Preprocessing minpaths for sum of disjoint products

Abstract

Network reliability algorithms which produce sums of disjoint products (SDP) are sensitive to the order in which the minimal pathsets are analyzed. The minpaths are preprocessed by choosing this order in the hope that an SDP algorithm will then provide a relatively efficient analysis. The most commonly used preprocessing strategy is to list the minpaths in order of increasing size. This paper gives examples for which this strategy is not optimal. A new preprocessing strategy which works well for SDP algorithms with single-variable inversion (SVI) is introduced. It is also observed that optimal preprocessing for SVI-SDP can be different from optimal preprocessing for SDP algorithms which use multiple-variable inversion; one reason for this is that MVI-SDP algorithms handle disjoint minpaths much more effectively than SVI-SDP algorithms do. Both kinds of SDP algorithms profit from prior reduction of elements and of subsystems which are in parallel or in series.

An efficient algorithm for the multi-state two separate minimal paths reliability problem with budget constraint

“…Therefore, if we find all the ðd; T; b; P 1 ; P 2 Þ-MPs, we can compute the system reliability, R d;T;b;P 1 ;P 2 , using some exact methods such as the inclusion-exclusion principle [14,15] or the sum of disjoint products [16,17]. Here, we briefly explain how R d;T;b;P 1 ;P 2 can be computed using the sum of disjoint products method.…”

“…In this kind of a network, the flow conservation law is not necessarily satisfied, i.e., the input and output are not necessarily equal [8][9][10]. Applying approximate methods such as Monte-Carlo simulation [4,13], or exact ones such as inclusion-exclusion principle [14,15], or sum of disjoint product [16,17], system reliability can be computed in terms of minimal cuts, or minimal paths .However, evaluating the system reliability is an NP-hard problem [30], and thus the problem continues to be interesting to investigate.…”

“…In an SFN, system reliability can be considered as the probability of transmitting a given demand amount, d units, of data (flow) from a source node to a sink node . A number of different algorithms have been proposed to compute this kind of reliability parameter [3,[13][14][15][16][17][18][19][20][21]. For example, Yan and Qian [19] presented several new results along with an improved algorithm.…”

A Parallel Strategy for the Logical‐probabilistic Calculus‐based Method to Calculate Two‐terminal Reliability

“…Methods that use SDP first enumerate minimal tie sets (minimal paths) and then apply SDP to disjoin the tie terms . A tie set is defined as a group of edges that form a path between s and t .…”

“…conducted several experiments on the preprocessing of path/cut terms in SDP . Another preprocessing strategy was mentioned by Balan and Traldi . Heidtmann compared his algorithm with Abraham's in terms of statistics and characteristics.…”