Routing and scheduling on a shoreline with release times
Management Science
A heuristic with worst-case analysis for minimax routing of two travelling salesmen on a tree
Discrete Applied Mathematics
(p-1)/(p+1)-approximate algorithms for p-traveling salemen problems on a tree with minmax objective
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Theoretical Computer Science
Linear time approximation schemes for vehicle scheduling problems
Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
Minmax subtree cover problem on cacti
Discrete Applied Mathematics
Minmax Tree Cover in the Euclidean Space
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Minmax subtree cover problem on cacti
Discrete Applied Mathematics
Approximation results for a min-max location-routing problem
Discrete Applied Mathematics
Approximating the minmax subtree cover problem in a cactus
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Improved approximation algorithms for routing shop scheduling
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Theoretical Computer Science
Vehicle routing problems on a line-shaped network with release time constraints
Operations Research Letters
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In this paper, given a path G with n vertices v1, v2....,vn and m identical vehicles, we consider a scheduling problem of the vehicles on the path. Each vertex vj in G has exactly one job j. Any of the n jobs must be served by some vehicle. Each job j has a release time rj and a handling time hj. A travel time We is associated with each edge e. The problem asks to find an optimal schedule of the m vehicles that minimizes the maximum completion time of all jobs. It is already known that the problem is NP-hard for any fixed m ≥ 2. In this paper, we first present an O(mn2) time 2-approximation algorithm to the problem, by using properties of optimal gapless schedules. We then give a nearly linear time algorithm that delivers a (2 + ε)-approximation solution for any fixed ε 0.