M. N. S. Swamy

Complexity of computation of a spanning tree enumeration algorithm

In 1968, Char [4] presented an algorithm to enumerate all the spanning trees of an undirected graph G . This algorithm starts with a known initial spanning tree of G , and generates all the other spanning trees along with certain spanning non-tree subgraphs of G . In this paper a detailed complexity analysis of Chars algorithm and methods to speed up the algorithm are discussed. Two heuristics for the selection of the initial spanning tree are suggested. These heuristics result in a considerable reduction in the number of spanning non-tree subgraphs generated. A technique called path compression, aimed at reducing the actual number of comparisons, is described. Computational results on several randomly generated graphs are presented to illustrate the improvement achieved.

SIMULATED ANNEALING AND TABU SEARCH ALGORITHMS FOR MULTIWAY GRAPH PARTITION

For a given graph G with vertex and edge weights, we partition the vertices into subsets to minimize the total weights for edges crossing the subsets (weighted cut size) under the constraint that the vertex weights are evenly distributed among the subsets. We propose two new effective graph partition algorithms based on simulated annealing and tabu search, and compare their performance with that of the LPK algorithm reported in Ref. 12. Extensive experimental study shows that both of our new algorithms produce significantly better solutions than the LPK algorithm (maximal and minimal improvements on average weighted cut size are roughly 51.8% and 10.5% respectively) with longer running time, and this advantage in solution quality would not change even if we run the LPK algorithm repeatedly with random initial solutions in the same time frame as required by our algorithms.

A Study of Recurrent Ladders Using the Polynomials Defined by Morgan-Voyce

Recurrent ladders have received considerable attention in the literature. In the present paper, the matrix parameters of a recurrent ladder network with general series and shunt arms are derived in terms of a set of polynomials, which were first defined by Morgan-Voyce in his studies on the special case of a resistive ladder. [11] Since the polynomials are factorizable, the matrix parameters can be conveniently utilized to yield network response to any given excitation. Also, the zeros and poles of any network function may be found in terms of the zeros of these polynomials. For purposes of illustration, response to a square-wave input has been worked out in detail in the case of an RC ladder. The chief merit of the analysis lies in its simplicity and compactness.

Graph-theoretic proof of a network theorem and some consequences

A graph-theoretic proof of a network theorem is given. Some consequences of this theorem in relation to the analysis of an algorithm are discussed.

On maximal planarization of nonplanar graphs

In this paper, we first point out that the planarization algorithm due to Ozawa and Takahashi [4] does not in general produce a maximal planar subgraph when applied on a nonplanar graph. However, we prove that the algorithm produces a maximal planar subgraph in the case of a complete graph.

Sensitivity invariants for nonlinear networks

For a general class of nonlinear networks, explicit expressions for sensitivities of a response due to nonlinear elements are derived. These expressions are used to establish invariance relationships for the sums of sensitivities over different sets of parameters of two classes of nonlinear networks. It is indicated how these relationships can be used to establish the invariant nature of the sum of higher order sensitivities and a lower bound for the quadratic sensitivity index.

Bounds on the sum of element sensitivity magnitudes for network functions

Bounds on the sum of element sensitivity magnitudes for transfer immittances, transfer voltage, and current ratios are established for networks consisting of resistors, capacitors, inductors, and gyrators. For RC and LC networks these bounds are given in terms of relevant driving-point functions and their frequency sensitivities. Further, for two-element-kind networks, bounds are given for the quadratic sensitivity index \phi .

Sensitivity invariants for linear time-invariant networks

For a general linear time-invariant network it is shown that the sum of the sensitivities, of any order, of a network function over different parameter sets is invariant. An expression is derived for calculating the sum of (k+l) th-order sensitivities knowing the same for k th-order sensitivities. It is also shown that lower bounds for the quadratic sensitivity index may be obtained by using the firstorder sensitivity invariants.

Active filter design using exponentially tapered RC lines

This correspondence describes a practical active lowpass network consisting of a cascade of a uniform and an exponential line, and a single voltage-controlled voltage source of finite-source resistance. The network is simulated on a digital computer and optimized with respect to pertinent network parameters. The sensitivity of the optimized network is studied with respect to the gain of the controlled source. It is shown that this sensitivity may be reduced by increasing the taper factor of the exponential line, and that the band-elimination action of the finite-source resistance may be overcome by the uniform line.

Driving-Point Function Synthesis Using Tapered RC Lines and Their Duals

Simple and composite lines have been defined for nonuniform transmission lines and their various configurations considered. The concept of duality has been extended to composite lines and their different configurations, and two theorems concerning these lines have been established. A procedure for realizing certain classes of irrational functions as driving-point functions has been presented using simple or composite RC lines and their duals. This includes the existing procedures for uniform and exponential lines.