2 research outputs found
Joint Size and Depth Optimization of Sorting Networks
Sorting networks are oblivious sorting algorithms with many interesting
theoretical properties and practical applications. One of the related classical
challenges is the search of optimal networks respect to size (number of
comparators) of depth (number of layers). However, up to our knowledge, the
joint size-depth optimality of small sorting networks has not been addressed
before. This paper presents size-depth optimality results for networks up to
channels. Our results show that there are sorting networks for
inputs that are optimal in both size and depth, but this is not the case for
and channels. For inputs, we were able to proof that
optimal-depth optimal sorting networks with layers require comparators
while optimal-size networks with comparators need layers. For
inputs we show that networks with or layers require at least
comparators (the best known upper bound for the minimal size). And for networks
with inputs and layers we need comparators, while for
layers the best known size is
SAT encodings for sorting networks, single-exception sorting networks and halvers
Sorting networks are oblivious sorting algorithms with many practical
applications and rich theoretical properties. Propositional encodings of
sorting networks are a key tool for proving concrete bounds on the minimum
number of comparators or depth (number of parallel steps) of sorting networks.
In this paper, we present new SAT encodings that reduce the number of variables
and clauses of the sorting constraint of optimality problems. Moreover, the
proposed SAT encodings can be applied to a broader class of problems, such as
the search of optimal single-exception sorting networks and halvers.
We obtain optimality results for single-exception sorting networks on inputs.Comment: Software available at https://github.com/jarfo/sor