### An Improved Vectorization Algorithm to Solve the d-MP Problem

#### Abstract

The d-minimal path (d-MP) problem is to find all the system state vectors (SSV) under which d units of data can be transmitted from a source node to a destination node in a stochastic-flow network (SFN). This problem has been very attractive in the last decades as one can compute the exact amount of the network’s reliability through the d-MPs. Although several algorithms have been proposed in the literature to address the problem, the research continues because it is NP-hard. Since the number of d-MPs grows exponentially with the size of the network, the available algorithms in the literature are not so practical. Hence, we employ the vectorization techniques for proposing an improved algorithm to address the problem. We conduct many experimental results on the known benchmarks and two hundred randomly generated SFNs in the sense of performance profile introduced by Dolan and Moré. The experimental results show the vectorization algorithm to be considerably more efficient than the non-vectorization ones.

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DOI: https://doi.org/10.5540/tcam.2022.024.01.00019

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