Finding exact hitting set solutions for systems biology applications using heterogeneous GPU clusters

A hybrid CPU‐GPU‐MIC algorithm for minimal hitting set enumeration

“…However, such algorithm is not capable of dealing with high dimension input sets (order of thousands of variables) and multiple GPUs. In our previous works, we also followed an exhaustive search driven approach, though with multiple GPUs and with hybrid CPU‐CPU‐MICs platforms, with many improvements in regards to scalability, memory consumption, and processing performance which enabled us to solve synthetic HSP instances with high dimension.…”

“…In contrast with our previous works, here, we are concerned about the Minimal Hitting Set (MHS for short) enumeration problem. In this problem, we call a subset H ⊆ X as a Minimal Hitting Set of if H is a Hitting Set (ie, H satisfies Equation ), but no other subset is a Hitting Set as well.…”

“…However, this growing effort is still small mostly due to two major hindrances: (i) these heterogeneous platforms demand hybrid algorithms to efficiently exploit all co‐processor architectures in conjunction and (ii) the efficiency of the usage of CPU‐GPU‐MIC platforms in a wide range of applications is not clearly known. In regards to HSP, a first attempt performed by our previous works to solve this problem with accelerator devices was to perform exhaustive search with multiple GPUs and with hybrid CPU‐GPU‐MICs platforms, where we could solve synthetic HSP instances constituted by thousands of variables and constraints. To the best of our knowledge, there is no exact MHS enumeration algorithm in the literature that makes use of accelerator devices (CPUs, GPUs, or MICs), either separately or in conjunction.…”

“…This satisfiability reasoning is present, for example, in problems from Systems Biology, such as genomic reversal distance, 1 classification models, 2 polymerase chain reaction experiments, 3 and gene regulatory networks (GRN) inference. [4][5][6][7][8] A common characteristic of these problems is that the input size of the modeled MHS and HSP instances is often large, making the retrieval of the exact solutions impracticable for traditional algorithms. Moreover, the MHS enumeration problem adds two major difficulties in comparison to the traditional HSP: (i) an MHS solution H must be a hitting set (similarly with HSP), but no other subset of H is allowed to be a hitting set, and (ii) we are not only concerned to enumerate MHSs of minimum size but as well all MHSs from a minimum size where solutions exist to a certain maximum size k. These difficulties lead to a considerably larger search space, and thus, enumerating MHSs of any size even for small instances is often impracticable for exact algorithms.With the advent of new accelerator technologies such as Many Integrated Core (MIC) architectures, 9 hybrid heterogeneous platforms composed of CPUs, GPUs, and MICs became a common occurrence in research centers.…”

“…In our previous works, 7,8 we proposed an enhanced exhaustive search algorithm for HSP that enumerates and evaluates all candidate solutions, which are encoded as combinations of variables of X, in increasing order of cardinality i, 1 ≤ i ≤ k and stops when a solution is found. It is important to note that, in this previous version, the algorithm stops at the smallest cardinality in which solutions exist, thus not necessarily executing up to cardinality k. In this work, we propose an extension of this algorithm that enables the enumeration of all MHSs up to cardinality k.…”