Parallel Online Directed Acyclic Graph Exploration for Atlasing Soft-Matter Assembly Configuration Spaces

TL;DR

The paper formalizes a version of parallel online directed acyclic graph (DAG) exploration, general enough to be readily mapped to many computational scenarios, and demonstrates the problem's occurrence in the scenario of energy landscape roadmapping or atlasing under pair-potentials.

Abstract

The paper formalizes a version of parallel online directed acyclic graph (DAG) exploration, general enough to be readily mapped to many computational scenarios. In both the offline and online versions, vertices are weighted with the work units required for their processing, at least one parent must be completely processed before a child is processed, and at any given time only one processor can work on any given vertex. The online version has the following additional natural restriction: only after a vertex is processed, are its required work units or its children known. Using the Actor Model of parallel computation, it is shown that a natural class of parallel online algorithms meets a simple competitive ratio bound. We demonstrate and focus on the problem's occurrence in the scenario of energy landscape roadmapping or atlasing under pair-potentials, a highly compute-and-storage intensive modeling component integral to diverse applications involving soft-matter assembly. The method is experimentally validated using a C++ Actor Framework (CAF) software implementation built atop EASAL (Efficient Atlasing and Search of Assembly Landscapes), a substantial opensource software suite, running on multiple CPU cores of the HiperGator supercomputer, demonstrating linear speedup results.

Figures (5)

• Figure 1: Stratification of the Roadmap: (a) shows a portion of the roadmap for the inset pair of input rigid molecular component s. Each node represents a region of configurations satisfying a specific set of active constraints. The red nodes represent regions with 2 active constraints. Each successive stratum (from left to right) contains regions with one additional active constraint until we reach the pink leaf nodes. (b) Regions in the roadmap shown with their Cartesian configuration sweeps. Each sweep is the union of Cartesian configurations in the corresponding region. (c) Ancestors and descendants of a node, shown with their active constraint sets. Figure adapted, courtesy PrabhuEtAl2020.
• Figure 2: Optimal and non-optimal allocation of tasks to processors. The horizontal axis represents time units and the vertical axis shows the processors. (a) In the optimal case, $T=2$, and in the non-optimal case, the $T=3$, making the competitive ratio 1.5. (b) In the optimal case, $T=4$, and in the non-optimal case, $T=7$, giving a competitive ratio of 1.75.
• Figure 3: List of rigid molecular component s used in the experiments.: (a) Narrow Convex (6 Atoms). (b) Narrow Concave (6 Atoms). (c) Narrow Concave (10 Atoms) (d) Wide Concave (20 Atoms).
• Figure 4: The number of compute cores used on the x-axis and the normalized wall time for atlasing the molecules (indicated at the top of every sub-figure) on the y-axis. Here r_s_ratio is the ratio of the average atomic radius in the molecule to the stepsize.
• Figure 5: The number of compute cores on the x-axis and the average number of atlas nodes discovered per second on the y-axis, while atlasing the molecules (indicated at the top of every sub-figure). Here r_s_ratio is the ratio of the average atomic radius in the molecule to the stepsize.