Which data structure is sorted by insertion and has fast "contains" check?

Question

I am looking for a data structure that preserves the order in which the elements were inserted and offers a fast "contains" predicate. I also need iterator and random access. Performance during insertion or deletion is not relevant. I am also willing to accept overhead in terms of memory consumption.

Background: I need to store a list of objects. The objects are instances of a class called Neuron and stored in a Layer. The Layer object has the following public interface:

class Layer {
public:
    Neuron *neuronAt(const size_t &index) const;
    NeuronIterator begin();
    NeuronIterator end();
    bool contains(const Neuron *const &neuron) const;
    void addNeuron(Neuron *const &neuron);
};

The contains() method is called quite often when the software runs, I've asserted that using callgrind. I tried to circumvent some of the calls to contains(), but is still a hot spot. Now I hope to optimize exactly this method.

I thought of using std::set, using the template argument to provide my own comparator struct. But the Neuron class itself does not give its position in the Layer away. Additionally, I'd like to have *someNeuronIterator = anotherNeuron to work without screwing up the order.

Another idea was to use a plain old C array. Since I do not care about the performance of adding a new Neuron object, I thought I could make sure that the Neuron objects are always stored linear in memory. But that would invalidate the pointer I pass to addNeuron(); at least I'd have to change it to point to the new copy I created to keep things linear aligned. Right?

Another idea was to use two data structures in the Layer object: A vector/list for the order, and a map/hash for lookup. But that would contradict my wish for an iterator that allowed operator* without a const reference, wouldn't it?

I hope somebody can hint an idea for a data structure or a concept that would satisfy my needs, or at least give me an idea for an alternative. Thanks!

Answer 1

If this contains check is really where you need the fastest execution, and assuming you can be a little intrusive with the source code, the fastest way to check if a Neuron belongs in a layer is to simply flag it when you insert it into a layer (ex: bit flag).

You have guaranteed O(1) checks at that point to see if a Neuron belongs in a layer and it's also fast at the micro-level.

If there can be numerous layer objects, this can get a little trickier, as you'll need a separate bit for each potential layer a neuron can belong to unless a Neuron can only belong in a single layer at once. This is reasonably manageable, however, if the number of layers are relatively fixed in size.

If the latter case and a Neuron can only belong to one layer at once, then all you need is a backpointer to Layer*. To see if a Neuron belongs in a layer, simply see if that backpointer points to the layer object.

If a Neuron can belong to multiple layers at once, but not too many at one time, then you could store like a little array of backpointers like so:

struct Neuron
{
    ...
    Layer* layers[4]; // use whatever small size that usually fits the common case
    Layer* ptr;
    int num_layers;
};

Initialize ptr to point to layers if there are 4 or fewer layers to which the Neuron belongs. If there are more, allocate it on the free store. In the destructor, free the memory if ptr != layers. You can also optimize away num_layers if the common case is like 1 layer, in which case a null-terminated solution might work better. To see if a Neuron belongs to a layer, simply do a linear search through ptr. That's practically constant-time complexity with respect to the number of Neurons provided that they don't belong in a mass number of layers at once.

You can also use a vector here but you might reduce cache hits on those common case scenarios since it'll always put its contents in a separate block, even if the Neuron only belongs to like 1 or 2 layers.

This might be a bit different from what you were looking for with a general-purpose, non-intrusive data structure, but if your performance needs are really skewed towards these kinds of set operations, an intrusive solution is going to be the fastest in general. It's not quite as pretty and couples your element to the container, but hey, if you need max performance...

Another idea was to use a plain old C array. Since I do not care about the performance of adding a new Neuron object, I thought I could make sure that the Neuron objects are always stored linear in memory. But that would invalidate the pointer I pass to addNeuron(); [...]

Yes, but it won't invalidate indices. While not as convenient to use as pointers, if you're working with mass data like vertices of a mesh or particles of an emitter, it's common to use indices here to avoid the invalidation and possibly to save an extra 32-bits per entry on 64-bit systems.

Update

Given that Neurons only exist in one Layer at a time, I'd go with the back pointer approach. Seeing if a neuron belongs to a layer becomes a simple matter of checking if the back pointer points to the same layer.

Since there's an API involved, I'd suggest, just because it sounds like you're pushing around a lot of data and have already profiled it, that you focus on an interface which revolves around aggregates (layers, e.g.) rather than individual elements (neurons). It'll just leave you a lot of room to swap out underlying representations when your clients aren't performing operations at the individual scalar element-type interface.

With the O(1) contains implementation and the unordered requirement, I'd go with a simple contiguous structure like std::vector. However, you do expose yourself to potential invalidation on insertion.

Because of that, if you can, I'd suggest working with indices here. However, that become a little unwieldy since it requires your clients to store both a pointer to the layer in which a neuron belongs in addition to its index (though if you do this, the backpointer becomes unnecessary as the client is tracking where things belong).

One way to mitigate this is to simply use something like std::vector<Neuron*> or ptr_vector if available. However, that can expose you to cache misses and heap overhead, and if you want to optimize that, this is where the fixed allocator comes in handy. However, that's a bit of a pain with alignment issues and a bit of a research topic, and so far it seems like your main goal is not to optimize insertion or sequential access quite as much as this contains check, so I'd start with the std::vector<Neuron*>.

Answer 2

You can get O(1) contains-check, O(1) insert and preserve insertion order. If you are using Java, looked at LinkedHashMap. If you are not using Java, look at LinkedHashMap and figure out a parallel data structure that does it or implement it yourself.

It's just a hashmap with a doubly linked list. The link list is to preserve order and the hashmap is to allow O(1) access. So when you insert an element, it makes an entry with the key, and the map will point to a node in the linked list where your data will reside. To look up, you go to the hash table to find the pointer directly to your linked list node (not the head), and get the value in O(1). To access them sequentially, you just traverse the linked list.

Answer 3

A heap sounds like it could be useful to you. It's like a tree, but the newest element is always inserted at the top, and then works its way down based on its value, so there is a method to quickly check if it's there.

Otherwise, you could store a hash table (quick method to check if the neuron is contained in the table) with the key for the neuron, and values of: the neuron itself, and the timestep upon which the neuron was inserted (to check its chronological insertion time).