Dynamic Memory-Aware Task-Tree Scheduling

Question

1. What have the authors contributed in "Dynamic memory-aware task-tree scheduling" ?

2. How is the processing size of a node proportional to its outgoing edge degree?

3. What is the problem of minimizing peak memory in a task graph?

4. What is the function that is used to re-allocate memory?

Accepted Answer

This paper revisits the execution of tree-shaped task graphs using multiple processors that share a bounded memory.. The authors present in this paper a novel heuristic solution that has a low complexity and is guaranteed to complete the tree within a given memory bound.. The authors compare their algorithm to state of the art strategies, and observe that on both actual execution trees and synthetic trees, they always perform better than these solutions, with average speedups between 1. 25 and 1. 45 on actual assembly trees.. Moreover, the authors show that the overhead of their algorithm is negligible even on deep trees ( 10 ), and would allow its runtime execution.. The key difficulty is to manage the order of the task executions so that the authors can achieve high parallelism while staying below the memory bound.

Accepted Answer

The processing size of a node is 10% of its outgoing edge weight and it processing time is proportional to its outgoing edge degree.

Accepted Answer

In the realm of sparse direct solvers, the problem of scheduling a tree so as to minimize peak memory has first been investigated by Liu [11] in the sequential case: he proposed an algorithm to find a peakmemory minimizing traversal of a task tree when the traversal is required to correspond to a postorder traversal of the tree.

Accepted Answer

At the beginning of the schedule, or each time a task completes, the MemBooking algorithm performs these three consecutive operations:1. Memory re-allocation: DispatchMemory (Algorithm 3) reallocates the memory used by a node that just finished its execution.

Accepted Answer

Note that MemBookingRedTree is not able to schedule most trees in a very constrained memory environment: when the memory bound is smaller that 1.4 times the minimum memory peak of a sequential postorder processing, MemBookingRedTree is unable to schedule 33% of the trees (or more) and thus is not included in the plot.

Accepted Answer

The authors want to process the resulting task tree on a parallel system made of p computing units, also named processors, sharing a global memory of limited size M .

Accepted Answer

Note that the two heuristics from the literature give very similar results: this is explained by the fact that MemBookingRedTree first transforms the trees before applying a smart booking strategy: on these trees, adding fictitious edges has the same effect than booking to much memory (as Activation does) and hinders the benefit of the booking strategy.

Accepted Answer

To give some hindsight on the importance of this factor, the authors decided to study the speedup of MemBooking compared to that of Activation as a function of the tree height.

Accepted Answer

Note that peak memory minimization is still a crucial question for direct solvers, as highlighted by Agullo et al. [2], who study the effect of processor mapping on memory consumption for multifrontal methods.

Accepted Answer

The authors have noticed in the simulations described in the next section that with eight processors, this new lower bound improved the classical lower bound in 22% of the case for on actual assembly trees, and in these cases the average increase in the bound was 46%.

Dynamic Memory-Aware Task-Tree Scheduling

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Most frequently asked questions

1. What have the authors contributed in "Dynamic memory-aware task-tree scheduling" ?

2. How is the processing size of a node proportional to its outgoing edge degree?

3. What is the problem of minimizing peak memory in a task graph?

4. What is the function that is used to re-allocate memory?

5. how many trees can be scheduled in a given memory environment?

6. How do the authors schedule a task tree?

7. What is the difference between the two heuristics?

8. What is the importance of the speedup factor?

9. What is the importance of peak memory minimization for direct solvers?

10. How many processors did the simulations improve?

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Citations

Dynamic Memory-Aware Task-Tree Scheduling

Scheduling task graphs on modern computing platforms

Modeling and Timing Analysis for Microkernel-Based Real-Time Embedded System

Algorithms for tree-shaped task partition and allocation on heterogeneous multiprocessors

Timing Analysis for Microkernel-based Real-Time Embedded System.

References

A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling

Various optimizers for single‐stage production

Direct Methods for Sparse Linear Systems

Hybrid scheduling for the parallel solution of linear systems

Scheduling Data-IntensiveWorkflows onto Storage-Constrained Distributed Resources

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