A graph partitioning approach to signal decoding with applications in biomedicine

A partitioning theorem is applied to reduce greatly the computational complexity involved in the search of graphs representing high-level constraints in one-dimensional and multidimensional biomedical signal-decoding problems. For an N node graph the overall solution will generally involve O( square root N) complexity, a significant reduction with respect to conventional decoding approaches. The authors highlight the following advantages of the partitioning approach over conventional left-to-right strategies. (1) The planar separator theorem (PST) used provides a drastic reduction in computational cost from O(N) to O( square root N). (2) The PST provides a flexible and systematic way of selecting nodes with which to make a high pruning safety per computational load evaluation of all the paths in the graph. (3) The partitioning can be done offline so that many 'preparations' of graph can be attempted before it is used in a search. (4) Since nodes are selected at scattered locations throughout the graph, rather than always from the left, better statistical use of the observations is made in doing evaluations in the partitioned case.<>