Number Of Cutsets Research Articles

Design and parameter study of banana crown mechanical cutting device.

Banana mechanical crown cutting tool which is a critical component of banana crown cutting machine is designed and studied in this paper. Experiments were designed to optimize parameters of the cutting tool. Indexes are cut surface quality grade of banana crown, maximum cutting force and useful power consumption. For banana preservation, get high grade of cut surface quality is more significant than consume less energy. Results of experiments show that the optimum parameters are as follows: cutting speed is about 50-60 mm/s, number of cut sets are about 4-6, angle between thick cutter and axis of banana rachis is about 5°, width of thick cutter is about 8-14 mm, thickness of thick cutter is about 2-3 mm, edge angle of thick cutter is between 20° and 30°, width of thin cutter is about 10-14 mm and thickness of thin cutter is about 0.2-0.4mm. This study helps to make the completely mechanical postharvest treatments for banana postharvest treatments.

Wireless Network Reliability Analysis for Arbitrary Network Topologies

In this paper, the outage performance of wireless networks with unstructured topologies is investigated. The network reliability perspective of graph theory is used to obtain the network outage polynomial of generalized wireless networks for both uncorrelated and correlated wireless channels. A relationship is established between the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max-flow min-cut</i> theorem and key communication performance indicators. The diversity order is equal to the size of the minimum cut-set between source and destination, and the coding gain is the number of cut-sets with size equal to the minimum cut. An ergodic capacity analysis of arbitrary network topologies based on the network outage polynomial is also presented. Numerical results are used to illustrate the technical definitions and verify the derivations.

A Fast and Accurate Failure Frequency Approximation for $k$ -Terminal Reliability Systems

This paper considers the problem of approximating the failure frequency of large-scale composite $\boldsymbol{k}$ -terminal reliability systems. In such systems, the nodes ( $\boldsymbol{k}$ of which are terminals) are connected through components, which are subject to random failure and repair processes. At any time, a system failure occurs if the surviving system fails to connect all the $\boldsymbol{k}$ terminals together. We assume that each component's up times and down times follow statistically independent stationary random processes, and these processes are statistically independent across the components. In this setting, the exact computation of failure frequency is known to be computationally intractable (NP-hard). In this paper, we present an algorithm to approximate the failure frequency for any given multiplicative error factor that runs in polynomial time in the number of (minimal) cutsets. Moreover, for the special case of all-terminal reliability systems, i.e., where all the nodes are terminals, we propose an algorithm for approximating the failure frequency within an arbitrary multiplicative error that runs in polynomial time in the number of nodes (which can be much smaller than the number of cutsets). Our simulation results confirm that the proposed method is much faster and more accurate than the standard Monte Carlo simulation technique for approximating the failure frequency.

Multilevel Monte Carlo for Reliability Theory

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the number of cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) — a simulation approach which is typically used for stochastic differential equation models — can be applied in reliability problems by carefully controlling the bias-variance tradeoff in approximating large system behaviour. In this first exposition of MLMC methods in reliability problems we address the canonical problem of estimating the expectation of a functional of system lifetime for non-repairable and repairable components, demonstrating the computational advantages compared to classical Monte Carlo methods. The difference in computational complexity can be orders of magnitude for very large or complicated system structures, or where the desired precision is lower.

Data Structures in Power System Reliability Estimation

In this paper a technique for the estimation of power system reliability using fault tree analysis (FTA) and the concept of data structures is presented. The proposed approach for representing the fault trees uses data structures concept and dynamic storage allocation which overcomes the dimensionality problem. This approach reduces the computational complexity and execution time. This method can efficiently handle systems having any number of cut-sets between the input-output nodes depending upon the available computer memory. Three sample power system networks are considered to test the efficiency of the algorithm developed and the computation times with different approaches are compared.

