approximation algorithm for estimating failure probability of multipath transmission

in a computer network where nodes can fail, multipath transmission can be used to increase the probability of successful transmission. however, even multipath transmission has a probability of failure, which depends on the selected paths. hence, estimating this probability of failure is of great importance for designing good multipath routing algorithms. in this paper, we show that it is np-hard to compute the failure probability of multipath transmission. therefore, we design a polynomial-time approximation algorithm for estimating this failure probability and give analysis of its error bounds. we also compare the results of our approximation algorithm with the results of matlab simulations.