Enumeration of trees from finite number of nodes

Abstract

Embodiments of methods, apparatuses, devices and/or systems for manipulating hierarchical sets of data are disclosed.

1 - 112 . (canceled) 
     
     
         113 . A method comprising:
 enumerating, by one or more hardware processors, tree hierarchies, in which a tree hierarchy comprises one or more signal data, configurable from a finite number (N) of nodes;   determining for the tree hierarchies, by the one or more hardware processors, natural numerals associated with particular ones of the tree hierarchies, the natural numerals being based, at least in part, on a predetermined association between the tree hierarchies and the natural numerals; and   storing, in at least one or more physical memories, the natural numerals, each natural numeral comprising one or more signal data, wherein the natural numerals are ordered to form an associated tree hierarchy that comprises an order of two or more component natural numerals.   
     
     
         114 . The method of  claim 113 , the method further comprising:
 identifying, by the one or more hardware processors, N−1 arrangements of subtree hierarchy slots coupled to a root node;   for an arrangement of subtree hierarchy slots:   determining, by the one or more hardware processors, one or more allocations of N−1 nodes among the subtree hierarchy slots in the arrangement, a subtree hierarchy slot being allocated a portion of the N−1 nodes; and   for the subtree hierarchy slots, enumerating, by the one or more hardware processors, one or more subtree hierarchies configurable from the portion of the N−1 nodes allocated to the subtree hierarchy slot.   
     
     
         115 . The method of  claim 114 , the method further comprising:
 associating, by the one or more hardware processors, the one or more subtree hierarchies for a subtree hierarchy slot with a natural numeral, wherein the natural numeral is based, at least in part, on the association between the one or more subtree hierarchies for the subtree hierarchy slot with the natural numeral; and   determining, by the one or more hardware processors, the natural numeral associated with a tree hierarchy from an allocation of the N−1 nodes among subtree hierarchies based, at least in part, upon a combination of the natural numerals associated with particular subtree hierarchies enumerated from the allocation of N−1 nodes.   
     
     
         116 . The method of  claim 115 , wherein the natural numeral associated with a tree hierarchy enumerated from an allocation of the N−1 nodes is based, at least in part, upon a set of ordered natural numerals associated with the particular subtree hierarchies enumerated from the allocation of N−1 nodes. 
     
     
         117 . The method of  claim 114 , wherein the method further comprises:
 identifying, by the one or more hardware processors, each tree hierarchy as being a composite of subtree hierarchies according to one of the N−1 arrangements of subtree hierarchy slots, N−1 nodes being allocated among the composite of subtree hierarchies, each subtree hierarchy in the composite of subtree hierarchies having a particular configuration of nodes which are allocated to that subtree hierarchy and being associated with a natural numeral based, at least in part, upon an association among the particular configuration of nodes which are allocated to that subtree hierarchy, and wherein the natural numeral associated with the tree hierarchy comprises a combination of the natural numerals associated with the subtree hierarchies in the composite of subtree hierarchies.   
     
     
         118 . The method of  claim 115 , the method further comprising:
 identifying an enumerated tree as being a composite of subtree hierarchies according to one of the N−1 arrangements of subtree hierarchy slots, N−1 nodes being allocated among the composite of subtree hierarchies, a subtree hierarchy in the composite of subtree hierarchies having a particular configuration of nodes which are allocated to the subtree hierarchy and being associated with a natural numeral based, at least in part, on the association between the one or more subtree hierarchies for the subtree hierarchy slot with the natural numeral, and   wherein the natural numeral associated with the tree hierarchy comprises a combination of the natural numerals associated with the subtree hierarchies in the composite of subtree hierarchies.   
     
     
         119 . The method of  claim 115 , wherein the method further comprises:
 identifying, by the one or more hardware processors, N−1 arrangements of subtree hierarchy slots, comprises identifying each of N−1 arrangements of subtree hierarchy slots coupled to the root node;   determining, by the one or more hardware processors, one or more allocations of N−1 nodes comprises determining the one or more allocations of N−1 nodes among the subtree hierarchy slots in the arrangement, each subtree hierarchy slot being allocated a portion of the N−1 nodes; and   enumerating, by the one or more hardware processors, one or more subtree hierarchies configurable from the portion of the N−1 nodes allocated to the subtree hierarchy slot comprises enumerating each of one or more subtree hierarchies configurable from the portion of the N−1 nodes allocated to the subtree hierarchy slot.   
     
     
         120 . The method of  claim 119 , the method further comprising:
 associating, by the one or more hardware processors, each of the one or more subtree hierarchies for each subtree hierarchy slot with a natural numeral, the natural numeral being based, at least in part, on the association between the one or more subtree hierarchies for the subtree hierarchy slot with the natural numeral; and   determining, by the one or more hardware processors, the natural numeral associated with each tree hierarchy enumerated from an allocation of the N−1 nodes, among subtree hierarchies based, at least in part, upon a combination of the natural numerals associated with particular subtree hierarchies enumerated from the allocation of N−1 nodes.   
     
     
         121 . The method of  claim 120 , wherein the natural numeral associated with each tree hierarchy enumerated from an allocation of the N−1 nodes is based, at least in part, upon a set of ordered natural numerals associated with the particular subtree hierarchies enumerated from the allocation of N−1 nodes. 
     
     
         122 . The method of  claim 113 , wherein the enumerating, by one or more hardware processors, tree hierarchies comprises:
 enumerating, by one or more hardware processors, the tree hierarchies configurable from exactly N nodes.   
     
