Efficient solutions to some transportation problems with applications to minimizing robot arm travel
SIAM Journal on Computing
Scheduling Parallel Machines On-line
SIAM Journal on Computing
Online computation and competitive analysis
Online computation and competitive analysis
On-line single-server dial-a-ride problems
Theoretical Computer Science
Serving Requests with On-line Routing
SWAT '94 Proceedings of the 4th Scandinavian Workshop on Algorithm Theory
Competitive Algorithms for the On-line Traveling Salesman
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
The Finite Capacity Dial-A-Ride Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
On-Line Dial-a-Ride Problems under a Restricted Information Model
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
The Online-TSP against Fair Adversaries
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
The Online Dial-a-Ride Problem under Reasonable Load
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Online dial-a-ride problem with time-windows under a restricted information model
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
On minimizing the maximum flow time in the online dial-a-ride problem
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
On the online dial-a-ride problem with time-windows
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
The on-line asymmetric traveling salesman problem
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Online k-server routing problems
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Algorithms for on-line order batching in an order picking warehouse
Computers and Operations Research
Competitive analysis of a dispatch policy for a dynamic multi-period routing problem
Operations Research Letters
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We consider the following online dial-a-ride problem (OLDARP): Objects are to be transported between points in a metric space. Transportation requests arrive online, specifying the objects to be transported and the corresponding source and destination. These requests are to be handled by a server which starts its work at a designated origin and which picks up and drops objects at their sources and destinations. The server can move at constant unit speed. After the end of its service the server returns to its start in the origin. The goal of OLDARP is to come up with a transportation schedule for the server which finishes as early as possible, i.e., which minimizes the makespan. We analyze several competitive algorithms for OLDARP and establish tight competitiveness results. The first two algorithms, REPLAN and IGNORE are very simple and natural: REPLAN completely discards its (preliminary) schedule and recomputes a new one when a new request arrives. IGNORE always runs a (locally optimal) schedule for a set of known requests and ignores all new requests until this schedule is completed. We show that both strategies, REPLAN and IGNORE, are 5/2-competitive. We then present a somewhat less natural strategy SMARTSTART, which in contrast to the other two strategies may leave the server idle from time to time although unserved requests are known. The SMARTSTART-algorithm has an improved competitive ratio of 2, which matches our lower bound.