TY - JOUR
T1 - Theory and practice in large carpooling problems
AU - Hartman, Irith Ben Arroyo
AU - Keren, Daniel
AU - Dbai, Abed Abu
AU - Cohen, Elad
AU - Knapen, Luk
AU - Yasar, Ansar Ul Haque
AU - Janssens, Davy
N1 - Funding Information: We have defined the carpooling problem as a graph-theoretic, NP-hard problem. If the drivers of the cars are known in advance then the problem is tractable and is of complexity O(|V|3). We found that the greedy linear algorithm gives close to optimal results in this case. We have also found and implemented quick and efficient incremental solutions for a ‘perturbed’ graph, where some of its edges change. In addition, we found and implemented a fast heuristic algorithm, based on an algebraic approach, which can be parallelized for very large graphs. We suggested and implemented on real data several heuristics for the general intractable problem using linear and almost linear heuristics, and compared between them. Finally, we defined extensions of the carpooling problems where the drivers are known, by allowing the passengers to indicate their priorities, and showed that these extensions are NP-hard. Acknowledgments The research leading to these results has received funding from the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement no 270833.
PY - 2014
Y1 - 2014
N2 - We address the carpooling problem as a graph-theoretic problem. If the set of drivers is known in advance, then for any car capacity, the problem is equivalent to the assignment problem in bipartite graphs. Otherwise, when we do not know in advance who will drive their vehicle and who will be a passenger, the problem is NP-hard. We devise and implement quick heuristics for both cases, based on graph algorithms, as well as parallel algorithms based on geometric/algebraic approach. We compare between the algorithms on random graphs, as well as on real, very large, data.
AB - We address the carpooling problem as a graph-theoretic problem. If the set of drivers is known in advance, then for any car capacity, the problem is equivalent to the assignment problem in bipartite graphs. Otherwise, when we do not know in advance who will drive their vehicle and who will be a passenger, the problem is NP-hard. We devise and implement quick heuristics for both cases, based on graph algorithms, as well as parallel algorithms based on geometric/algebraic approach. We compare between the algorithms on random graphs, as well as on real, very large, data.
KW - Carpooling
KW - Gradient Projection Algorithm
KW - Incremental Algorithms
KW - Linear Programming
KW - Maximum Weighted Matching
KW - Scalability
KW - Star Partition Problem
UR - http://www.scopus.com/inward/record.url?scp=84902688622&partnerID=8YFLogxK
U2 - 10.1016/j.procs.2014.05.433
DO - 10.1016/j.procs.2014.05.433
M3 - مقالة من مؤنمر
SN - 1877-0509
VL - 32
SP - 339
EP - 347
JO - Procedia Computer Science
JF - Procedia Computer Science
T2 - 5th International Conference on Ambient Systems, Networks and Technologies, ANT 2014 and 4th International Conference on Sustainable Energy Information Technology, SEIT 2014
Y2 - 2 June 2014 through 5 June 2014
ER -
