Strongly and transitive chordal graphs and their applications in complexity analysis of triangular decomposition

—This paper presents a solution to the problem of searching for cavernous fractured zones and the zones that determine reservoir heterogeneity in Famennian deposits of one of the licensed sections of the Republic of Bashkortostan. The use of an integrated approach to the study of azimuthal horizontal-transverse isotropy of rocks using wellbore data and modern methods for processing areal seismic data for carbonate deposits associated with the development of organogenic structures is described. The results of using the full-azimuth angular migration technology are obtained. The introduction of high-tech approaches at the research site using full-azimuth seismic data processing, spectral decomposition, AVA/AVAZ inversion, and complex analysis of dynamic properties of the wave field in conjunction with well logging and core data makes it possible to identify the distorted zones of the carbonate reservoir associated with changes in the characteristics of the rock skeleton, the presence of a porous-cavernous-fracture void space and lithological replacement zones, as well as secondary processes, thereby reducing the risks associated with subsequent production drilling.

Many graph search algorithms use a vertex labeling to compute an ordering of the vertices. We examine such algorithms which compute a peo (perfect elimination ordering) of a chordal graph and corresponding algorithms which compute an meo (minimal elimination ordering) of a non-chordal graph, an ordering used to compute a minimal triangulation of the input graph. We express all known peo-computing search algorithms as instances of a generic algorithm called MLS (maximal label search) and generalize Algorithm MLS into CompMLS, which can compute any peo. We then extend these algorithms to versions which compute an meo and likewise generalize all known meo-computing search algorithms. We show that not all minimal triangulations can be computed by such a graph search, and, more surprisingly, that all these search algorithms compute the same set of minimal triangulations, even though the computed meos are different. Finally, we present a complexity analysis of these algorithms. An extended abstract of part of this paper was published in WG 2005 .