Skip to main content

Optimal Matching Between Spatial Datasets

  • Living reference work entry
  • First Online:
Encyclopedia of GIS
  • 75 Accesses

Synonyms

Graph incremental algorithm; Linear optimization; Spatial matching

Definition

In spatial databases, optimal matching refers to an assignment A between two set of spatial datasets (e.g., customers P and service providers Q) such that the assignment \(A \subseteq Q \times P\) optimizes the quality of services (i.e., the quality of an assignment pair (q, p) can be measured by their Euclidean distance) subject to their capacity constraints (i.e., a service can serve up to kcustomers concurrently). Typically this problem can be solved by combinatorial optimization solvers or network flow based solutions, where these solutions require a distance-based affiliation matrix between the service providers and clients. For large spatial datasets, the affiliation matrix is expensive to compute and it may be too large to fit in main memory. Motivated by this challenge, some efficient algorithms are proposed for optimal matching that employ novel pruning strategies, based on the spatial...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  • Beckmann N, Kriegel H-P, Schneider R, Seeger B (1990) The R∗-tree: an efficient and robust access method for points and rectangles. In: SIGMOD conference, Atlantic City, NJ, USA, pp 322–331

    Google Scholar 

  • Corral A, Manolopoulos Y, Theodoridis Y, Vassilakopoulos M (2000) Closest pair queries in spatial databases. In: SIGMOD conference, Dallas, Texas, USA, pp 189–200

    Google Scholar 

  • Derigs U (1981) A shortest augmenting path method for solving minimal perfect matching problems. Networks 11(4):379–390

    Article  MathSciNet  MATH  Google Scholar 

  • Gabow HN, Tarjan RE (1991) Faster scaling algorithms for general graph-matching problems. J ACM 38(4):815–853

    Article  MathSciNet  MATH  Google Scholar 

  • Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69(1):9–15

    Article  MathSciNet  MATH  Google Scholar 

  • Goldberg AV, Kennedy R (1995) An efficient cost scaling algorithm for the assignment problem. Math. Program 71:153–177

    MathSciNet  MATH  Google Scholar 

  • Gross O (1959) The bottleneck assignment problem. P (Rand Corporation). Rand Corporation

    Google Scholar 

  • Gusfield D, Irving RW (1989) The stable marriage problem: structure and algorithms. MIT, Cambridge

    MATH  Google Scholar 

  • Guttman A (1984) R-trees: a dynamic index structure for spatial searching. In: SIGMOD conference, Boston, Massachusetts, USA, pp 47–57

    Google Scholar 

  • Hjaltason GR, Samet H (1999) Distance browsing in spatial databases. ACM Trans Database Syst 24(2): 265–318

    Article  Google Scholar 

  • Hung M (1983) A polynomial simplex method for the assignment problem. Oper Res 31:595–600

    Article  MathSciNet  MATH  Google Scholar 

  • Kuhn HW (1955) The Hungarian method for the assignment problem. Nav Res Logist Q 2:83–97

    Article  MathSciNet  MATH  Google Scholar 

  • Long C, Wong RC-W, Yu PS, Jiang M (2013) On optimal worst-case matching. In: Proceedings of the ACM SIGMOD international conference on management of data (SIGMOD), New York, USA, 22–27 June 2013, pp 845–856

    Google Scholar 

  • Munkres J (1957) Algorithms for the assignment and transportation problems. J Soc Ind Appl Math 5(1): 32–38

    Article  MathSciNet  MATH  Google Scholar 

  • Orlin JB, Lee Y (1993) QuickMatch–a very fast algorithm for the assignment problem. Working papers 3547-93., Massachusetts Institute of Technology (MIT), Sloan School of Management

    Google Scholar 

  • Sellis TK, Roussopoulos N, Faloutsos C (1987) The R+-tree: a dynamic index for multi-dimensional objects. In: VLDB, Brighton, England, pp 507–518

    Google Scholar 

  • U LH, Mamoulis N, Yiu ML (2008) Computation and monitoring of exclusive closest pairs. IEEE Trans Knowl Data Eng 20(12):1641–1654

    Google Scholar 

  • U LH, Mouratidis K, Mamoulis N (2010) Continuous spatial assignment of moving users. VLDB J 19(2): 141–160

    Google Scholar 

  • U LH, Mouratidis K, Yiu ML, Mamoulis N (2010) Optimal matching between spatial datasets under capacity constraints. ACM Trans Database Syst 35(2):9:1–9:44

    Google Scholar 

  • Wong RC-W, Tao Y, Fu AW-C, Xiao X (2007) On efficient spatial matching. In: VLDB, University of Vienna, Austria, pp 579–590

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Leong Hou U .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this entry

Cite this entry

U, L. (2015). Optimal Matching Between Spatial Datasets. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-23519-6_1518-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23519-6_1518-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Cham

  • Online ISBN: 978-3-319-23519-6

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

Publish with us

Policies and ethics