Capacity-Constrained Network-Voronoi Diagram

Yang, KwangSoo; Shekhar, Apurv Hirsh; Oliver, Dev; Shekhar, Shashi

doi:10.1109/icde.2016.7498423

Cited by 3 publications

(4 citation statements)

References 7 publications

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“…This results in highly restrictive scope of possible improvement. For instance, the METIS approach cannot create balanced and contiguous partitions [97]. (3) Multi-level approaches perform graph partitioning by varying the granularity of the graphs [80,90,91].…”

Section: Approachesmentioning

confidence: 99%

“…Capacity-Constrained Network-Voronoi Diagram. Problems like districting, specially school districting, can be treated as a Capacity Constrained Network-Voronoi Diagram (CCNVD): "Given a graph and a set of service center nodes, a CCNVD partitions the graph into a set of contiguous service areas that meet service center capacities and minimize the sum of the shortest distances from graph-nodes to allotted service centers" [96,97]. For the school districting problem, the service centers represent the spatial units containing schools inside them.…”

Section: Approachesmentioning

confidence: 99%

“…For the school districting problem, the service centers represent the spatial units containing schools inside them. The Pressure Equalizer (PE) algorithm and its variants were proposed by Yang et al [96,97] to address CCNVD. However, some important differences do exist.…”

Section: Approachesmentioning

confidence: 99%

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Memetic algorithms for Spatial Partitioning problems

Biswas,

Chen,

Chen

et al. 2022

Preprint

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Spatial optimization problems (SOPs) are characterized by spatial relationships governing the decision variables, objectives, and/or constraint functions. In this article, we focus on a specific type of SOP called spatial partitioning, which is a combinatorial problem due to the presence of discrete spatial units. Exact optimization methods do not scale with the size of the problem, especially within practicable time limits. This motivated us to develop population-based metaheuristics for solving such SOPs. However, the search operators employed by these population-based methods are mostly designed for real-parameter continuous optimization problems. For adapting these methods to SOPs, we apply domain knowledge in designing spatially-aware search operators for efficiently searching through the discrete search space while preserving the spatial constraints. To this end, we put forward a simple yet effective algorithm called swarm-based spatial memetic algorithm (SPATIAL) and test it on the school (re)districting problem. Detailed experimental investigations are performed on real-world datasets to evaluate the performance of SPATIAL. Besides, ablation studies are performed to understand the role of the individual components of SPATIAL. Additionally, we discuss how SPATIAL is helpful in the real-life planning process and its applicability to different scenarios and motivate future research directions.

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Section: Approachesmentioning

confidence: 99%

Section: Approachesmentioning

confidence: 99%

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Memetic algorithms for Spatial Partitioning problems

Biswas,

Chen,

Chen

et al. 2022

Preprint

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“…The current state of the art most relevant to our work includes the work done in the area of network voronoi diagrams without capacities [6,3], network voronoi diagrams under capacity constraints [13,10,9], weighted voronoi diagrams [1] and optimal location queries (e.g., [14,11,5,4]) Work done in the area of network voronoi diagrams without capacities [6,3] assume that the service centers have infinite capacity, an assumption not suitable in many real-world scenarios. On the other hand, work done in the area of network voronoi diagrams with capacities [13,10,9,12] did not consider the notion of "overload penalty." They perform allotments (of demand units) in an iterative fashion as long as there exists a service center with available capacity.…”

Section: Limitations Of Related Workmentioning

confidence: 99%

Optimal Load Balanced Demand Distribution under Overload Penalties

Ramnath¹,

Gunturi²

2020

Preprint

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Input to the Load Balanced Demand Distribution (LBDD) consists of the following: (a) a set of service centers; (b) a set of demand nodes and; (c) a cost matrix containing the cost of assignment for each (demand node, service center) pair. In addition, each service center is also associated with a notion of capacity and a penalty which is incurred if it gets overloaded. Given the input, the LBDD problem determines a mapping from the set of n demand vertices to the set of k service centers, n k. The objective is to determine a mapping that minimizes the sum of the following two terms: (i) the total cost between demand units and their allotted service centers and, (ii) total penalties incurred. The problem of LBDD finds its application in a variety of applications. An instance of the LBDD problem can be reduced to an instance of the min-cost bi-partite matching problem. The best known algorithm for min-cost matching in an unbalanced bipartite graph yields a complexity of O(n 3 k). This paper proposes novel allotment subspace re-adjustment based approach which allows us to characterize the optimality of the mapping without invoking matching or mincost flow. This approach yields an optimal solution with time complexity O(nk 3 + nk 2 log n), and also allows us to efficiently maintain an optimal allotment under insertions and deletions.

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