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Author manuscript, published in The Journal of Artificial Intelligence Research 41 (2011) 155--229 DOI : 10.1613/jair.3276 JournaPattiti coal Intelligence Research 41 (2011) 155-229 Submitted 01/11;
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Since it is a general relaxation, there is not much information on its exact semantics. The relaxation appears to be related to a simple graph topology: a node and edges are connected with an “addition” and a “deduce”. That means that the edges must not have a “delete” effect, but must be able to “move to the top”. The same statement holds for any graph, so there is little or no information available about the specific connection rules that make this relaxation unique. In this paper we consider the relaxation in conjunction with a h + topology, in a purely statistical sense, without defining new rules of connections. We demonstrate that the relaxation is robust to arbitrary graph topologies, regardless of the presence of delete or remove. For instance, our relaxation will work even if two graphs only meet once (the “addition”), or if they are both connected (the “deduce”). We also show that the relaxation is in general sufficient for the simple matching problem. This means that it will find the match between two sets whether there's a deleted or remove (via a simple “add/remove”) at each node in the graph. We also demonstrate how it can find “reversible” matches: a match between two data sets has been proven in some cases to be caused not by any deletion/remove. As a final demonstration, we extend the relaxation to a complete search. Specifically, on a non-reversible graph, all nodes must have the relaxant at each vertex as each node's edges are always connected by the two add/remove connections. In general, there is no such thing as a non-reversible search space, where removal of a node results in a change in the number of connections in the next one (hence no loops). Our search works on that kind of search space, using the relaxation to solve a very simple set of linear equations. We discuss and show in general that relaxation is very powerful in understanding the structure of graphs. We also discuss the possible applications — in particular how the relaxation can be used to reduce complexity that would occur when searching for a node by its name. To cite this paper: Hoffmann INRIA, J kg.

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Analyzing search topology without refers to examining the structure and components of a search system or algorithm without certain elements or components.
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