Local Computation Schemes with Partially Ordered Preferences

Abstract. Many computational problems linked to reasoning under uncertainty can be expressed in terms of computing the marginal(s) of the combination of a collection of (local) valuation functions. Shenoy and Shafer showed how such a computation can be performed using only local computations. A major strength of this work is that it is based on an algebraic description: what is proved is the correctness of the local computation algorithm under a few axioms on the algebraic structure. The instantiations of the framework in practice make use of totally ordered scales. The present paper focuses on problems of optimization over partially ordered scales, including problems that do not rely on a semilattice, and examines how they can be cast in the Shafer-Shenoy framework so as to satisfy the axioms for local computation and thus benefit from local computation algorithms. It also provides many examples of preference relations, thus showing that each of the algebraic structures explored here has its own interest.

QoS Routing: Average Complexity and Hopcount in m Dimensions

QoS routing is expected to be an essential building block of a future, efficient and scalable QoS-aware network architecture. We present SAMCRA, an exact QoS routing algorithm that guarantees to find a feasible path if such a path exists. The complexity of SAMCRA is analyzed. Because SAMCRA is an exact algorithm, most findings can be applied to QoS routing in general. The second part of this paper discusses how routing with multiple independent constraints affects the hopcount distribution. Both the complexity as the hopcount analysis indicate that for a special class of networks, QoS routing exhibits features similar to single-parameter routing.Network Architectures and ServicesElectrical Engineering, Mathematics and Computer Scienc