Processing data using sequential dependencies

Abstract

Methods and apparatus for processing data using sequential dependencies are disclosed herein. An example method includes modifying a first number of values in a sequence of a data set to generate a modified sequence such that each difference between each successive pair of values is within a threshold. A satisfiability metric is determined for the modified sequence based on a relationship between a number of modifications to the values in the sequence and a size of the sequence.

We claim: 
     
         1 . A method, comprising:
 modifying, via a processor, a first number of values in a sequence of a data set to generate a modified sequence such that each difference between each pair of successive values is within a threshold; and   determining, via the processor, a satisfiability metric for the modified sequence based on a relationship between a number of modifications to the values in the sequence and a size of the sequence.   
     
     
         2 . The method of  claim 1 , wherein the sequence represents investment data. 
     
     
         3 . The method of  claim 1 , wherein the sequence represents traffic data. 
     
     
         4 . The method of  claim 1 , wherein the sequence represents weather data. 
     
     
         5 . The method of  claim 1 , wherein the satisfiability metric represents a ratio between the number of modifications and the size of the sequence. 
     
     
         6 . The method of  claim 1 , wherein the sequence is a first sequence, the modified sequence is a first modified sequence, the satisfiability metric is a first satisfiability metric, and further comprising:
 modifying a second number of values in a second sequence of the data set to generate a second modified sequence;   determining a second satisfiability metric for the second modified sequence based on a relationship between a number of modifications to values in the second sequence and a size of the second sequence; and   selecting one of the first or second sequences based on a comparison of the first satisfiability metric and the second satisfiability metric.   
     
     
         7 . The method of  claim 6 , wherein the first sequence and the second sequence are subsets of the data set. 
     
     
         8 . The method of  claim 6 , further comprising summarizing the selection of the first sequence or second sequence in a table. 
     
     
         9 . The method of  claim 6 , wherein selecting one of the first sequence or the second sequence comprises determining which of the first satisfiability metric or the second satisfiability metric corresponds to a lesser number of modifications in proportion to the respective size of the first sequence and the second sequence. 
     
     
         10 . A machine readable memory comprising instructions which, when executed, cause a machine to perform operations comprising:
 modifying a first number of values in a sequence of a data set to generate a modified sequence such that each difference between each successive pair of values satisfies a threshold; and   determine a satisfiability metric for the modified sequence based on a relationship between a number of modifications to the values in the sequence and a size of the sequence.   
     
     
         11 . The memory of  claim 10 , wherein determining the satisfiability metric comprises determining a ratio between the number of modifications and the size of the sequence. 
     
     
         12 . The memory of  claim 10 , wherein the sequence is a first sequence, the modified sequence is a first modified sequence, the satisfiability metric is a first satisfiability metric, and further comprising instructions which, when executed, cause the machine to perform operations comprising:
 modifying a second number of values in a second sequence of the data set to generate a second modified sequence;   determining a second satisfiability metric for the second modified sequence based on a relationship between a number of modifications to values in the second sequence and a size of the second sequence; and   selecting one of the first or second sequences based on a comparison of the first satisfiability metric and the second satisfiability metric.   
     
     
         13 . The memory of  claim 12 , wherein the first sequence and the second sequence are subsets of the data set. 
     
     
         14 . The memory of  claim 12 , further comprising summarizing the selection of the first sequence or second sequence in a table. 
     
     
         15 . The memory of  claim 12 , wherein selecting one of the first sequence or the second sequence comprises determining which of the first satisfiability metric or the second satisfiability metric corresponds to a lesser number of modifications in proportion to the respective size of the first sequence and the second sequence. 
     
     
         16 . An apparatus comprising:
 a memory comprising machine readable instructions; and   a processor which, when executing the instructions, performs operations comprising:
 modifying a first number of values in a sequence of a data set to generate a modified sequence such that each difference between each successive pair of values meets a threshold; and 
 determining a satisfiability metric for the modified sequence based on a relationship between a number of modifications to the values in the sequence and a size of the sequence. 
   
     
     
         17 . The apparatus of  claim 16 , wherein determining the satisfiability metric comprises determining a ratio between the number of modifications and the size of the sequence. 
     
     
         18 . The apparatus of  claim 16 , wherein the sequence is a first sequence, the modified sequence is a first modified sequence, the satisfiability metric is a first satisfiability metric, and the operations further comprise:
 modifying a second number of values in a second sequence of the data set to generate a second modified sequence;   determining a second satisfiability metric for the second modified sequence based on a relationship between a number of modifications to values in the second sequence and a size of the second sequence; and   selecting one of the first or second sequences based on a comparison of the first satisfiability metric and the second satisfiability metric.   
     
     
         19 . The apparatus of  claim 18 , wherein the first sequence and the second sequence are subsets of the data set. 
     
     
         20 . The apparatus of  claim 18 , wherein the operations further comprise determining which of the first satisfiability metric or the second satisfiability metric corresponds to a lesser number of modifications in proportion to the respective size of the first sequence and the second sequence.