Abstract
Input to the problem of Load Balanced Network Voronoi Diagram (LBNVD) consists of the following: (a) a road network represented as a directed graph; (b) locations of service centers (e.g., schools in a city) as vertices in the graph and; (c) locations of demand (e.g., school children) also as vertices in the graph. In addition, each service center is also associated with a notion of capacity and an overload penalty which is “charged” if the service center gets overloaded. Given the input, the goal of the LBNVD problem is to determine an assignment where each of the demand vertices is allotted to a service center. The objective here is to generate an assignment which minimizes the sum of the following two terms: (i) total distance between demand vertices and their allotted service centers and, (ii) total penalties incurred while overloading the service centers. The problem of LBNVD finds its application in the domain of urban planning. Research literature relevant to this problem either assume infinite capacity or do not consider the concept of “overload penalty.” These assumptions are relaxed in our LBNVD problem. We develop a novel algorithm for the LBNVD problem and provide a theoretical upper bound on its worst-case performance (in terms of solution quality). We also present the time complexity of our algorithm and compare against the related work experimentally using real datasets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In case it had more boundary vertices, it would have considered the boundary vertex which lead to lowest increase in objective function.
References
Wikipedia: Catchment area. http://en.wikipedia.org/w/index.php?title=Catchment%20area
Okabe, A., et al.: Generalized network voronoi diagrams: concepts, computational methods, and applications. Int. J. GIS 22(9), 965–994 (2008)
Demiryurek, U., Shahabi, C.: Indexing network voronoi diagrams. In: Lee, S., Peng, Z., Zhou, X., Moon, Y.-S., Unland, R., Yoo, J. (eds.) DASFAA 2012. LNCS, vol. 7238, pp. 526–543. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29038-1_38
Yang, K., et al.: Capacity-constrained network-voronoi diagram. IEEE Trans. Knowl. Data Eng. 27(11), 2919–2932 (2015)
U, L.H., et al.: Optimal matching between spatial datasets under capacity constraints. ACM Trans. Database Syst. 35(2), 9:1–9: 44 (2010)
U, L.H., et al.: Capacity constrained assignment in spatial databases. In: Proceeding of the International Conference on Management of Data (SIGMOD), pp. 15–28 (2008)
Aurenhammer, F.: Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16(1), 78–96 (1987)
Yao, B., et al.: Dynamic monitoring of optimal locations in road network databases. VLDB J. 23(5), 697–720 (2014)
Xiao, X., Yao, B., Li, F.: Optimal location queries in road network databases. In: Proceedings of the 27th International Conference on Data Engineering (ICDE), pp. 804–815 (2011)
Diabat, A.: A capacitated facility location and inventory management problem with single sourcing. Optim. Lett. 10(7), 1577–1592 (2016)
Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms, 2nd edn. McGraw-Hill Higher Education, New York (2001)
Delling, D., et al.: PHAST: hardware-accelerated shortest path trees. J. Parallel Distrib. Comput. 73(7), 940–952 (2013)
Bast, H., et al.: Fast routing in road networks with transit nodes. Science 316(5824), 566 (2007)
Jing, N., et al.: Hierarchical encoded path views for path query processing: an optimal model and its performance evaluation. IEEE Trans. KDE 10(3), 409–432 (1998)
Bortnikov, E., Khuller, S., Li, J., Mansour, Y., Naor, J.S.: The load-distance balancing problem. Networks 59(1), 22–29 (2012)
Kleinberg, J., Tardos, E.: Algorithm Design. Pearson Education, London (2009)
Acknowledgement
We would like to thank Prof Sarnath Ramnath, St. Cloud State University and the reviewers of DEXA 2018 for giving their valuable feedback towards improving this paper. This paper was in part supported by the IIT Ropar, Infosys Center for AI at IIIT Delhi and DST SERB (ECR/2016/001053).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Mehta, A., Malik, K., Gunturi, V.M.V., Goel, A., Sethia, P., Aggarwal, A. (2018). Load Balancing in Network Voronoi Diagrams Under Overload Penalties. In: Hartmann, S., Ma, H., Hameurlain, A., Pernul, G., Wagner, R. (eds) Database and Expert Systems Applications. DEXA 2018. Lecture Notes in Computer Science(), vol 11029. Springer, Cham. https://doi.org/10.1007/978-3-319-98809-2_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-98809-2_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-98808-5
Online ISBN: 978-3-319-98809-2
eBook Packages: Computer ScienceComputer Science (R0)