Ž . X Given a series-parallel network network, for short N, its dual network N is given by interchanging the series connection and the parallel connection of network N. We usually use a series-parallel graph to represent a network. Let w x w X x X G N and G N be graph representations of N and N , respectively. A sequence Ž w x w X x. of edges e , e , . . . , e is said to form a common trail on ...

We use activity networks (task graphs) to model parallel programs and consider series-parallel extensions of these networks. Our motivation is two-fold: the benefits of series-parallel activity networks and the modelling of programming constructs, such as those imposed by current parallel computing environments. Series-parallelisation adds precedence constraints to an activity network, usually ...

The three well-known graph classes, planar graphs(P), series-parallel graphs (SP) and outer planar graphs(OP) satisfy the following proper inclusion relation: OP ⊂ SP ⊂ P . It is known that box(G) ≤ 3 if G ∈ P and box(G) ≤ 2 if G ∈ OP . Thus it is interesting to decide whether the maximum possible value of the boxicity of series-parallel graphs is 2 or 3. In this paper we construct a series-par...

In this paper we present algorithms for drawing series parallel digraphs with as much symmetry as possible. The first step is to compute a certain kind of automorphism, called an “upward planar automorphism” for an input series parallel digraph. The next step uses these automorphisms to construct a symmetric drawing of the graph. We present several variations of the second step, with visibility...

We give a simpler proof of Seymour’s Theorem on edge-coloring series-parallel multigraphs and derive a linear-time algorithm to check whether a given series-parallel multigraph can be colored with a given number of colors.

Let G be a series-parallel graph with integer edge weights. A p-coloring of G is a mapping of vertices of G into Zp (ring of integers modulo p) so that the distance between colors of adjacent vertices u and v is at least the weight of the edge uv. We describe a quadratic time p-coloring algorithm where p is either twice the maximum edge weight or the largest possible sum of three weights of edg...

Suppose that k series, all having the same autocorrelation function, are observed in parallel at n points in time or space. From a single series of moderate length, the autocorrelation paramater β can be estimated with limited accuracy, so we aim to increase the information by formulating a suitable model for the joint distribution of all series. Three Gaussian models of increasing complexity a...

This article presents an up-to-date review of the several extraction methods commonly used to determine the value of the threshold voltage of MOSFETs. It includes the different methods that extract this quantity from the drain current versus gate voltage transfer characteristics measured under linear operation conditions for crystalline and non-crystalline MOSFETs. The various methods presented...