AN IMPROVED ALGORITHM FOR SOLVING ALL D-MPS IN MULTI-STATE NETWORKS

Reliability is a desirable performance indicator of many real-world systems to measure the quality level. One general method for evaluating multi-state reliability is using d-minimal paths （d-MPs）. However, being an NP-hard problem, searching for all d-MPs is a rather challenging task. This paper proposes an improved algorithm to solve the d-MP problem. To reduce the search space of d-MPs, a concept of lower capacity bound is introduced into the d-MP problem, and an effective technique is developed to fred lower capacity bounds. Meanwhile, the fast enumeration method which is a recent improvement to the traditional enunaeration method is employed to solve d-MPs. In addition, by introducing the operation of transforming undirected edges into directed edges, the proposed algorithm is applicable to solving both directed networks and undirected networks. Through numerical experiments, it is found that the proposed algorithm holds a distinct advantage over the existing methods in solving all d-MPs.

计算网络两终端可靠度的新分解算法

网络可靠度是衡量网络性能的一个核心指标,随着网络模型被广泛应用于现实生活,人们对网络可靠度的研究也越来越重视。针对不交和算法和因子分解算法在计算网络可靠度方面存在的不足,给出一个计算网络两终端可靠度的新分解算法。该算法具有如下的优点:不需要提前枚举网络的所有极小路和所有极小割;通过引入网络化简操作和新的分解技术。该算法每次可以分解多条边的状态,从而它能够更快速、更高效地去分解网络的状态向量集,使得网络可靠度的计算更简单,更高效。通过实例以及和其他算法的比较验证了所提出算法的正确性和有效性。

基于网络化简和向量集分解的网络两终端可靠度算法

可靠度是衡量网络性能最重要的指标之一,不交和算法和因子分解算法是计算网络可靠度最重要的两种方法。不交和算法需要提前枚举网络所有极小路或极小割,因子分解算法虽然不需要枚举极小路或极小割,但每次只能分解一条边的状态。为了克服这两种算法的不足,基于网络化简和向量集分解,提出一个计算网络可靠度的高效、实用算法。该算法具有如下特点:a)算法首先求得网络的不可靠度,进而可得网络的可靠度;b)算法不需要提前枚举网络所有极小路和极小割;c)通过引入网络化简操作和向量集分解方法,算法每次可以分解多条边的状态,从而能更快速、更高效地实现对网络边的状态进行分解。最后通过实例以及与其他算法的比较验证了所提出算法的正确性和有效性。