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===Sublinear data structures===
When data is already organized into a [[data structure]], it may be possible to perform selection in an amount of time that is sublinear in the number of values. As a simple case of this, for data already sorted into an array, selecting the {{nowrap|<math>k</math>th}} element may be performed by a single array lookup, in constant time.
For data organized as a [[binary heap]] it is possible to perform selection in {{nowrap|time <math>O(k)</math>,}} independent of the size <math>n</math> of the whole tree, and faster than the <math>O(k\log n)</math> time bound that would be obtained from {{nowrap|[[best-first search]].{{r|frederickson}}}} This same method can be applied more generally to data organized as any kind of heap-ordered tree (a tree in which each node stores one value in which the parent of each non-root node has a smaller value than its child). This method of performing selection in a heap has been applied to problems of listing multiple solutions to combinatorial optimization problems, such as finding the [[k shortest path routing|{{mvar|k}} shortest paths]] in a weighted graph, by defining a [[State space (computer science)|state space]] of solutions in the form of an [[implicit graph|implicitly defined]] heap-ordered tree, and then applying this selection algorithm to this {{nowrap|tree.{{r|kpaths}}}} In the other direction, linear time selection algorithms have been used as a subroutine in a [[priority queue]] data structure related to the heap, improving the time for extracting its {{nowrap|<math>k</math>th}} item from <math>O(\log n)</math> to {{nowrap|<math>O(\log^* n+\log k)</math>;}} here <math>\log^* n</math> is the {{nowrap|[[iterated logarithm]].{{r|bks}}}}
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