Abstract
Input to the capacity constrained assignment (CCA) problem over road networks consists of the following: (a) a road network represented as a directed graph; (b) a set of public service units (e.g., flu-clinics, schools) as vertices in the graph and; (c) a set of demand locations (e.g., people or school children) also as vertices in the graph. 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 goal of CCA problem is to determine a mapping between the set of demand vertices and the set of service centers. The objective here is to generate a mapping which minimizes the sum of the total distance between demand vertices and their associated service centers, and the total penalty incurred. CCA problem has value addition potential in the domain of urban planning. CCA problem can be reduced to min-cost bipartite matching. However, optimal algorithms for min-cost bipartite matching do not scale beyond graphs of size few thousand nodes. Moreover, its non-trivial to parallelize optimal algorithms for min-cost bipartite matching due to their inherent iterative nature. The current relevant work in the area of parallel algorithms is limited to problems like finding max-flow and maximum cardinality matching, which are fundamentally different than min-cost bipartite matching. In this paper, we propose a novel assignment subspace re-organization based approach (ASRAC) for the CCA problem. ASRAC can load-balance and take full advantage of multi-core systems to speed-up execution. Our experimental results indicate that our proposed algorithm (ASRAC) can scale up to large graphs while maintaining better solution quality over alternative approaches.
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Acknowledgement
Microsoft Azure credits (AI for Health scheme), Mr Kapish Malik, DST (ECR/2016/001053) and IIT Ropar.
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Mishra, A., Gunturi, V.M.V., Ramnath, S. (2020). A Multi-threaded Algorithm for Capacity Constrained Assignment over Road Networks. In: Qiu, M. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2020. Lecture Notes in Computer Science(), vol 12452. Springer, Cham. https://doi.org/10.1007/978-3-030-60245-1_9
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