1. Adaptable Priority Queues1 3 a 5 g 4 e © 2013 Goodrich, Tamassia, Goldwasser

2. Adaptable Priority Queues2 Items and 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 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() © 2013 Goodrich, Tamassia, Goldwasser

3. Adaptable Priority Queues3 Example  Online trading system where orders to purchase and sell a stock are stored in two priority queues (one for sell orders and one for buy orders) as (p,s) entries: The key, p, of an order is the price The value, s, for an entry is the number of shares A buy order (p,s) is executed when a sell order (p’,s’) with price p’ s) A sell order (p,s) is executed when a buy order (p’,s’) with price p’>p is added (the execution is complete if s’>s)  What if someone wishes to cancel their order before it executes?  What if someone wishes to update the price or number of shares for their order? © 2013 Goodrich, Tamassia, Goldwasser

4. Adaptable Priority Queues4 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). © 2013 Goodrich, Tamassia, Goldwasser

5. Adaptable Priority Queues5 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 © 2013 Goodrich, Tamassia, Goldwasser

6. Adaptable Priority Queues6 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 header nodes/positions items 2 c 4 c 5 c 8 c © 2013 Goodrich, Tamassia, Goldwasser

7. Adaptable Priority Queues7 Heap Implementation  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 4 a 2 d 6 b 8 g 5 e 9 c © 2013 Goodrich, Tamassia, Goldwasser

8. Adaptable Priority Queues8 Performance  Improved times thanks to location-aware items are highlighted in red MethodUnsorted ListSorted ListHeap len, is_empty O(1)O(1)O(1) add O(1)O(n)O(log n) min O(n)O(1)O(1) remove_min O(n)O(1)O(log n) remove O(1)O(1)O(log n) update O(1)O(n)O(log n) © 2013 Goodrich, Tamassia, Goldwasser