Package org.jheaps.tree

Class BinaryTreeSoftAddressableHeap<K,V>

java.lang.Object
org.jheaps.tree.BinaryTreeSoftAddressableHeap<K,V>
Type Parameters:
K - the type of keys maintained by this heap
V - the type of values maintained by this heap
All Implemented Interfaces:
Serializable, AddressableHeap<K,V>, MergeableAddressableHeap<K,V>
public class BinaryTreeSoftAddressableHeap<K,V> extends Object implements MergeableAddressableHeap<K,V>, Serializable
A binary tree soft addressable heap. The heap is sorted according to the natural ordering of its keys, or by a Comparator provided at heap creation time, depending on which constructor is used.

If n elements are inserted into a soft heap, then up to εn of the elements still contained in the heap, for a given error parameter ε, may be corrupted, i.e., have their keys artificially increased. In exchange for allowing these corruptions, each soft heap operation is performed in O(log 1/ε) amortized time. Note that n here is the number of elements inserted into the heaps, not the current number of elements in the heap which may be considerably smaller. Moreover the user has no control on which elements may be corrupted.

This variant of the soft heap is due to Kaplan and Zwick, described in detail in the following paper:

  • Haim Kaplan and Uri Zwick, A simpler implementation and analysis of Chazelle's Soft Heaps, In Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2009), 477--485, 2009.

Note that the operation decreaseKey() always throws an UnsupportedOperationException as a soft heap does not support such an operation.

All the above bounds, however, assume that the user does not perform cascading melds on heaps such as: 

 d.meld(e);
 c.meld(d);
 b.meld(c);
 a.meld(b);
The above scenario, although efficiently supported by using union-find with path compression, invalidates the claimed bounds.

Note that the ordering maintained by a soft heap, like any heap, and whether or not an explicit comparator is provided, must be consistent with equals if this heap is to correctly implement the Heap interface. (See Comparable or Comparator for a precise definition of consistent with equals.) This is so because the Heap interface is defined in terms of the equals operation, but a pairing heap performs all key comparisons using its compareTo (or compare) method, so two keys that are deemed equal by this method are, from the standpoint of the heap, equal. The behavior of a heap is well-defined even if its ordering is inconsistent with equals; it just fails to obey the general contract of the Heap interface.

Note that this implementation is not synchronized. If multiple threads access a heap concurrently, and at least one of the threads modifies the heap structurally, it must be synchronized externally. (A structural modification is any operation that adds or deletes one or more elements or changing the key of some element.) This is typically accomplished by synchronizing on some object that naturally encapsulates the heap.

Author:
Dimitrios Michail
See Also:

  • Constructor Details

    • BinaryTreeSoftAddressableHeap

      public BinaryTreeSoftAddressableHeap(double errorRate)
      Constructs a new, empty heap, using the natural ordering of its keys. All keys inserted into the heap must implement the Comparable interface. Furthermore, all such keys must be mutually comparable: k1.compareTo(k2) must not throw a ClassCastException for any keys k1 and k2 in the heap. If the user attempts to put a key into the heap that violates this constraint (for example, the user attempts to put a string key into a heap whose keys are integers), the insert(Object key) call will throw a ClassCastException.
      Parameters:
      errorRate - the error rate
      Throws:
      IllegalArgumentException - if the error rate is less or equal to zero
      IllegalArgumentException - if the error rate is greater or equal to one

    • BinaryTreeSoftAddressableHeap

      public BinaryTreeSoftAddressableHeap(double errorRate, Comparator<? super K> comparator)
      Constructs a new, empty heap, ordered according to the given comparator. All keys inserted into the heap must be mutually comparable by the given comparator: comparator.compare(k1, k2) must not throw a ClassCastException for any keys k1 and k2 in the heap. If the user attempts to put a key into the heap that violates this constraint, the insert(Object key) call will throw a ClassCastException.
      Parameters:
      errorRate - the error rate
      comparator - the comparator that will be used to order this heap. If null, the natural ordering of the keys will be used.
      Throws:
      IllegalArgumentException - if the error rate is less or equal to zero
      IllegalArgumentException - if the error rate is greater or equal to one

  • Method Details

    • isEmpty

      public boolean isEmpty()
      Returns true if this heap is empty.
      Specified by:
      isEmpty in interface AddressableHeap<K,V>
      Returns:
      true if this heap is empty, false otherwise

    • size

      public long size()
      Returns the number of elements in the heap.
      Specified by:
      size in interface AddressableHeap<K,V>
      Returns:
      the number of elements in the heap

    • comparator

      public Comparator<? super K> comparator()
      Returns the comparator used to order the keys in this AddressableHeap, or null if this heap uses the natural ordering of its keys.
      Specified by:
      comparator in interface AddressableHeap<K,V>
      Returns:
      the comparator used to order the keys in this heap, or null if this addressable heap uses the natural ordering of its keys

    • clear

      public void clear()
      Clear all the elements of the heap. After calling this method all handles should be considered invalidated and the behavior of methods AddressableHeap.Handle.decreaseKey(Object) and AddressableHeap.Handle.delete() is undefined.
      Specified by:
      clear in interface AddressableHeap<K,V>

    • meld

      public void meld(MergeableAddressableHeap<K,V> other)
      Meld a heap into the current heap. After the operation the other heap will be empty and will not permit further insertions.
      Specified by:
      meld in interface MergeableAddressableHeap<K,V>
      Parameters:
      other - a merge-able heap
      Throws:
      IllegalArgumentException - if other has a different error rate

    • insert

      public AddressableHeap.Handle<K,V> insert(K key, V value)
      Insert a new element into the heap.
      Specified by:
      insert in interface AddressableHeap<K,V>
      Parameters:
      key - the element's key
      value - the element's value
      Returns:
      a handle for the newly added element

    • insert

      public AddressableHeap.Handle<K,V> insert(K key)
      Insert a new element into the heap with a null value.
      Specified by:
      insert in interface AddressableHeap<K,V>
      Parameters:
      key - the element's key
      Returns:
      a handle for the newly added element

    • findMin

      public org.jheaps.tree.BinaryTreeSoftAddressableHeap.SoftHandle<K,V> findMin()
      Find an element with the minimum key.
      Specified by:
      findMin in interface AddressableHeap<K,V>
      Returns:
      a handle to an element with minimum key

    • deleteMin

      public AddressableHeap.Handle<K,V> deleteMin()
      Delete and return an element with the minimum key. If multiple such elements exists, only one of them will be deleted. After the element is deleted the handle is invalidated and only method AddressableHeap.Handle.getKey() and AddressableHeap.Handle.getValue() can be used.
      Specified by:
      deleteMin in interface AddressableHeap<K,V>
      Returns:
      a handle to the deleted element with minimum key