Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scheduling Trees of Malleable Tasks for Sparse Linear Algebra   Scientific workloads are often described as directed acyclic task graphs. In
this paper, we focus on the multifrontal factorization of sparse matrices,
whose task graph is structured as a tree of parallel tasks. Among the existing
models for parallel tasks, the concept of malleable tasks is especially
powerful as it allows each task to be processed on a time-varying number of
processors. Following the model advocated by Prasanna and Musicus for matrix
computations, we consider malleable tasks whose speedup is $p^\alpha$, where
$p$ is the fractional share of processors on which a task executes, and
$\alpha$ ($0 < \alpha \leq 1$) is a parameter which does not depend on the
task. We first motivate the relevance of this model for our application with
actual experiments on multicore platforms. Then, we study the optimal
allocation proposed by Prasanna and Musicus for makespan minimization using
optimal control theory. We largely simplify their proofs by resorting only to
pure scheduling arguments. Building on the insight gained thanks to these new
proofs, we extend the study to distributed multicore platforms. There, a task
cannot be distributed among several distributed nodes. In such a distributed
setting (homogeneous or heterogeneous), we prove the NP-completeness of the
corresponding scheduling problem, and propose some approximation algorithms. We
finally assess the relevance of our approach by simulations on realistic trees.
We show that the average performance gain of our allocations with respect to
existing solutions (that are thus unaware of the actual speedup functions) is
up to 16% for $\alpha=0.9$ (the value observed in the real experiments).

28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat