Background Fault tree analysis (FTA) is a well established method for qualitative as well as probabilistic reliability and safety analysis. Fault trees are Boolean models and thus do not support modelling of dynamic effects like sequence dependencies between fault events. In order to overcome this limitations, dynamic fault tree methods were defined previously. Most of these are based on comple...

A graph G = (V , E) is arbitrarily partitionable if for any sequence τ of positive integers adding up to |V |, there is a sequence of vertex-disjoint subsets of V whose orders are given by τ , and which induce connected subgraphs. Such a graph models, e.g., a computer network which may be arbitrarily partitioned into connected subnetworks. In this paper we study the structure of such graphs and...

We investigate two parameterized algorithmic schemes for graphical models that can accommodate trade-offs between time and space: 1) AND/OR Cutset Conditioning (AOC(i)) and 2) Variable Elimination with Conditioning (VEC(i)). We show that AOC(i) is better than the vanilla versions of VEC(i), and use the guiding principles of AOC(i) to improve VEC(i). Finally, we show that the improved versions o...

Expanding parameters of graphs (magnification constant, edge and vertex cutset expansion) are related by very simple inequalities to forwarding parameters (edge and vertex forwarding indices). This shows that certain graphs have eccentricity close to the diameter. Connections between the forwarding indices and algebraic parameters like the smallest eigenvalue of the Laplacian or the genus of th...

A minimal cutset of a tree directed from the leaves to the root is a minimal set of vertices such that every path from a leaf to the root meets at least one of these vertices. An order relation on the set of minmal cutsets can be deened: U V if and only if every vertex of U is on the path from some vertex in V to the root. Motivated by the design of eecient cryptographic digital signature schem...

Given a directed graph G = (V,A) with arbitrary arc costs, the Elementary Shortest Path Problem (ESPP) consists of finding a minimum-cost path between two nodes s and t such that each node of G is visited at most once. If negative costs are allowed, the problem is NP-hard. In this paper, several integer programming formulations for the ESPP are compared. We present analytical results based on a...

In this paper, we consider two variance reduction schemes that exploit the structure of the primal graph of the graphical model: Rao-Blackwellised w-cutset sampling and AND/OR sampling. We show that the two schemes are orthogonal and can be combined to further reduce the variance. Our combination yields a new family of estimators which trade time and space with variance. We demonstrate experime...

Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs measurement on system that entangled 1. Based the no-cloning theorem, perfect impossible. This leads to introduction of MAC model noisy cribbing. In causal and non-causal scenarios, before input 1 sent through channel. Hence, 2's may inflict "state collapse" for Achiev...

Uplink and downlink cloud radio access networks are modeled as two-hop ${K}$ -user ${L}$ -relay networks, whereby small base-stations act relays for end-to-end communications connected to a central processor via orthogonal fronthaul links of finite capacities. Simplified versions network compress–forward (or noisy coding) distributed decode–forward presented establish inner bounds on the capaci...