Modular Circulation and Applications to Traffic Management
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.
KeywordsNetwork flows and circulations Traffic management Approximation algorithms NP-hard problems
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- 1.Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall (1993)Google Scholar
- 2.Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms, 2nd edn. McGraw-Hill Higher Education (2001)Google Scholar
- 4.Dresner, K.M., Stone, P.: A multiagent approach to autonomous intersection management. J. Artif. Int. Res. 31, 591–656 (2008)Google Scholar
- 5.Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co. (1979)Google Scholar
- 10.Vial, J.J.B., Devanny, W.E., Eppstein, D., Goodrich, M.T.: Scheduling autonomous vehicle platoons through an unregulated intersection. In: Goerigk, M., Werneck, R. (eds.) 16th Wkshp. Alg. Approaches Transport. Model., Opt., and Syst. (ATMOS 2016), vol. 54, pp. 1–14 (2016)Google Scholar