An on-line graph coloring algorithm with sublinear performance ratio
Discrete Mathematics
On-Line Coloring and Recursive Graph Theory
SIAM Journal on Discrete Mathematics
Handbook of combinatorics (vol. 1)
Parallel and on-line graph coloring
Journal of Algorithms
On-line chain partitions of orders
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
Discrete Applied Mathematics
On the performance of the First-Fit coloring algorithm on permutation graphs
Information Processing Letters
Dispatching Buses in Parking Depots
Transportation Science
Shunting of Passenger Train Units in a Railway Station
Transportation Science
Journal of Discrete Algorithms
On minimum k-modal partitions of permutations
Journal of Discrete Algorithms
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This paper aims to start an analytical study of the computational complexity of some online shunting problems. We analyze the following problem. Consider a train station consisting of a set of parallel tracks. Each track can be approached from one side only or from both sides and the number of trains per track may be limited or not. The departure times of the trains are fixed according to a given time table. The problem is to assign a track to each train as soon as it arrives and such that it can leave the station on time without being blocked by any other train. We show that this problem can be modeled with online coloring of graphs. Depending on the constraints, the graphs can be overlap graphs (also known as circle graphs) or permutation graphs, and the coloring can be bounded or classical. This paper covers several combinations of these cases.