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WADS 2017: Algorithms and Data Structures pp 277-288

# Modular Circulation and Applications to Traffic Management

• Philip Dasler
• David M. Mount
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10389)

## Abstract

We introduce a variant of the well-known minimum-cost circulation problem in directed networks, where vertex demand values are taken from the integers modulo $$\lambda$$, for some integer $$\lambda \ge 2$$. More formally, given a directed network $$G = (V,E)$$, each of whose edges is associated with a weight and each of whose vertices is associated with a demand taken over the integers modulo $$\lambda$$, the objective is to compute a flow of minimum weight that satisfies all the vertex demands modulo $$\lambda$$. This problem is motivated by a problem of computing a periodic schedule for traffic lights in an urban transportation network that minimizes the total delay time of vehicles. We show that this modular circulation problem is solvable in polynomial time when $$\lambda = 2$$ and that the problem is NP-hard when $$\lambda = 3$$. We also present a polynomial time algorithm that achieves a $$4(\lambda - 1)$$-approximation.

## Keywords

Network flows and circulations Traffic management Approximation algorithms NP-hard problems

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## Copyright information

© Springer International Publishing AG 2017

## Authors and Affiliations

1. 1.Department of Computer Science and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA