7.5 Evaluation
95
• the number of modules, the number of nodes in G is minimized, i.e.
min :
v∈ ˆ
V
⎛
⎝
u∈ ˆ
V
e (u,v)
⎞
⎠ .
The quality criteria connection depth is always optimal because the constraints
described in Sect. 7.4.2 ensure direct connections between modules realizing consecutive operations defined in the experiments and, hence, also no payload droplet
re-injections at the MPU are required.
7.5 Evaluation
The proposed approach results in an automatic method, which enables designers to
efficiently generate application-specific architectures for a given set of experiments
and user-defined parameters such as the maximal number of module instances and
objective functions employing the desired quality criteria. The resulting architectures are optimized or even optimal with respect to the provided settings and criteria.
In order to demonstrate and evaluate the applicability of the proposed method,
the evaluations focus on the performance of the proposed method as well as the
improvements of application-specific architectures compared to ring architectures.
7.5.1 Performance Evaluation
Determining G is a computationally hard problem because, for each experiment
φ ∈ , the SMT-solver has to determine the respective modules (i.e., valid
assignments for the ex φ[p] i -variables). Here, a huge number of possibilities exist.
For example, let r be the maximal number of allowed instances for all modules and
let |φ| be the length of an experiment. Then, for each of the |φ| positions, r variables
are introduced (namely ex φ[p] 1 , . . . , ex φ[p] r ) where exactly one of them has to be
equal to 1—resulting in r possible combinations. Multiplying these combinations
for all |φ| positions would yield r |φ| combinations for an experiment to be realized—
an exponential complexity. This becomes even more complex when all experiments
in are considered.
In order to evaluate whether the proposed method is capable of dealing with
this complexity, evaluations using randomly generated benchmarks (i.e., randomly
generated sets of experiments) have been performed because these benchmarks can
be scaled with respect to the number of experiments and their lengths. This way,
the performance of the proposed method with respect to various problem sizes can
be evaluated. In this performance evaluation, the problem size (with respect to the
95
• the number of modules, the number of nodes in G is minimized, i.e.
min :
v∈ ˆ
V
⎛
⎝
u∈ ˆ
V
e (u,v)
⎞
⎠ .
The quality criteria connection depth is always optimal because the constraints
described in Sect. 7.4.2 ensure direct connections between modules realizing consecutive operations defined in the experiments and, hence, also no payload droplet
re-injections at the MPU are required.
7.5 Evaluation
The proposed approach results in an automatic method, which enables designers to
efficiently generate application-specific architectures for a given set of experiments
and user-defined parameters such as the maximal number of module instances and
objective functions employing the desired quality criteria. The resulting architectures are optimized or even optimal with respect to the provided settings and criteria.
In order to demonstrate and evaluate the applicability of the proposed method,
the evaluations focus on the performance of the proposed method as well as the
improvements of application-specific architectures compared to ring architectures.
7.5.1 Performance Evaluation
Determining G is a computationally hard problem because, for each experiment
φ ∈ , the SMT-solver has to determine the respective modules (i.e., valid
assignments for the ex φ[p] i -variables). Here, a huge number of possibilities exist.
For example, let r be the maximal number of allowed instances for all modules and
let |φ| be the length of an experiment. Then, for each of the |φ| positions, r variables
are introduced (namely ex φ[p] 1 , . . . , ex φ[p] r ) where exactly one of them has to be
equal to 1—resulting in r possible combinations. Multiplying these combinations
for all |φ| positions would yield r |φ| combinations for an experiment to be realized—
an exponential complexity. This becomes even more complex when all experiments
in are considered.
In order to evaluate whether the proposed method is capable of dealing with
this complexity, evaluations using randomly generated benchmarks (i.e., randomly
generated sets of experiments) have been performed because these benchmarks can
be scaled with respect to the number of experiments and their lengths. This way,
the performance of the proposed method with respect to various problem sizes can
be evaluated. In this performance evaluation, the problem size (with respect to the