Efficient Nonserial Polyadic Dynamic Programming on the Cell Processor

Abstract

Dynamic programming (DP) is an effective technique for many search and optimization problems. However, the high arithmetic complexity limits its extensive use. Although modern processor architectures with multiple cores and SIMD (single instruction multiple data) instructions provide increasingly high computing power, even the state-of-the-art fully optimized algorithm still largely underutilizes modern multi-core processors. In this paper we propose to improve one family of DP, nonserial polyadic DP (NPDP), targeting a heterogeneous multi-core architecture, the Cell Broadband Engine. We first design a new data layout which efficiently utilizes the onchip memory system of the Cell processor. Next we devise a CellNPDP algorithm with two tiers. The first tier is a SPE (a co-processor on the Cell processor) procedure which efficiently computes a block of data that can fit into one SPE's local store. The second tier is a parallel procedure which enables all SPEs to efficiently compute all blocks of data. To evaluate CellNPDP, we use both performance modeling and experiments. The performance model reveals that the processor utilization of NPDP can be independent of the problem size. To empirically evaluate CellNPDP, we use two platforms: the IBM QS20 dual-Cell blade and a CPU platform with two latest quad-core CPUs. On both platforms, the processor utilization of CellNPDP is larger than 60%, which demonstrates that our optimizations and CellNPDP can be architecture-independent. Compared to the state-of-the-art fully optimized algorithm on the CPU platform, CellNPDP is 44-fold faster for singleprecision and 28-fold faster for double-precision, which is a significant improvement to NPDP.

Statically Optimal Binary Search Tree Computation Using Non-Serial Polyadic Dynamic Programming on GPU's

“…This implementationprovidesaparallelalgorithmforamulticorearchitecturethatexploitsfinegrain parallelism and non-uniform data dependence of a non-serial polyadic dynamic programming algorithm.Thisarticleutilizestilingtoovercomethelimitationsofcachememorywhenverylarge datasetsareusedduringcomputationandachievesconsiderableperformanceimprovement. Liu, Wang,Jiang,Li,&Yang,(2011)providesaparallelimplementationofZukeralgorithmonCell Broadband engine. They design data structures for that particular architecture and also address communicationissuesbetweenthreads.…”

Space-Time Loop Tiling for Dynamic Programming Codes

“…Increasing dynamic programming code performance is not a trivial problem because, in general, that code exposes affine non-uniform data dependence patterns typical for nonserial polyadic dynamic programming (NPDP) [1], preventing tiling the innermost loop in a loop nest that restricts code locality improvement. There are many state-of-theart manual transformations for DP algorithms [2][3][4][5] and dedicated software [6][7][8].…”

Tiling Nussinov’s RNA folding loop nest with a space-time approach

“…The Nussinov kernel involves mathematical operations over affine control loops whose iteration space can be represented by the polyhedral model [11]. However, the Nussinov RNA folding acceleration is still a challenging task for modern compilers because that code is within nonserial polyadic dynamic programming (NPDP), which is a particular family of dynamic programming with non-uniform data dependences, and it, as mentioned above, is more difficult to be optimized [7].…”