Abstract:
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In this paper we present and analyze new sequential and parallel
heuristics to approximate the Minimum Linear Arrangement problem
(MinLA). The heuristics consist in obtaining a first global solution
using Spectral Sequencing and improving it locally through Simulated
Annealing. In order to accelerate the annealing process, we present a
special neighborhood distribution that tends to favor moves with high
probability to be accepted. We show how to make use of this
neighborhood to parallelize the Metropolis stage on distributed memory
machines by mapping partitions of the input graph to processors and
performing moves concurrently. The paper reports the results obtained
with this new heuristic when applied to a set of large graphs,
including graphs arising from finite elements methods and graphs
arising from VLSI applications. Compared to other heuristics, the
measurements obtained show that the new heuristic improves the
solution quality, decreases the running time and offers an excellent
speedup when ran on a commodity network made of nine personal
computers. |