Abstract:
Abstract. Given n identical objects (pegs), placed at arbitrary initial locations, we consider the problem of transporting them eciently to n target locations (slots) with a vehicle that can carry at most k pegs at a time. This problem is referred to as k-delivery TSP, and it is a generalization of the Traveling Salesman Problem. We give a 5-approximation algorithm for the problem of minimizing the total distance traveled by the vehicle. There are two kinds of transportations possible | one that could drop pegs at intermediate locations and pick them up later in the route for delivery (preemptive) and one that transports pegs to their targets directly (non-preemptive). In the former case, by exploiting the freedom to drop, one may be able to nd a shorter delivery route. We construct a non-preemptive tour that is within a factor 5 of the optimal preemptive tour. In addition we show that the ratio of the distances traveled by an optimal non-preemptive tour versus a preemptive tour is bounded by 4.
Citations
|
7715
|
Computers and Intractability: A Guide to the Theory of NP-Completeness
– Garey, Johnson
- 1979
|
|
889
|
Graph Theory with Applications
– Bondy, Murty
- 1976
|
|
292
|
The Art of Computer Programming, Vol. 3: Sorting and Searching
– Knuth
- 1973
|
|
223
|
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
– Arora
- 1996
|
|
130
|
Guillotine subdivisions approximate polygonal subdivisions: Part III - Faster polynomial-time approximation scheme for geometric network optimization, preprint
– Mitchell
- 1997
|
|
80
|
Nearly linear time approximation scheme for Euclidean TSP and other geometric problems
– ARORA
- 1997
|
|
56
|
Approximation algorithms for some routing problems
– Frederickson, Hecht, et al.
- 1978
|
|
27
|
Efficient solutions to some transportation problems with applications to minimizing robot arm travel
– Atallah, Kosaraju
- 1988
|
|
23
|
Preemptive ensemble motion planning on a tree
– Frederickson, Guan
- 1992
|
|
14
|
Approximation algorithms for robot grasp and delivery
– Chalasani, Motwani, et al.
- 1996
|
|
11
|
Covering points in the plane by k-tours: towards a polynomial time approximation scheme for general k
– Asano, Katoh, et al.
- 1997
|
|
11
|
A note on the complexity of a simple transportation problem
– Frederickson
- 1993
|
|
9
|
Vehicle Routing with Backhauls: Models, Algorithms and Case Studies
– Casco, Golden, et al.
- 1988
|
|
9
|
Rinnooy Kan. Bounds and heuristics for capacitated routing problems
– Haimovich, G
- 1985
|
|
8
|
Approximation algorithms for the capacitated traveling salesman problem with pick-ups and deliveries
– Anily, Bramel
- 1997
|
|
7
|
Restricted delivery problems on a network," Networks
– Arkin, Hassin, et al.
- 1997
|
|
6
|
Two combinatorial problems associated with external sorting
– Karp
- 1972
|
|
3
|
The swapping problem," Networks
– Anily, Hassin
- 1992
|
|
2
|
Vehicle routing," in The traveling salesman problem, edited by
– Christo
- 1985
|
|
1
|
Preemptiveensemble motion planning on a tree
– Frederickson, Guan
- 1992
|
|
