Computing Time-varying Network Reliability using Binary Decision Diagrams

TL;DR

This work addresses computing the time-varying network reliability $\sigma(G)$ for temporal graphs, where reliability hinges on journeys with non-decreasing time labels. The authors extend static-network BDD approaches to TVNs by first constructing a journey ZDD to compactly represent possible journeys, then applying a superset operation to obtain a BDD for the set of STRES-containing subgraphs, and finally performing a bottom-up dynamic programming to compute $\sigma(G)$. The key contributions are (i) a new frontier-based search-based method for enumerating journeys (FBSJE) to build the journey ZDD, (ii) conversion of the journey ZDD to a BDD for $\mathcal{S}_G$, and (iii) empirical demonstrations of substantial speedups (up to $4$ orders of magnitude) over prior SDP-based methods across complete and grid-temporal graphs. The results indicate that the approach scales to hundreds of links and offers a practical exact method for TVN reliability with broad applicability to space, vehicular, and drone networks.

Abstract

Computing the reliability of a time-varying network, taking into account its dynamic nature, is crucial for networks that change over time, such as space networks, vehicular ad-hoc networks, and drone networks. These networks are modeled using temporal graphs, in which each edge is labeled with a time indicating its existence at a specific point in time. The time-varying network reliability is defined as the probability that a data packet from the source vertex can reach the terminal vertex, following links with increasing time labels (i.e., a journey), while taking into account the possibility of network link failures. Currently, the existing method for calculating this reliability involves explicitly enumerating all possible journeys between the source and terminal vertices and then calculating the reliability using the sum of disjoint products method. However, this method has high computational complexity. In contrast, there is an efficient algorithm that uses binary decision diagrams (BDDs) to evaluate the reliability of a network whose topology does not change over time. This paper presents an efficient exact algorithm that utilizes BDDs for computing the time-varying network reliability. Experimental results show that the proposed method runs faster than the existing method up to four orders of magnitude.

Figures (12)

• Figure 1: Example of a temporal graph. Numbers in parentheses indicate time labels. As examples, multi-hop and single-hop $s$-$z$ journeys are shown on the right side of the figure.
• Figure 2: Binary decision tree.
• Figure 3: BDD.
• Figure 4: ZDD.
• Figure 6: Temporal graph $G$.