Termination detection algorithm

The refinement procedure utilises the fact that if some query node Q(X) has another node Q(fV) at some specific distance ) ( and/or angle), and if some database node D(Z) matches with Q(W), then there must also be some node D(Y) at the appropriate distance(s) from D(Z) which matches with Q(X) this is a necessary, but not sufficient, condition for a subgraph isomorphism to be present (except in the limiting case of all the query nodes having been matched, when the condition is both necessary and sufficient). The refinement procedure is called before each possible assignment of a database node to a query node and the matched substructure is increased by one node if, and only if, the condition holds for all nodes W, X, Y and Z. The basic algorithm terminates once a match has been detected or until a mismatch has been confirmed [70] it is easy to extend the algorithm to enable the detection of all matches between a query pattern and a database structure, as is required for applications such as those discussed here. 

Detection of structure isomorphism. For structure isomorphism problems, the algorithm is used to generate atom-atom correspondences between two chemical structures. In this case, as soon as one MCSS has been detected the search terminates immediately. 

In Table 13.1 a comparison of the results obtained with the used Location Estimation Algorithms using the data collected with the two mobile terminals is presented. To be noticed that for the HTC mobile phone all five references were detected and for the other mobile phone only four references were detected at each sampling point. In this test a value of = 3 was used and the weights used for the Weighted k-Nearest Neighbour were 0. 7, 0. 2 and 0. 1, as in [7]. 

Fig. 19.19 Pacemaker output settings for lowest current drain and maximum longevity induction of an endless loop tachycardia during an atrial capture threshold test in a patient with a Pacesetter Affinity DR pacing system. The automatic PMT detection and termination algorithm recognized the tachycardia and promptly terminated it. Meanwhile, the recording provided details as to the tachycardia interval and the retrograde conduction interval providing guidance as to programming the PVARP.

Corollary 6.4.1 If the constraints implied by the constraint graph G are inconsistent, then the algorithm will detect the inconsistency and terminate after +i iterations. 

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