Local re-adjustment based approaches for load balanced network voronoi diagram

Abstract

Input to the Load Balanced Network Voronoi Diagram (LBNVD) consists of the following: (a) a transportation network represented as a directed graph; (b) locations of public service units (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 a penalty which is incurred if it gets overloaded. Given the input, the goal of the LBNVD problem is to determine a partition of the demand vertices around service centers where each service center gets a unique partition. The objective here is to generate a partition which minimizes the sum of the total distance between demand vertices and their associated service center and the penalties incurred. The problem of LBNVD finds its application in the domain of urban planning. The current state of the art related to LBNVD makes simplifying assumptions such as infinite capacity or total capacity being equal to the total demand. We propose a novel concept of Local Re-Adjustment based approaches for the problem of LBNVD. Using this concept, we propose three algorithms for the LBNVD problem. The proposed algorithms are evaluated both theoretically and experimentally using real datasets.