Calculating exact top-event probabilities using Σ-Patrec

This paper presents a method for calculating top-event exact probability. This responds to a surge in the application of probabilistic risk assessment (PRA) techniques to ecological and weapon safety assessments. In these domains, basic event probabilities can be large; events characterizing human error and some natural phenomena are typical examples. The method described combines the /spl Sigma/II algorithm of Corynen and the pattern recognition scheme of Keen et al. The PC-based program that is developed using this method is called /spl Sigma/II-Patrec and computes the exact probability of top-event of a system fault-tree model as defined by its cut sets. The /spl Sigma/II module partitions and disjoints the cut sets and solves the resultant sub-models recursively. The pattern recognition module reduces the computational complexity by recognizing repeated sub-models in the calculation process and thus avoiding repeated evaluations. /spl Sigma/II-Patrec is designed to quantify the fault-tree models of both coherent and incoherent systems, and interfaces with the graphic package, SEATREE, for interactive generation of fault trees. In the anticipated case, the /spl Sigma/II-Patrec method of evaluation of exact top-event probability is polynomial in the number of cut sets; it can, however, be weakly exponential in the worst case. Either way, this method results in a substantial reduction in computation requirements compared to the inclusion-exclusion method. The algorithm is described through an example problem. The results of several experiments with large accident sequence are also presented.

Reliability Computations for Planar Networks

The two-terminal reliability problem for an undirected network involves calculating the probability that two distinguished sites are connected by a path of working edges. This problem is known to be NP-hard, even for the special case of planar systems. We present efficient data structures and algorithms for manipulating planar networks and for generating both paths an cutsets in such networks. A pseudopolynomial algorithm is then implemented, based on these generation procedures, to calculate two-terminal reliability for planar networks; that is, the algorithm's time complexity is polynomially bounded in the number of paths (or the number of cutsets). Computational experience with this implementation is also presented, showing that it provides a substantial improvement over previous implementations of the pseudopolynomial algorithm. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

A Cutset Approach to Reliability Evaluation in Communication Networks

A global reliability measure called 'network reliability' (NR) is the probability that a call entering a probabilistic network at any originating node can reach every other node. This concept is quite useful in multiterminal networks such as computer networks and parallel processors, etc. A simple technique is presented for evaluating NR in symbolic form. The method is based on cutsets and is computationally advantageous with respect to the spanning tree approach. It requires fewer cutsets to be manipulated in the process of determining the NR expression. The number of cutsets is approximately half that of spanning trees even for a small sized computer communication network and there is a further improvement in the situation for larger networks.

Approaches to Comparing Cut-Set Enumeration Algorithms

It is inadequate to compare computation algorithms solely by running programs on standard examples, especially small examples. Running-time and storage-requirements should be reported for a range of problem sizes. Procedures whose resource consumption grows exponentially with problem size (e.g. cut-set enumeration) can never solve large examples, even if one fine-tunes the code for maximum efficiency. It is necessary to judge an algorithm by criteria which are independent of the particular implementation (i.e. machine, language, data representation, or programmer). Number of cut-sets generated is one such measure; the number of pairs of cut-sets checked for containment is a much better measure of computing time. Computational efficiencies of bottom-up and top-down approaches are compared. It appears that bottom-up approaches are superior if modules are elaborated separately, but the margin of superiority is not over-whelming. Finally, when a data representation is suggested, favorable and unfavorable behaviors of the representation must be analyzed. The analysis is illustrated for three representations used for cut-sets.

Master cutset matrix

A systematic method of generation of all possible cutsets of a complete graph and of arranging them as a master cutset matrix is proposed, so that all possible cuts of any other graph with the same or smaller number of nodes may be obtained by simple modifications to it. Apart from the wide choice it provides in the selection of the cutsets for network studies, the enumeration of all cutsets plays a significant role in flow-network studies. A few properties of the master cutset matrix and its subclasses are discussed, including a formula for the number of cutsets in which a given set of edges appears, a recurrence relationship between the number of cutsets in different masters, and a procedure for determining the number of cutsets in an arbitrary graph. The methods discussed are also suitable for adaptation to computer.

Incompletely partitioned networks†

ABSTRACT A method is given for testing whether a graph G is an incompletely partitioned graph. The method is based on a simple criterion applied to the square of the adjacency matrix of the complement of Q. Further, a formula to determine the number of cut sets in such a graph is given, extending the previously available results for the number of cut sets in a graph.

On the Number of Cut Sets of a Class of Graphs†

ABSTRACT In network theory, the concept of cut set plays an important role and the need for listing all cut sets of a given network often arises. In this paper an expression for the number of cut sets of a graph G is obtained by considering the structure of G¯, its complement with respect to the complete graph having the same number of vertices. The expression is valid with certain restrictions on the structure of G¯. However, by applying suitable corrections to the expression, some of the restrictions can be lifted and the number of cut sets of G can be obtained in all cases except when G¯ contains four-edge circuits.