On-line 3-chromatic graphs—II: critical graphs
Discrete Mathematics
Guaranteeing Fair Service to Persistent Dependent Tasks
SIAM Journal on Computing
On the performance of the First-Fit coloring algorithm on permutation graphs
Information Processing Letters
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Developments from a June 1996 seminar on Online algorithms: the state of the art
Scheduling with conflicts on bipartite and interval graphs
Journal of Scheduling - Special issue: On-line scheduling
On-line partitioning for on-line scheduling with resource conflicts
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
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Dynamics is an inherent feature of many real life systems so it is natural to define and investigate the properties of models that reflect their dynamic nature. Dynamic graph colorings can be naturally applied in system modeling, e.g. for scheduling threads of parallel programs, time sharing in wireless networks, session scheduling in high-speed LAN's, channel assignment in WDM optical networks as well as traffic scheduling. In the dynamic setting of the problem, a graph we color is not given in advance and new vertices together with adjacent edges are revealed one after another at algorithm's input during the coloring process. Moreover, independently of the algorithm, some vertices may lose their colors and the algorithm may be asked to color them again. We formally define a dynamic graph coloring problem, the dynamic chromatic number and prove various bounds on its value. We also analyze the effectiveness of the dynamic coloring algorithm Dynamic-Fit for selected classes of graphs. In particular, we deal with trees, products of graphs and classes of graphs for which Dynamic-Fit is competitive. Motivated by applications, we state the problem of dynamic coloring with discoloring constraints for which the performance of the dynamic algorithm Time-Fit is analyzed and give a characterization of graphs k-critical for Time-Fit. Since for any fixed k 0 the number of such graphs is finite, it is possible to decide in polynomial time whether Time-Fit will always color a given graph with at most k colors.