In the connection location-allocation problem we are given a set of material flows between pairs of existing facilities each of which must be routed through a connection facility. The objective is to minimize the total transportation costs by locating a given number of connections and allocating the flows accordingly.For this problem many properties and solution methods of the well-known facility location-allocation problem can be transferred, among others the construction line algorithm, an exact solution method based on discretization results under polyhedral gauge distances.We have implemented construction line algorithms for the connection location-allocation problem without restrictions as well as in the presence of forbidden regions or barriers. We considered various distance functions, ranging from the Manhattan distance to mixed polyhedral gauge distances and applied hull properties to further reduce the dominating set.

The purpose of this review is to summarize current knowledge of the etiology of euthyroid and toxic multinodular goiter (MNG) with respect to the epidemiology, clinical characteristics, and molecular pathology.In reconstructing the line of events from early thyroid hyperplasia to MNG we will argue the predominant neoplastic character of nodular structures, the nature of known somatic mutations, and the importance of mutagenesis. Furthermore, we outline direct and indirect consequences of these somatic mutations for thyroid pathophysiology and summarize information concerning a possible genetic background of euthyroid goiter.Finally, we discuss uncertainties and open questions in differential diagnosis and therapy of euthyroid and toxic MNG.

Euthyroid goiter is characterized by diffuse or nodular enlargement of the thyroid gland. Iodine deficiency and cigarette smoking have been identified as important environmental factors. However, family and twin pair studies suggest a strong genetic predisposition. Therefore, we performed the first extended genome-wide scan to identify susceptibility loci that predispose for euthyroid goiter using 450 microsatellite markers in 18 extended Danish, German, and Slovakian families. Parametric and nonparametric multipoint linkage analyses were performed. The highest nonparametric LOD scores were obtained for chromosomes 2q and 3p with values of 2.54 at D2S1363 and 2.25 at D3S3038, respectively. Assuming heterogeneity and dominant inheritance, heterogeneity LOD scores (HLOD) of 2.71 and 1.94 were calculated for 2q and 3p, respectively. Furthermore, nonparametric LOD scores of 1.87 (HLOD 1.39) at D7S1808 on 7q and 1.79 (HLOD 1.80) at D8S264 on 8p were obtained. Haplotyping of families contributing to the linkage signals revealed four families compatible with a putative locus on 3p and one family each showing strict cosegregation with the loci on 2q, 7q, and 8p. The four novel candidate loci corroborate the assumed heterogeneity in the etiology of euthyroid familial goiter. For the first time, a more prevalent putative locus, present in 20% of the families investigated, was identified.

Iodine deficiency is the most important etiological factor for euthyroid endemic goiter. However, family and twin pair studies also strongly indicate a genetic prediposition. In euthyroid goiters molecular defects in the thyroglobulin (TG), and Na+/I− symporter (NIS) gene have been identified. Numerous mutations in the Pendrin (PDS) gene have been found in families with PDS characterized by deafness and euthyroid goiter. Moreover, family studies indicated two major candidate loci MNG-1 on chromosome 14q31 and Xp22. However, all previous linkage studies investigated only one family. To clarify the general relevance of these previously identified two major candidate loci for the etiology of euthyroid goiter we investigated four families with a total number of 74 family members by linkage analysis with microsatellite markers. Moreover, we analyzed the thyroid candidate genes TG, thyroperoxidase (TPO), NIS, TSH receptor, and PDS. In a further family with 12 members in whom we have previously demonstrated linkage to the MNG-1 locus we investigated the Xp22 locus and the PDS gene in addition to our initial study. Linkage analysis results of our study are not significant enough to definitely exclude or confirm linkage to the investigated candidate genes and loci. Nevertheless, we obtained very weak indications for possible linkage to Xp22 in one family by a maximal multipoint LOD score of 1.15, and cosegregation of haplotypes among affected family members. Moreover, in another family linkage to PDS was indicated by a maximal multipoint LOD score of 1.87 as well as cosegregation of haplotypes. However, sequencing of the PDS gene did not reveal germline mutations. A significant total NPL score of 6.5 for PDS over all families most likely indicated linkage to a genomic region close to PDS. Furthermore, the likelihood of linkage to MNG-1 and Xp22 is reduced, because multipoint LOD scores were below 1 or negative. In all families there was no significant evidence for linkage for the thyroid candidate genes TG, TPO, NIS, or the TSH receptor. In conclusion, a general role of MNG-1 and Xp22 for the etiology of euthyroid goiter is unlikely but cannot clearly excluded. The multipoint parametric and nonparametric LOD scores further suggest genetic heterogeneity in the etiology of familial euthyroid goiter. To identify other susceptibility loci it is necessary to perform genome-wide linkage analysis studies with more families.