P3D-DFS

Chapel-based implementation of a Productivity- and Performance-aware Parallel Distributed Depth-First Search algorithm, namely P3D-DFS. The latter is a generic and general algorithm that can be instantiated on numerous tree-based problems. It is based on the DistBag-DFS distributed data structure, which employs an underlying Work Stealing (WS) mechanism to balance workload across multiple Chapel's locales.

Chapel

Chapel is a programming language designed for productive parallel computing on large-scale systems. Chapel supports a multi-threaded execution model via high-level abstractions for data parallelism, task parallelism, concurrency, and nested parallelism. Chapel's locale type enables users to specify and reason about the placement of data and tasks on a target architecture in order to tune for locality and affinity. Chapel supports global-view data aggregates with user-defined implementations, permitting operations on distributed data structures to be expressed in a natural manner.

Our implementation relies on Chapel 2.3.0 and might not compile and run for other versions.

The DistBag-DFS distributed data structure

The DistBag-DFS distributed data structure is a parallel-safe distributed multi-pool implementation that is unordered and incorporates a WS mechanism that balances workload across multiple locales, transparently to the user. It can contain either predefined-Chapel types, user-defined types or external ones (e.g. C structures). This data structure has been derived from the DistBag data structure supplied is the DistributedBag Chapel's module, and revised in two different ways: (1) we propose a new scheduling policy of its elements as well as a new synchronization mechanism using non-blocking split-deques, and (2) we redefine the underlying WS mechanism.

Compilation & Execution

• Step 1: Set up your Chapel environment according to the machine on which your code is expected to run, and build Chapel. Some predefined configuration scripts are provided in the chpl_config directory.
• Step 2: Compile with make and execute with:

./main.o --mode=distributed ${problem-specific options} -nl 2

where:

• --mode is the execution mode, i.e. sequential, multicore, or distributed;
• For the list of supported problems and options, see below;
• -nl is the number of Chapel's process(es), typically the number of computer nodes in distributed setting.

Supported problems

Branch-and-Bound algorithms (B&B)

B&B are exact optimization algorithms exploring implicitly constructed trees by successively applying branching, bounding and pruning operators. Each tree node corresponds to a subproblem (the initial problem defined on a restricted domain) and children nodes are obtained by further restricting the search space.

• The Permutation Flow-shop Scheduling problem (PFSP)
• The 0/1-Knapsack problem

Backtracking algorithms

Backtracking is an algorithmic technique for solving problems recursively by trying to build a solution incrementally, one piece at a time, removing those solutions that fail to satisfy the constraints of the problem at any point in time.

• The Unbalanced Tree-Search benchmark (UTS)
• The N-Queens problem

Experimental results

The following figures show the absolute speed-up achieved by P3D-DFS and MPI+X baseline implementations on large unbalanced tree-based problems, considering different granularities (fine, medium, coarse). For each figure, most coarse-grained is top-right, most fine-grained is bottom-left.

Fig.1 - P3D-DFS vs. MPI-PBB on B&B applied to PFSP.

Fig.2 - P3D-DFS vs. MPI-PUTS on UTS.

Related publications

1. G. Helbecque, T. Carneiro, N. Melab, J. Gmys, P. Bouvry. PGAS Data Structure for Unbalanced Tree-Based Algorithms at Scale. Computational Science – ICCS 2024 (ICCS). vol 14834, 2024. DOI: 10.1007/978-3-031-63759-9_13.
2. G. Helbecque, J. Gmys, N. Melab, T. Carneiro, P. Bouvry. Parallel distributed productivity-aware tree-search using Chapel. Concurrency Computation Practice Experience, 35(27):e7874, 2023. DOI: 10.1002/cpe.7874.
3. G. Helbecque, J. Gmys, T. Carneiro, N. Melab, P. Bouvry. Towards a scalable load balancing for productivity-aware tree-search. The 10th Annual Chapel Implementers and Users Workshop (CHIUW), June 2023, online.
4. G. Helbecque, J. Gmys, N. Melab, T. Carneiro, P. Bouvry. Productivity-aware Parallel Distributed Tree-Search for Exact Optimization. International Conference on Optimization and Learning (OLA), May 2023, Malaga, Spain.