Abstract. Algorithms for series-parallel graphs can be extended to arbitrary two-terminal dags if node reductions are used along with series and parallel reductions. A node reduction contracts a vertex with unit in-degree (out-degree) into its sole incoming (outgoing) neighbor. This paper gives an O(n2"5) algorithm for minimizing node reductions, based on vertex cover in a transitive auxiliary graph. Applications include the analysis of PERT networks, dynamic programming approaches to network problems, and network reliability. For NP-hard problems one can obtain algorithms that are exponential only in the minimum number of node reductions rather than the number of vertices. This gives improvements if the underlying graph is nearly series-parallel.

Tree contraction is a powerful technique for solving a large number of graph problems on families of recursively definable graphs. The method is based on processing the parse tree associated with a member of such a family of graphs in a bottom-up fashion, such that the solution to the problem is obtained at the root of the tree. Sequentially, this can be done in linear time with respect to the size of the input graph. In parallel, efficient and even cost optimal tree contraction algorithms have also been developed. In this paper we show how the method can be applied to compute the cardinality of the minimum vertex cover of a two-terminal series-parallel graph. We then construct a real-time paradigm for this problem and show that in the new computational environment, a parallel algorithm is superior to the best possible sequential algorithm, in terms of the accuracy of the solution computed. Specifically, there are cases in which the solution produced by a parallel algorithm ...

In this paper we develop a new linear-time algorithm for the recognition of series parallel graphs. The algorithm is based on a succinct representation of series parallel graphs for which the presence of an arc can be tested in constant time; space utilization is linear in the number of vertices. We show how to compute such a representation in linear time from a breadth-first spanning tree. Furthermore, we present a precise condition for the existence of such succinct representations in general, which is, for instance, satisfied by planar graphs.

Quantitative Trust Management (QTM) provides a dynamic interpretation of authorization policies for access control decisions based on upon evolving reputations of the entities involved. QuanTM, a QTM system, selectively combines elements from trust management and reputation management to create a novel method for policy evaluation. Trust management, while effective in managing access with delegated credentials (as in PolicyMaker and KeyNote), needs greater flexibility in handling situations of partial trust. Reputation management provides a means to quantify trust, but lacks delegation and policy enforcement. This paper reports on QuanTM’s design decisions and novel policy evaluation procedure. A representation of quantified trust relationships, the trust dependency graph, and a sample QuanTM application specific to the KeyNote trust management language, are also proposed.

This paper introduces a persistent agent called skeptic who supplies instances from well-defined equivalence classes to test and benchmark SAT solvers. On such classes, metrics such as max/min ratio of time-to-solve should approach the value of 1.0. Experiments suggested by the skeptic on the instances of the same class show (1) the time-to-solve max/min ratios for a given solver can exhibit a range from 2 to 1000 and beyond, and (2) max/min ratios for another solver may be several orders of magnitude better, including a significantly lower time-to-solve average value. Both of these factors point out that (1) SAT solvers can not only be much improved but also more reliably tested for any such improvement, and (2) the intrinsic complexity or `hardness' of SAT instances cannot be gauged reliably with the current generation of SAT solvers.

In this paper, a parallel algorithm is given that, given a graph G = (V; E), decides whether G is a series parallel graph, and if so, builds a decomposition tree for G of series and parallel composition rules. The algorithm uses O(log |E| log |E|) time and O(|E|) operations on an EREW PRAM, and O(log |E|) time and O(|E|) operations on a CRCW PRAM (note that if G is a simple series parallel graph, then |E| = O(|V|)). With the same time and processor resources, a tree-decomposition of width at most two can be built of a given series parallel graph, and hence, very efficient parallel algorithms can be found for a large number of graph problems on series parallel graphs, including many well known problems, e.g., all problems that can be stated in monadic second order logic. The results hold for undirected series parallel graphs graphs, as well as for directed series parallel graphs.

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The problem of scheduling precedence graphs for which every task has to be executed in a non-uniform interval is considered, with interprocessor communication delays. For the following classes of graphs we will present a polynomial time algorithm that finds minimumlateness schedules. 1. Outforests on two processors. 2. Series-parallel graphs and opposing forests with the least urgent parent property (to be defined) on two processors. 3. Inforests with the least urgent parent property on m processors.

The subclass of directed series-parallel graphs plays an important role in computer science. To determine whether a graph is series-parallel is a well studied problem in algorithmic graph theory. Fast sequential and parallel algorithms for this problem have been developed in a sequence of papers. For series-parallel graphs methods are also known to solve the reachability and the decomposition problem time efficiently. However, no dedicated results have been obtained for the space complexity of these problems -- the topic of this paper. For this special class of graphs, we develop deterministic algorithms for the recognition, reachability, decomposition and the path counting problem that use only logarithmic space. Since for arbitrary directed graphs reachability and path counting are believed not to be solvable in log-space the main contribution of this work are novel deterministic path finding routines that work correctly in series-parallel graphs, and a characterization...

When a parallel computation is represented in a formalism that imposes series-parallel structure on its task graph, it becomes amenable to automated analysis and scheduling. Unfortunately, its execution time will usually also increase as precedence constraints are added to ensure series-parallel structure. Bounding the slowdown ratio would allow an informed tradeoff between the benefits of a restrictive formalism and its cost in loss of performance. This dissertation deals with series-parallelising task graphs by adding precedence constraints to a task graph, to make the resulting task graph series-parallel. The weak bounded slowdown conjecture for series-parallelising task graphs is introduced. This states that the slowdown is bounded if information about the workload can be used to guide the selection of which precedence constraints to add. A theory of best series-parallelisations is developed to investigate this conjecture. Partial evidence is presented that the weak slowdown bound is likely to be 4/3, and this bound is shown to be tight.