On the distance constrained vehicle routing problem
Operations Research
Resource-constrained geometric network optimization
Proceedings of the fourteenth annual symposium on Computational geometry
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
Introduction to Algorithms
Algorithms for Capacitated Vehicle Routing
SIAM Journal on Computing
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FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for deadline-TSP and vehicle routing with time-windows
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximations for minimum and min-max vehicle routing problems
Journal of Algorithms
Budgeted matching and budgeted matroid intersection via the gasoline puzzle
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Minimum vehicle routing with a common deadline
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
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In this article we study several routing problems that generalize shortest paths and the traveling salesman problem. We consider a more general model that incorporates the actual cost in terms of gas prices. We have a vehicle with a given tank capacity. We assume that at each vertex gas may be purchased at a certain price. The objective is to find the cheapest route to go from s to t, or the cheapest tour visiting a given set of locations. We show that the problem of finding a cheapest plan to go from s to t can be solved in polynomial time. For most other versions, however, the problem is NP-complete and we develop polynomial-time approximation algorithms for these versions.