
>> >>>>>
>> >>>>> https://github.com/apache/commons-collections/pull/131 <
>> https://github.com/apache/commons-collections/pull/131> <
>> >> https://github.com/apache/commons-collections/pull/131 <
>> https://github.com/apache/commons-collections/pull/131>> <
>> >>>> https://github.com/apache/commons-collections/pull/131 <
>> https://github.com/apache/commons-collections/pull/131> <
>> >> https://github.com/apache/commons-collections/pull/131 <
>> https://github.com/apache/commons-collections/pull/131>>>
>> >>>>
>> >>>> OK. I’ll take a look.
>> >>>>
>> >>>> I’ve been thinking about the counting Bloom filter and the backing
>> >>>> storage. In summary:
>> >>>>
>> >>>> 1. The backing storage should be a fixed array.
>> >>>> 2. Merging a Hasher should count duplicate indices, not flatten them
>> all
>> >>>> to a single count.
>> >>>>
>> >>>> For background I’ve used the standard formulas to estimate the
>> number of
>> >>>> indices that will be non-zero in a Bloom filter. The wikipedia page
>> >> gives
>> >>>> this formula for the expected number of bits set to 0 (E(q)) if you
>> have
>> >>>> inserted i elements into a filter of size m using k hash functions:
>> >>>>
>> >>>> E(q) = (1 - 1/m)^ki"
>> >>>>
>> >>>> So a rough guess of the number of indices (bits) used by a filter is
>> >>>> 1-E(q).
>> >>>>
>> >>>> Here is a table of Bloom filters with different collision
>> probabilities
>> >>>> and the proportion of bits that will be set when 1%, 10%, 100% of the
>> >>>> capacity of the filter has been met:
>> >>>>
>> >>>> n p m k I E(q) bits
>> >>>> 1000 1E-04 19171 13 10 0.9932 0.0068
>> >>>> 1000 1E-04 19171 13 100 0.9344 0.0656
>> >>>> 1000 1E-04 19171 13 1000 0.5076 0.4924
>> >>>> 1000 1E-05 23963 17 10 0.9929 0.0071
>> >>>> 1000 1E-05 23963 17 100 0.9315 0.0685
>> >>>> 1000 1E-05 23963 17 1000 0.4919 0.5081
>> >>>> 1000 1E-06 28756 20 10 0.9931 0.0069
>> >>>> 1000 1E-06 28756 20 100 0.9328 0.0672
>> >>>> 1000 1E-06 28756 20 1000 0.4988 0.5012
>> >>>> 10000 1E-06 287552 20 100 0.9931 0.0069
>> >>>> 10000 1E-06 287552 20 1000 0.9328 0.0672
>> >>>> 10000 1E-06 287552 20 10000 0.4988 0.5012
>> >>>>
>> >>>> The point is that if you create a Bloom filter and fill it to 10% of
>> the
>> >>>> intended capacity the number of indices used will be about 6-7% of
>> the
>> >>>> filter bits.
>> >>>>
>> >>>> So how to store the counts? Currently the counting bloom filter uses
>> a
>> >>>> TreeMap<Integer, Integer>. I tried:
>> >>>>
>> >>>> TreeMap<Integer, Integer>
>> >>>> HashMap<Integer, Integer>
>> >>>> TreeSet<MutableCount>
>> >>>> HashSet<MutableCount>
>> >>>> int[]
>> >>>>
>> >>>> The MutableCount is a custom object that stores the bit index and
>> uses
>> >> it
>> >>>> for a hash code and then has a mutable integer count field. It allows
>> >> the
>> >>>> count to be incremented/decremented if the object is in the set:
>> >>>>
>> >>>> static final class MutableCount implements
>> Comparable<MutableCount> {
>> >>>> final int key;
>> >>>> int count;
>> >>>> // etc
>> >>>> }
>> >>>>
>> >>>> This is adapted from the Bag<T> collection which stores an item count
>> >> with
>> >>>> a MutableInteger. Here the mutable count is part of the same object T
>> >>>> inserted into the Set. So you can find the object, change the count
>> and
>> >> not
>> >>>> have to put it back into the set. This is more efficient than
>> changing
>> >> the
>> >>>> Integer stored in a Map.
>> >>>>
>> >>>> I’ve estimated memory usage using an idea based on this article from
>> >>>> JavaWorld: Java Tip 130: Do you know your data size? [1].
>> >>>>
>> >>>> Basically you:
>> >>>>
>> >>>> - create an object and throw it away. All classes are then
>> initialised.
>> >>>> - Then you free memory (run garbage collection) and get the current
>> >> memory
>> >>>> usage
>> >>>> - Then create a lot of your object (held in an array)
>> >>>> - Then measure memory usage again
>> >>>> - memory = (after - before) / count
>> >>>>
>> >>>> Here is some example output for n bits set in size m:
>> >>>>
>> >>>> 13107 / 262144 (0.050) : TreeMap<Integer, Integer> = 733947
>> bytes
>> >>>> 26214 / 262144 (0.100) : TreeMap<Integer, Integer> = 1467866
>> bytes
>> >>>> 13107 / 262144 (0.050) : TreeSet<MutableCount> = 838928
>> bytes
>> >>>> 26214 / 262144 (0.100) : TreeSet<MutableCount> = 1677776
>> bytes
>> >>>> 13107 / 262144 (0.050) : HashMap<Integer, Integer> = 1677712
>> bytes
>> >>>> 26214 / 262144 (0.100) : HashMap<Integer, Integer> = 2306739
>> bytes
>> >>>> 13107 / 262144 (0.050) : HashSet<MutableCount> = 1782664
>> bytes
>> >>>> 26214 / 262144 (0.100) : HashSet<MutableCount> = 2516656
>> bytes
>> >>>> 0 / 262144 (0.000) : int[] = 1048608
>> bytes
>> >>>> 0 / 262144 (0.000) : short[] = 524320
>> bytes
>> >>>>
>> >>>> The estimate is accurate to 0.0001% for the arrays so the method is
>> >>>> working. The HashMap was created with the capacity set to the
>> expected
>> >>>> capacity of the filter (m).
