Traversal recursion: a practical approach to supporting recursive applications

Abstract

Many capabdltles that are needed for recursive apphcatlons In engmeermg and project management are not well supported by the usual formslatlons of recursionWe Identify a class of recurstons called "traversal recurslons" (which model traversals of a dtrected graph) that have tw3 Important properties they can supply the necessary capabdlttes and efficient processmg algorithms have been defined for them First we present a taxonomy of traversal recurslons based on propertles of the recursIon on graph structure and on unusual types of metadata This taxonomy IS explolted to Identify solvable recursions and to select an execution algorithmWe show how graph traversal can sometimes outperform the more general Iteration algorithm Finally we show how a conventional query optimtzer architecture can be extended to handle recurstve queries and views 1 Introduction

Extending the data warehouse for service provisioning data

“…Our definition of pair-wise queries has been motivated from related literature on recursive queries (e.g. [ 35,31,44,49]). As will be explained, we use the structural properties of the underlying process that generates the data to define a partial order among the views.…”

“…State A spawns two parallel processes that are being synchronized later at state D. An event that leaves state A collects measures x i along all four edges (A, B), (B, D), (A, C) and (C, D). In order for our framework to apply for this case we need to define the meaning of an aggregation for pair (A, D) (similar to path-aggregation in [44]). If timing information is of use then sum(P A!D (r)) can be defined as max(x 1 + x 2 , x 3 + x 4 ).…”

An efficient path computation model for hierarchically structured topographical road maps

“…Previously suggested transitive closure or graph traversal algorithms [2], [8], [13], [16], [17], [20], [33], [35], [42] are not directly applicable to topographical_road_map (source, destination, cost) for the computation of a minimum cost path due to the very large volume of data they have to search. Thus, we need an efficient database organization method for structuring the topographical road map to speed up the computation of a minimum cost path.…”

Efficient management of transitive relationships in large data and knowledge bases

“…Recently, database researchers have recognized its utility in querying databases -in fact, it has been argued that transitivity is the dominant form of recursion that is of practical utility [2, 24,27].…”