The probability of union events is always important in management science. Many real life applications use such probability in their core implementations. The most popular method to calculate the probability of union events is the Inclusion-Exclusion Principle (IEP), which originates from the idea of Abraham de Moivre (1718). However, the computation complexity is exact O(2n), and no matter what the events are, the complexity order can not be decreased. A much efficient method namely Recursive Inclusion-Exclusion Principle (RIEP) was constructed by rearranging its equation to its recursive form. The computation complexity is also O(2n) in the worse cases, but it usually has 10 times efficiency than IEP in the normal cases. This paper proposed a novel reduction method for the RIEP to calculate the probability of union events, which can obtain over 100 times efficiency than RIEP in normal cases, and in the worse cases, it has at least the same complexity as that of RIEP. Some benchmarks on network reliability applications show that the proposed approach is very efficient.
[1]
G. Jasmon,et al.
A Method for Evaluating All the Minimal Cuts of a Graph
,
1987,
IEEE Transactions on Reliability.
[2]
Fred S. Roberts,et al.
Applied Combinatorics, Second Edition
,
2009
.
[3]
Yuanlong Shen,et al.
A new simple algorithm for enumerating all minimal paths and cuts of a graph
,
1995
.
[4]
Yi-Kuei Lin,et al.
Search for All Minimal Paths in a General Large Flow Network
,
2012,
IEEE Transactions on Reliability.
[5]
Charles J. Colbourn,et al.
The Combinatorics of Network Reliability
,
1987
.
[6]
Wei-Chang Yeh.
A simple algorithm to search for all MCs in networks
,
2006,
Eur. J. Oper. Res..
[7]
U. Abel,et al.
Determination of All Minimal Cut-Sets between a Vertex Pair in an Undirected Graph
,
1982,
IEEE Transactions on Reliability.