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Adaptable Priority Queues

a. 3. g. e. 5. 4. Adaptable Priority Queues. An item stores a (key, value) pair Item fields: _key : the key associated with this item _value : the value paired with the key associated with this item. Priority Queue ADT: add (k, x) inserts an item with key k and value x

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Adaptable Priority Queues

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  1. a 3 g e 5 4 Adaptable Priority Queues Adaptable Priority Queues

  2. An item stores a (key, value) pair Item fields: _key: the key associated with this item _value: the value paired with the key associated with this item Priority Queue ADT: add(k, x)inserts an item with key k and value x remove_min()removes and returns the item with smallest key min()returns, but does not remove, an item with smallest key len(P), is_empty() Items and Priority Queues Adaptable Priority Queues

  3. standby airline passenger application • A standby passenger with a pessimistic attitude may become tired of waiting and decide to leave ahead of the boarding time • Another standby passenger finds her gold frequent-flyer card and shows it to the agent Adaptable Priority Queues

  4. Methods of the Adaptable Priority Queue ADT • remove(loc): Remove from P and return item e for locator loc. • update(loc,k,v): Replace the key-value pair for locator, loc, with (k,v). Adaptable Priority Queues

  5. Locators • A locator-aware item identifies and tracks the location of its (key, value) object within a data structure • Intuitive notion: • Coat claim check • Valet claim ticket • Reservation number • Main idea: • Since items are created and returned from the data structure itself, it can return location-aware items, thereby making future updates easier Adaptable Priority Queues

  6. List Implementation • A location-aware list item is an object storing • key • value • position (or rank) of the item in the list • In turn, the position (or array cell) stores the entry • Back pointers (or ranks) are updated during swaps trailer nodes/positions header c c 5 8 c c 2 4 items Adaptable Priority Queues

  7. Heap Implementation d 2 • A location-aware heap item is an object storing • key • value • position of the item in the underlying heap • In turn, each heap position stores an item • Back pointers are updated during item swaps a b 4 6 g e c 8 5 9 Adaptable Priority Queues

  8. Performance • Improved times thanks to location-aware items are highlighted in red Method Unsorted List Sorted List Heap len, is_emptyO(1) O(1) O(1) addO(1) O(n) O(log n) minO(n) O(1) O(1) remove_minO(n) O(1) O(log n) removeO(1)O(1)O(logn) updateO(1)O(n) O(logn) Adaptable Priority Queues

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