>> >>>>
>> >>>> I’ve chosen these sizes because at 5% full a HashSet is less memory
>> >>>> efficient than using a fixed size array, and at 10% the TreeSet is
>> also
>> >>>> less efficient.
>> >>>>
>> >>>> Note that the java.util.Tree/HashSet versions just wrap a Map and
>> >> insert a
>> >>>> dummy object for all keys in the Map. So here a Set is not as
>> efficient
>> >> as
>> >>>> a Map because in the Map test I always inserted the same Integer
>> object
>> >>>> representing 1. This would be the same as using a Set with an Integer
>> >> key
>> >>>> but here the Set had to contain the MutableCount which has an extra
>> int
>> >>>> field and is larger than an Integer.
>> >>>>
>> >>>> These data lead me to think that a counting Bloom filter should just
>> >> use a
>> >>>> fixed size backing array:
>> >>>>
>> >>>> - If created using the same Shape as a standard Bloom filter it uses
>> a
>> >>>> fixed size. This has high memory cost when the filter is empty but
>> when
>> >> it
>> >>>> exceeds 10% of the intended capacity it is more efficient than a
>> dynamic
>> >>>> backing storage.
>> >>>> - All operations will operate in order(n) time for an operation with
>> >>>> another filter with n indices. Each individual index count in the
>> filter
>> >>>> will have order(1) time for access/update. Performance will be
>> limited
>> >> by
>> >>>> the memory cache of the entire array.
>> >>>>
>> >>>> The issue is that a counting Bloom filter with a very low number of
>> >>>> inserted items will be memory inefficient. But under what
>> circumstance
>> >> will
>> >>>> such a filter be used in a short-term lifecycle? If it is simply to
>> >> merge
>> >>>> into another filter then this can be done using a merge with a
>> Hasher.
>> >> If
>> >>>> counts are to be merged then perhaps we provide a method to merge
>> counts
>> >>>> using the same data structure returned by the CountingBloomFilter
>> >>>> getCounts() method, e.g. using a stream of <index,count> pairs:
>> >>>>
>> >>>> Stream<int[]> getCounts();
>> >>>> void add(Stream<int[]> counts);
>> >>>>
>> >>>> The issue here is the Shape and HashFunctionIdentity of the origin of
>> >> the
>> >>>> merge cannot be validated. So just leave it out and use the merge
>> with a
>> >>>> Hasher.
>> >>>>
>> >>>>
>> >>>> Thus the next issue with the counting Bloom filter implementation.
>> >>>> Currently when it merges with a Hasher it puts all the indices into a
>> >> Set
>> >>>> and so will only increment the count by 1 for each index identified
>> by
>> >> the
>> >>>> Hasher. This appears to miss the entire point of the counting Bloom
>> >> filter.
>> >>>> If I hash an objects to generate k indices I would hope that I do
>> get k
>> >>>> indices. But the hash may not be perfect and I may get [1, k] indices
>> >> with
>> >>>> some duplications. This is part of the signature of that object with
>> the
>> >>>> given hash. So surely a counting Bloom filter should accommodate
>> this.
>> >> If
>> >>>> my Hasher generates the same index 20 times this should result in the
>> >> count
>> >>>> of that index incrementing by 20.
>> >>>>
>> >>>> The result if that if an object is added direct to a counting Bloom
>> >> filter
>> >>>> using a Hasher it will have a different result that if added to a
>> >> standard
>> >>>> Bloom filter and then that filter added to the counting Bloom filter.
>> >>>>
>> >>>> Opinions on this?
>> >>>>
>> >>>> Alex
>> >>>>
>> >>>>
>> >>>>
>> >>>> [1] http://www.javaworld.com/javaworld/javatips/jw-javatip130.html <
>> http://www.javaworld.com/javaworld/javatips/jw-javatip130.html>
>> >>>>
>> >>>>>
>> >>>>> On Tue, Feb 25, 2020 at 12:35 AM Alex Herbert <
>> >> alex.d.herb...@gmail.com <mailto:alex.d.herb...@gmail.com>>
>> >>>>> wrote:
>> >>>>>
>> >>>>>> I have created a PR that contains most of the changes discussed in
>> >> this
>> >>>>>> thread (see [1]).
>> >>>>>>
>> >>>>>> Please review the changes and comment here or on GitHub.
>> >>>>>>
>> >>>>>> I have left the CountingBloomFilter alone. I will reimplement the
>> >>>>>> add/subtract functionality as discussed into another PR.
>> >>>>>>
>> >>>>>> Alex
>> >>>>>>
>> >>>>>> [1] https://github.com/apache/commons-collections/pull/133 <
>> https://github.com/apache/commons-collections/pull/133> <
>> >>>>>> https://github.com/apache/commons-collections/pull/133 <
>> https://github.com/apache/commons-collections/pull/133>>
>> >>>>>>
>> >>>>>>
>> >>>>>>
>> >>>>>
>> >>>>> --
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>> >>>>
>> >>>>
>> >>>
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>> http://www.linkedin.com/in/claudewarren> <
>> >> http://www.linkedin.com/in/claudewarren <
>> http://www.linkedin.com/in/claudewarren>>
>> >>
>> >
>> >
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>>
>
>
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