Routing and scheduling on a shoreline with release times
Management Science
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Constrained TSP and Low-Power Computing
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Approximation Hardness of TSP with Bounded Metrics
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
On-Line Algorithms for the Dynamic Traveling Repair Problem
Journal of Scheduling
Theoretical Computer Science
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We consider makespan minimization for vehicle scheduling problems on trees with release and handling times. 2-approximation algorithms were known for several variants of the single vehicle problem on a path [16]. A 3/2-approximation algorithm was known for the single vehicle problem on a path where there is a fixed starting point and the vehicle must return to the starting point upon completion [13]. Karuno, Nagamochi and Ibaraki give a 2-approximation algorithm for the single vehicle problem on trees. We develop a linear time PTAS for the single vehicle scheduling problem on trees which have a constant number of leaves. This PTAS can be easily adapted to accommodate various starting/ending constraints. We then extended this to a PTAS for the multiple vehicle problem where vehicles operate in disjoint subtrees. For this problem, the only previous result is a 2-approximation algorithm for paths [10]. Finally, we present competitive online algorithms for some single vehicle scheduling problems.