     
         123 . An apparatus comprising:
 means for enumerating tree hierarchies, in which a tree hierarchy comprises one or more signal data, configurable from a finite number (N) of nodes;   means for determining for the tree hierarchies, natural numerals associated with particular ones of the tree hierarchies, the natural numerals being based, at least in part, on a predetermined association between the tree hierarchies and the natural numerals; and   means for storing, in at least one or more physical memories, the natural numerals, each natural numeral comprising one or more signal data, wherein the natural numerals are ordered to form an associated tree hierarchy that comprises an order of two or more component natural numerals.   
     
     
         124 . The apparatus of  claim 123 , the apparatus further comprising:
 means for identifying N−1 arrangements of subtree hierarchy slots coupled to a root node;   means for determining one or more allocations of N−1 nodes among the subtree hierarchy slots in an identified arrangement of subtree hierarchy slots, a subtree hierarchy slot being allocated a portion of the N−1 nodes; and   means for enumerating one or more subtree hierarchies, configurable from the portion of the N−1 nodes allocated to the subtree hierarchy slot.   
     
     
         125 . The apparatus of  claim 124 , the apparatus further comprising:
 means for associating the one or more subtree hierarchies for a subtree hierarchy slot with a natural numeral, the natural numeral being based, at least in part, on the association between the one or more subtree hierarchies for the subtree hierarchy slot with the natural numeral; and   means for determining the natural numeral associated with a tree hierarchy enumerated from an allocation of the N−1 nodes among subtree hierarchies based, at least in part, upon a combination of the natural numerals, associated with particular subtree hierarchies enumerated from the allocation of N−1 nodes.   
     
     
         126 . The apparatus of  claim 125 , wherein the natural numeral associated with a tree hierarchy enumerated from an allocation of the N−1 nodes is based, at least in part, upon a set of ordered natural numerals associated with the particular subtree hierarchies enumerated from the allocation of N−1 nodes. 
     
     
         127 . The apparatus of  claim 124 , the apparatus further comprising:
 means for identifying each tree hierarchy, represented by one or more signal data, as being a composite of subtree hierarchies according to one of the N−1 arrangements of subtree hierarchy slots, N−1 nodes being allocated among the composite of subtree hierarchies, each subtree hierarchy in the composite of subtree hierarchies having a particular configuration of nodes which are allocated to that subtree hierarchy and being associated with a natural numeral based, at least in part, upon an association among the particular configuration of nodes which are allocated to that subtree hierarchy, and wherein the natural numeral associated with the tree hierarchy comprises a combination of the natural numerals associated with the subtree hierarchies in the composite of subtree hierarchies.   
     
     
         128 . The apparatus of  claim 127 , the apparatus further comprising:
 means for identifying an tree hierarchy as being a composite of subtree hierarchies according to one of the N−1 arrangements of subtree hierarchy slots, N−1 nodes being allocated among the composite of subtree hierarchies, a subtree hierarchy in the composite of subtree hierarchies having a particular configuration of nodes which are allocated to the subtree hierarchy and being associated with a natural numeral based, at least in part, upon the association among the particular configuration of nodes which are allocated to that subtree hierarchy, and wherein the natural numeral associated with the tree hierarchy comprises a combination of the natural numerals associated with the subtree hierarchies in the composite of subtree hierarchies.   
     
     
         129 . The apparatus of  claim 124 , the apparatus further comprising:
 means for identifying N−1 arrangements of subtree hierarchy slots comprises means for identifying each of N−1 arrangements of subtree hierarchy slots coupled to the root node;   means for determining one or more allocations of N−1 nodes comprises means for determining one or more allocations of N−1 nodes among the subtree hierarchy slots in the arrangement, each subtree hierarchy slot being allocated a portion of the N−1 nodes; and   means for enumerating one or more subtree hierarchies, configurable from the portion of the N−1 nodes allocated to the subtree hierarchy slot comprises means for enumerating each of one or more subtree hierarchies configurable from the portion of the N−1 nodes allocated to the subtree hierarchy slot.   
     
     
         130 . The apparatus of  claim 129 , the apparatus further comprising:
 means for associating each of the one or more subtree hierarchies for each subtree hierarchy slot with a natural numeral, the natural numeral being based, at least in part, on the association between the one or more subtree hierarchies for the subtree hierarchy slot with the natural numeral; and   means for determining the natural numeral associated with each tree hierarchy from an allocation of the N−1 nodes among subtree hierarchies based, at least in part, upon a combination of the natural numerals associated with particular subtree hierarchies enumerated from the allocation of N−1 nodes, wherein the natural numeral associated with each tree enumerated from an allocation of the N−1 nodes is based, at least in part, upon a set of ordered natural numerals associated with the particular subtree hierarchies enumerated from the allocation of N−1 nodes.   
     
     
         131 . The apparatus of  claim 123 , wherein means for enumerating tree hierarchies comprises:
 means for enumerating the tree hierarchies configurable from exactly N nodes.   
     
     
         132 . An apparatus comprising a computing device, the computing device configured to:
 enumerate tree hierarchies, in which a tree hierarchy comprises one or more signal data, configurable from a finite number (N) of nodes;   determine for the tree hierarchies, natural numerals to be associated with particular ones of the tree hierarchies, the natural numerals to be based, at least in part, on a predetermined association between tree hierarchies and natural numerals; and   store, in at least one or more physical memories, the natural numerals, each natural numeral comprising one or more signal data, wherein the natural numerals are ordered to form an associated tree hierarchy that comprises an order of two or more component natural numerals.