Locating battery charging stations to facilitate almost shortest paths

Abstract We study a facility location problem motivated by requirements pertaining to the distribution of charging stations for electric vehicles: Place a minimum number of battery charging stations at a subset of nodes of a network, so that battery-powered electric vehicles will be able to move between destinations using “ t -spanning” routes, of lengths within a factor t > 1 of the length of a shortest path, while having sufficient charging stations along the way. We give constant-factor approximation algorithms for minimizing the number of charging stations, subject to the t -spanning constraint. We study two versions of the problem, one in which the stations are required to support a single ride (to a single destination), and one in which the stations are to support multiple rides through a sequence of destinations, where the destinations are revealed one at a time.

[1]  Andrew Chi-Chih Yao,et al.  On Constructing Minimum Spanning Trees in k-Dimensional Spaces and Related Problems , 1977, SIAM J. Comput..

[2]  Michael Segal,et al.  A simple improved distributed algorithm for minimum CDS in unit disk graphs , 2005, WiMob'2005), IEEE International Conference on Wireless And Mobile Computing, Networking And Communications, 2005..

[3]  Rajiv Gandhi,et al.  Distributed Algorithms for Coloring and Domination in Wireless Ad Hoc Networks , 2004, FSTTCS.

[4]  Majid Sarrafzadeh,et al.  Theoretical Bound and Practical Analysis of Connected Dominating Set in Ad Hoc and Sensor Networks , 2008, DISC.

[5]  F. Frances Yao,et al.  Two-Phased Approximation Algorithms for Minimum CDS in Wireless Ad Hoc Networks , 2008, 2008 The 28th International Conference on Distributed Computing Systems.

[6]  Minming Li,et al.  Tighter Approximation Bounds for Minimum CDS in Wireless Ad Hoc Networks , 2009, ISAAC.

[7]  Weili Wu,et al.  Minimum connected dominating sets and maximal independent sets in unit disk graphs , 2006, Theor. Comput. Sci..

[8]  Charles J. Colbourn,et al.  Unit disk graphs , 1991, Discret. Math..

[9]  Deying Li,et al.  A polynomial‐time approximation scheme for the minimum‐connected dominating set in ad hoc wireless networks , 2003, Networks.

[10]  Weili Wu,et al.  Analysis on Theoretical Bounds for Approximating Dominating Set Problems , 2009, Discret. Math. Algorithms Appl..

[11]  Giri Narasimhan,et al.  Geometric spanner networks , 2007 .

[12]  Peng-Jun Wan,et al.  Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks , 2004, Mob. Networks Appl..

[13]  Prosenjit Bose,et al.  Stable Roommates Spanner , 2013, Comput. Geom..

[14]  Stefan Funke,et al.  Placement of Loading Stations for Electric Vehicles: No Detours Necessary! , 2014, AAAI.

[15]  Carl Gutwin,et al.  Classes of graphs which approximate the complete euclidean graph , 1992, Discret. Comput. Geom..

[16]  Stefan Funke,et al.  Enabling E-Mobility: Facility Location for Battery Loading Stations , 2013, AAAI.

[17]  Harry B. Hunt,et al.  Simple heuristics for unit disk graphs , 1995, Networks.