Accelerating Consensus by Spectral Clustering and Polynomial Filters

It is known that polynomial filtering can accelerate the convergence towards average consensus on an undirected network. In this paper the gain of a second-order filtering is investigated. A set of graphs is determined for which consensus can be attained in finite time, and a preconditioner is proposed to adapt the undirected weights of any given graph to achieve fastest convergence with the polynomial filter. The corresponding cost function differs from the traditional spectral gap, as it favors grouping the eigenvalues in two clusters. A possible loss of robustness of the polynomial filter is also highlighted

Schema architecture and their relationships to transaction processing in distributed database systems

We discuss the different types of schema architectures which could be supported by distributed database systems, making a clear distinction between logical, physical, and federated distribution. We elaborate on the additional mapping information required in architecture based on logical distribution in order to support retrieval as well as update operations. We illustrate the problems in schema integration and data integration in multidatabase systems and discuss their impact on query processing. Finally, we discuss different issues relevant to the cooperation (or noncooperation) of local database systems in a heterogeneous multidatabase system and their relationship to the schema architecture and transaction processing

Simulation of quantum walks and fast mixing with classical processes

We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains (LMCs), that is, classical Markov chains with added memory. We show that LMCs can simulate the mixing behavior of any quantum walk, under a commonly satisfied invariance condition. This allows us to answer an open question on how the graph topology ultimately bounds a quantum walk's mixing performance, and that of any stochastic local evolution. The results highlight that speedups in mixing and transport phenomena are not necessarily diagnostic of quantum effects, although superdiffusive spreading is more prominent with quantum walks. The general simulating LMC construction may lead to large memory, yet we show that for the main graphs under study (i.e., lattices) this memory can be brought down to the same size employed in the quantum walks proposed in the literature

Query Modification in Object-oriented Database Federation

We discuss the modification of queries against an integrated view in a federation of object-oriented databases. We present a generalisation of existing algorithms for simple global query processing that works for arbitrarily defined integration classes. We then extend this algorithm to deal with object-oriented features such as queries involving path expressions and nesting. We show how properties of the OO-style of modelling relationships through object references can be exploited to reduce the number of subqueries necessary to evaluate such querie

On Region Algebras, XML Databases, and Information Retrieval

This paper describes some new ideas on developing a logical algebra for databases that manage textual data and support information retrieval functionality. We describe a first prototype of such a system