A parallel and incremental algorithm for efficient unique signature discovery on DNA databases

Abstract

Background: DNA signatures are distinct short nucleotide sequences that provide valuable information that is used for various purposes, such as the design of Polymerase Chain Reaction primers and microarray experiments. Biologists usually use a discovery algorithm to find unique signatures from DNA databases, and then apply the signatures to microarray experiments. Such discovery algorithms require to set some input factors, such as signature length l and mismatch tolerance d, which affect the discovery results. However, suggestions about how to select proper factor values are rare, especially when an unfamiliar DNA database is used. In most cases, biologists typically select factor values based on experience, or even by guessing. If the discovered result is unsatisfactory, biologists change the input factors of the algorithm to obtain a new result. This process is repeated until a proper result is obtained. Implicit signatures under the discovery condition (l, d) are defined as the signatures of length < or = l with mismatch tolerance > or = d. A discovery algorithm that could discover all implicit signatures, such that those that meet the requirements concerning the results, would be more helpful than one that depends on trial and error. However, existing discovery algorithms do not address the need to discover all implicit signatures.

Results: This work proposes two discovery algorithms - the consecutive multiple discovery (CMD) algorithm and the parallel and incremental signature discovery (PISD) algorithm. The PISD algorithm is designed for efficiently discovering signatures under a certain discovery condition. The algorithm finds new results by using previously discovered results as candidates, rather than by using the whole database. The PISD algorithm further increases discovery efficiency by applying parallel computing. The CMD algorithm is designed to discover implicit signatures efficiently. It uses the PISD algorithm as a kernel routine to discover implicit signatures efficiently under every feasible discovery condition.

Conclusions: The proposed algorithms discover implicit signatures efficiently. The presented CMD algorithm has up to 97% less execution time than typical sequential discovery algorithms in the discovery of implicit signatures in experiments, when eight processing cores are used.

Figure 1

An example of the first potential problem of parallel signature discovery. The tasks can be completed in 22 time units by a single-processor computer. The overall processing time is 15 units for a two-processor computer, which exceeds the optimal processing time, 11 units.

Figure 2

The result of moving long tasks forward in the processing order list. The long tasks are moved forward in the processing order list in Figure 2, yielding the new processing order list. The overall processing time for a two-processor computer is 11 units, which equals the optimal processing time.

Figure 3

An example of the second potential problem of parallel signature discovery. The tasks can be completed in 24 units by a single-processor computer. The overall processing time is 19 units for a two-processor computer, which exceeds the optimal processing time, 12 units.

Figure 4

The result of moving long tasks forward in the processing order list. The long tasks are moved forward in the processing order list in Figure 4, yielding the new processing order list. The overall processing time for a two-processor computer is 16 units, which still exceeds the optimal processing time.

Figure 5

The result of dividing long tasks into short tasks in the processing order list. Task F in Figure 5 is divided into two tasks with identical processing times, yielding the new task list. The overall processing time for a two-processor computer is 12 units, which equals the optimal processing time.