Multidimensional Traversals for Normalization Constants

In many m~iltidimensional systems, including models of computer and network systems and particle systems, t,he eqnilibrillm distribution of state probabilities anti other performance measl~res hinges on t,he explicit numerical deterrnination of a normalization constant. When the nornializat,ion constant is the a s11n1 of simple, computable functions defined on lattice-points in a constrained space, which is the case for a large class of problems, we show that, t.he normalization constant can be obtained in a time that is directly proportior~al to the size of the space. 1% present an algorithm that is a tree-based variant of dept,h-first search which minimizes the usage of a stack, offering efficient execution for problems in many dimensions. Using simple complexity arguments as well as experimental resnlts, we show that the algorithm offers run-tirnes that are a many-fold improvement over previously proposetf nlultitfimensional recurrences. Categories and subject descriptors: H.4.m. [Information Systems Applications]:hliscellaneo~is General terms: Algorithms, hleasurement, Performance.