Abstract
In several economical, statistical and geographical applications, a territory must be subdivided into functional regions. Such regions are not fixed and politically delimited, but should be identified by analyzing the interactions among all its constituent localities. This is a very delicate and important task, that often turns out to be computationally difficult. In this work we propose an innovative approach to this problem based on the solution of minimum cut problems over an undirected graph called here transitions graph. The proposed procedure guarantees that the obtained regions satisfy all the statistical conditions required when considering this type of problems. Results on real-world instances show the effectiveness of the proposed approach.
Similar content being viewed by others
References
Andersen, R., Chung, F., Lang, K.: Local graph partitioning using PageRank vectors. In: Proceeding of 47th Annual IEEE Symposium on Foundations of Computer Science, pp. 475–486 (2006)
Bichot, C.E., Siarry, P.: Graph Partitioning. ISTE - Wiley, London (2011)
Brinkmeier, M.: A simple and fast min-cut algorithm. Theory Comput. Syst. 41(2), 369–380 (2007)
Bruni, R., Bianchi, G.: Effective classification using binarization and statistical analysis. IEEE Transactions on Knowledge and Data Engineering 27(9), 2349–2361 (2015)
Canello, J., Pavone, P.: Mapping the multifaceted patterns of industrial districts: a new empirical procedure with application to Italian data. Reg. Stud. (2015). doi:10.1080/00343404.2015.1011611
Casado-Díaz, J.M., Coombes, M.G.: The delineation of 21st century local labour market areas: a critical review and research agenda. Boletín de la Asociación de Geógrafos Españoles 57, 7–32 (2011)
Coombes, M.G., Openshaw, S.: The use and definition of Travel-to-Work Areas in Great Britain: some comments. Reg. Stud. 16(2), 141–149 (1982)
Coombes, M.G., Green, A.E., Openshaw, S.: An efficient algorithm to generate official statistical reporting areas: the case of the 1984 Travel-to-Work Areas revision in Britain. J. Oper. Res. Soc. 37, 943–953 (1986)
Coombes, M.G.: Defining boundaries from syntetic data. Environ. Plan. 32, 1499–1518 (2000)
Dahmann, D.C., Fitzsimmons, J.D. (eds.) Metropolitan and nonmetropolitan areas: new approaches to geographical definition. Bureau of the Census Working Paper 12, Washington: Bureau of the Census (1995)
Diestel, R.: Graph Theory, 4th edn. Springer, New York (2010)
Di Giacinto, V., Gomellini, M., Micucci, G., Pagnini, M.: Mapping local productivity advantages in Italy: industrial districts, cities or both? J. Econ. Geogr. 14(2), 365–394 (2014)
Duque, J.C., Ramos, R., Suriach, J.: Supervised regionalization methods: a survey. Int. Region. Sci. Rev. 30, 195–220 (2007)
Farmer, C.J.Q., Steward Fotheringam, A.: Network-based functional regions. Environ. Plan. 43, 2723–2741 (2011)
Fischer, M.M.: Regional taxonomy: a comparison of some hierarchic and non-hierarchic strategies. Region. Sci. Urban Econ. 10, 503–537 (1980)
Flórez-Revuelta, F., Casado-Díaz, J.M., Martínez-Bernabeu, L.: An evolutionary approach to the delineation of functional areas based on travel-to-work flows. Int. J. Autom. Comput. 5(1), 10–21 (2008)
Fortunato, S., Barthélemy, M.: Resolution limit in community detection. Proc. Natl. Acad. Sci. USA 104(1), 36–41 (2007)
Fusco, G., Caglioni, M.: Hierarchical clustering through spatial interaction data. The case of commuting flows in South-Eastern France. LNCS 6782, 135–151 (2011)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99(12), 7821–7826 (2002)
Goodman, J.F.B.: The definition and analysis of local labour markets: some empirical problems. Br. J. Ind. Rel. 8, 179–186 (1970)
Guimerá, R., Sales-Pardo, M., Amaral, L.: Modularity from fluctuations in random graphs and complex networks. Phys. Rev. E 70, 025101 (2004)
