On Counting the Number of Consistent Genotype Assignments for Pedigrees

Consistency checking of genotype information in pedigrees plays an important role in genetic analysis and for complex pedigrees the computational complexity is critical. We present here a detailed complexity analysis for the problem of counting the number of complete consistent genotype assignments. Our main result is a polynomial time algorithm for counting the number of complete consistent assignments for non-looping pedigrees. We further classify pedigrees according to a number of natural parameters like the number of generations, the number of children per individual and the cardinality of the set of alleles. We show that even if we assume all these parameters as bounded by reasonably small constants, the counting problem becomes computationally hard (#P-complete) for looping pedigrees. The border line for counting problems computable in polynomial time (i.e. belonging to the class FP) and #P-hard problems is completed by showing that even for general pedigrees with unlimited number of generations and alleles but with at most one child per individual and for pedigrees with at most two generations and two children per individual the counting problem is in FP

Forecasting Regional Labor Market Developments under Spatial Autocorrelation

Because of heterogeneity across regions, economic policy measures are increasingly targeted at the regional level and, therefore, require regional forecasts. The data available to compute regional forecasts are usually a pseudo panel of a limited number of observations over time and a large number of regions strongly interacting with each other. Traditional time-series techniques applied to distinct time series of regional data are probably a suboptimal forecasting strategy. Although both linear and nonlinear models have been applied and evaluated to forecast socioeconomic variables, spatial interactions among regions are often ignored. This article evaluates the ability of spatial error and spatial lag models to correct for misspecifications due to neglected spatial autocorrelation in the data. The empirical application on short-term forecasts of employment in 326 West German regions shows that the superimposed spatial structure that is required for the estimation of spatial models improves the forecasting performance of nonspatial models. </jats:p