D. J. Guan, Routing a vehicle of capacity greater than one, Discrete Applied Mathematics 81 (1998), no. 1, 41--57. 169  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a 9 5 approximation algorithm for the stacker craneproblem on general graphs. An improved algorithm for trees with performance 5 4 is given in [FG93] On paths the stacker crane problem can be solved in polynomial time [AK88] The problem CDARP with server capacity C 1 has been addressed in [Gua98, CR98] For capacity C 1 the problem becomes NP hard even on paths. In [CR98] an approximation algorithm with performance # C log n log log n) was given, where C denotes the capacity of the server and n denotes the number of vertices in the graph. We will investigate CDARP with server capacity ....

....of the correctness and the performance of the algorithm is divided into several parts. It is contained in Sections 7.3 to 7.5. Elevator with capacity 2 and path G[E] representing the transportation network. Guan showed that the CDARP is NP hard even on paths if the capacity of the server is two [Gua98] A version of the proof can be found in [Wei00] The preemptive version is polynomial time solvable on paths [Gua98] but NP hard even on trees and even if the capacity of the server is one [FG93] In [CR98] an approximation algorithm for the CDARP on general graphs with performance # C log n ....

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D. J. Guan, Routing a vehicle of capacity greater than one, Discrete Applied Mathematics 81 (1998), no. 1, 41--57. 169

....15, 16] Frederickson and Guan [16] showed that the unit capacity non preemptive case is NP hard on trees. A special case of the preemptive problem on the line for general k was considered by Karp [23] see also Knuth [24, Section 5.4.8] who called it the static elevator scheduling problem. Guan [19] improved Karp s result to give a fast algorithm for the preemptive case on the line for general k and proved NP hardness for the non preemptive problem on the line with k = 2 as well as the preemptive problem on trees with k = 2. Arkin, Hassin and Klein [2] investigated the problem with k = 1 and ....

....capacity; i.e. for any capacity p k, the approximation ratio is still O( p k) 4. 3 Line metrics For points on a line, where the distances are measured along the line, we provide an algorithm with approximation ratio of 2 for the Capacitated Dial a Ride problem (non preemptive case) Guan [19] showed that the problem can be solved optimally in polynomial time if drops are allowed (preemptive case) Due to lack of space, we omit the proof of the following theorem. Theorem 10 There is an algorithm that runs in polynomial time for the non preemptive Capacitated Diala Ride problem with a ....

D. J. Guan, \Routing a vehicle of capacity greater than one," Discrete Applied Mathematics, 81:41-57, (1998).

....15, 16] Frederickson and Guan [16] showed that the unit capacity non preemptive case is NP hard on trees. A special case of the preemptive problem on the line for general k was considered by Karp [23] see also Knuth [24, Section 5.4.8] who called it the static elevator scheduling problem. Guan [19] improved Karp s result to give a fast algorithm for the preemptive case on the line for general k and proved NP hardness for the non preemptive problem on the line with k = 2 as well as the preemptive problem on trees with k = 2. Arkin, Hassin and Klein [2] investigated the problem with k = 1 and ....

....capacity; i.e. for any capacity p k, the approximation ratio is still O( p k) 4. 3 Line metrics For points on a line, where the distances are measured along the line, we provide an algorithm with approximation ratio of 2 for the Capacitated Dial a Ride problem (nonpreemptive case) Guan [19] showed that the problem can be solved optimally in polynomial time if drops are allowed (preemptive case) Due to lack of space, we omit the proof of the following theorem. Theorem 10 There is an algorithm that runs in polynomial time for the non preemptive Capacitated Dial a Ride problem with a ....

D. J. Guan, "Routing a vehicle of capacity greater than one," Discrete Applied Mathematics, 81:41-57, (1998).

....that the problem can be solved in polynomial time on paths but is NP hard on caterpillars. Approximation algorithms for general graphs and also improved results for trees are presented. Preemptive versions of DARP, where objects are allowed to be dropped at intermediate vertices, are studied in [11, 8]. 3. THE SIMULATION MODEL Our simulation programs are built on top of AMSEL [1] a callable C library to design event based simulation programs. The input data consists of a set of event points, a set of modules, and a collection of requests. Every request becomes an object which flows through the ....

D. J. Guan, Routing a vehicle of capacity greater than one, Discrete Applied Mathematics 81 (1998), no. 1, 41--57.

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D. J. Guan, Routing a vehicle of capacity greater than one, Discrete Applied Mathematics 81 (1998), no. 1, 41-57.

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D. J. Guan, Routing a vehicle of capacity greater than one, Discrete Applied Mathematics 81 (1998), no. 1, 41--57.

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D. J. Guan, Routing a vehicle of capacity greater than one, Discrete Applied Mathematics 81 (1998), no. 1, 41--57. KONRAD-ZUSE-ZENTRUM F UR INFORMATIONSTECHNIK BERLIN, DEPARTMENT OPTIMIZATION, TAKUSTR. 7, 14195 BERLIN-DAHLEM, GERMANY. E-mail address: fascheuer,krumke,rambaug@zib.de

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