Hao, J.X., Orlin, J.B.: A faster algorithm for finding the minimum cut in a directed graph. J. Algorithm. 17(3), 424–446 (1994)
Hopcroft, J., Tarjan, R.: Efficient algorithms for graph manipulation. Commun. ACM 16(6), 372–378 (1973)
ISTAT: I sistemi locali del lavoro 2011. Nota metodologica (2015) Retrieved from http://www3.istat.it/salastampa/comunicati/non_calendario/20050721_00/testointegrale.pdf. Accessed 18 Sept 2015
Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1999)
Kim, H., Chun, Y., Kim, K.: Delimitation of functional regions using a p-regions problem approach. Int. Region. Sci. Rev. (2013). doi:10.1177/0160017613484929
van der Laan, L., Schalke, R.: Reality versus policy: the delineation and testing of local labour market and spatial policy areas. Eur. Plan. Stud. 9(2), 201–221 (2001)
Leskovec, J., Lang, K.J., Mahoney, M.W.: Network empirical comparison of algorithms for community detection. In: Proceedings of the 19th International Conference on World Wide Web, WWW 2010, April 26–30, AACM New York, NY (2010)
Martínez-Bernabeu, L., Flórez-Revuelta, F., Casado-Díaz, J.M.: Grouping genetic operators for the delineation of functional areas based on spatial interaction. Expert Syst. Appl. 39, 6754–6766 (2012)
Masser, I., Brown, P.J.B.: Hierarchical aggregation procedures for interaction data. Environ. Planning 7, 509–523 (1975)
Nagamochi, H., Ibaraki, T.: Computing edge-connectivity in multigraphs and capacitated graphs. SIAM J. Discr. Math. 5, 54–66 (1992)
Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, New York (1988)
Orasi, A., Sforzi, F.: I sistemi locali del lavoro 2001. ISTAT research report published online (2005). http://www.istat.it/it/files/2014/12/nota-metodologica_SLL2011_rev20150205.pdf. Accessed 18 Sept 2015
Ricca, F., Scozzari, A., Simeone, B.: Political districting: from classical models to recent approaches. Ann. Oper. Res. 204, 271–299 (2013)
Sforzi, F., Openshaw, S., Wymer, C.: La delimitazione di sistemi spaziali sub-regionali: scopi, algoritmi, applicazioni. In: 3rd AISRe Annual Conference, Venezia, 10–12 Nov 1982
Sforzi, F. (ed.): I mercati locali del lavoro in Italia. ISTAT-IRPET, Seminario su: Identificazione di sistemi territoriali. Analisi della struttura sociale e produttiva in Italia, Roma 3–4 Dec 1986
Sforzi, F. (ed.): I Mercati Locali del Lavoro in Italia. Franco Angeli, Milan (1989)
Sforzi, F., Openshaw, S., Wymer, C.: La procedura di identificazione dei sistemi locali del lavoro. ISTAT, I Sistemi Locali del Lavoro 1991, pp. 235–247, Rome (1997)
Sforzi, F.: From administrative spatial units to local labour market areas. Some remarks on the unit of investigation of regional economics with particular reference to the applied research in Italy. In: Fernández-Vázquez, E., Rubiera-Morollón, F. (eds.) Defining the Spatial Scale in Modern Regional Analysis, pp. 3–21. Springer, Berlin (2012)
Smart, M.W.: Labour market areas: uses and definition. Progr. Planning 2(4), 239–353 (1974)
Stoer, M., Wagner, F.: A simple min-cut algorithm. J. ACM 44(4), 585–591 (1997)
van der Zwan, J., van der Wel, R., de Jong, T., Floor, H.: Flowmap 7.2 Manual. Faculty of Geosciences, University of Utrecht, Utrecht (2005)
White, S., Smyth, P.A.: Spectral clustering approach to finding communities in graphs. In: Proceedings of the 5th SIAM International Conference on Data Mining, pp. 76–84 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bianchi, G., Bruni, R., Reale, A. et al. A min-cut approach to functional regionalization, with a case study of the Italian local labour market areas. Optim Lett 10, 955–973 (2016). https://doi.org/10.1007/s11590-015-0980-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11590-015-0980-6