Worst-case Computation Time Research Articles

Efficient algorithms for finding the K best paths through a trellis

A set of algorithms is presented for finding the best set of K mutually exclusive paths through a trellis of N nodes, with worst-case computation time bounded by N/sup 3/log n for a fixed-precision computation. The algorithms are based on a transformation of the K-path trellis problem into an equivalent minimum-cost network flow (MCNF) problem. The approach allows the application of efficient MCNF algorithms, which can obtain optimal solutions orders of magnitude faster than the algorithm proposed by J.K. Wolf et al. (1989). The resulting algorithms extend the practicality of the trellis formulation (in terms of required computations) to multiobject tracking problems with much larger numbers of targets and false alarms. A response by Wolf et al. is included. >

Worst Case Bounds for Maximal Compatible Subsets

An exact upper bound is found for the number of maximal compatible subsets of an n-state incompletely specified sequential machine (ISSM). This bound, on the order of 3n/3, iS also a worst case computer storage and computation time limit for any algorithm to find maximal compatibles.