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.
Please help me write a proper abstract based on the patent claims. 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.