We describe a timing analysis algorithm which can achieve the efficiency of RC tree analysis while retaining much of the generality of Asymptotic Waveform Estimation. RC tree analysis from switch level simulation is generalized to handle piecewise linear transistor models, non tree topologies, floating capacitors, and feedback. For simple switch level models the complexity is O(n). The algorith...

We propose a simple real-valued generalization of the well known integer-valued Erdös number as a topological, non-metric measure of the ‘closeness’ felt between two nodes in an undirected, weighted graph. These real-valued Erdös numbers are asymmetric and are able to distinguish between network topologies that standard distance metrics view as identical. We use this measure to study some simpl...

Abstract. There have been many heuristic algorithms finding multicast trees proposed over the past few years. The necessity for finding a better and more suitable algorithm is still a current and important challenge. The article presents a new multicast routing algorithm for finding a multicast tree in packet networks. The objective of the K-Shortest Path Multicast Algorithm (KSPMA) is to minim...

If U and V are topologies on an abstract set X, then the triple (X, U, V) is a bitopological space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued funct...

In this paper we find an exact formula for the eigenvalues of the iteration matrix of the Generalized Diffusion method (GDF) used in load balancing. This provides us with the optimum value of the extrapolation parameter, i.e. the parameter endowing GDF with extra flexibility compared to other iterative methods. We apply our technique to the broad class of n-D torus interconnection topologies an...

This paper studies the stability of synchronized states in networks, where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of Stuart-Landau oscillators, it is shown how the stability of synchronized solutions in networks with distributed delay coupling can be determined through a sem...

In the present paper we introduce and study L-pre-T0-, L-pre-T1-, L-pre-T2 (L-pre-Hausdorff)-, L-pre-T3 (L-preregularity)-, L-pre-T4 (L-pre-normality)-, L-pre-strong-T3-, L-pre-strong-T4-, L-pre-R0-, L-pre-R1-separation axioms in (2, L)-topologies where L is a complete residuated lattice. Sometimes we need more conditions on L such as the completely distributive law or that the ”∧” is distribut...

The interconnection of a large number of processors and other devices to form a parallel/distributed computing system is a research area receiving a great deal of attention. One method is to use a multistage network. This paper compares two classes of multistage networks by examining two representative networks: the Generalized Cube and the Augmented Data Manipulator. The two topologies are com...