Bonomo, Flavia and Mattia, Sara and Oriolo, Gianpaolo (2010) Bounded coloring of co-comparability graphs and the pickup and delivery tour combination problem. Technical Report. Department of Computer and System Sciences Antonio Ruberti, Roma.
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Abstract
The Double Traveling Salesman Problem with Multiple Stacks is a vehicle routing problem in which pickups and deliveries must be performed in two independent networks. The items are stored in stacks and repacking is not allowed. Given a pickup and a delivery tour, the problem of checking if there exists a valid distribution of items into s stacks of size h that is consistent with the given tours, is known as Pickup and Delivery Tour Combination (PDTC) problem. In the paper, we show that the PDTC problem can be solved in polynomial time when the number s of stacks is fixed but the size of each stack is not. We build upon the equivalence between the PDTC problem and the bounded coloring (BC) problem on permutation graphs: for the latter problem, s is the number of colors and h is the number of vertices that can get a same color. We show that the BC problem can be solved in polynomial time when s is a fixed constant on co-comparability graphs, a superclass of permutation graphs. To the contrary, the BC problem is known to be hard on permutation graphs when h >= 6 is a fixed constant, but s is unbounded [25].
| Item Type: | Monograph (Technical Report) |
|---|---|
| Uncontrolled Keywords: | bounded coloring, capacitated coloring, equitable coloring, per-mutation graphs, scheduling problems, thinness |
| Subjects: | 600 Tecnologia - Scienze applicate > 620 Ingegneria e attivita' affini > 629 Altri rami dell'ingegneria |
| Depositing User: | Sapienza Università di Roma Dipartimento di Ingegneria informatica, automatica e gestionale |
| Date Deposited: | 30 Mar 2010 |
| Last Modified: | 20 May 2010 12:03 |
| URI: | http://eprints.bice.rm.cnr.it/id/eprint/1445 |
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