An on-line graph coloring algorithm with sublinear performance ratio
Discrete Mathematics
Online matching with blocked input
Information Processing Letters
Smallest-last ordering and clustering and graph coloring algorithms
Journal of the ACM (JACM)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Lower bounds for on-line graph problems with application to on-line circuit and optical routing
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Delayed information and action in on-line algorithms
Information and Computation
Randomized Lower Bounds for Online Path Coloring
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Advice complexity of online coloring for paths
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Tight bounds for online vector bin packing
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Circumference, chromatic number and online coloring
Combinatorica
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An algorithm for vertex-coloring graphs is said to be online if each vertex is irrevocably assigned a color before any later vertices are considered. We show that such algorithms are inherently ineffective. The performance ratio of any such algorithm can be no better than &OHgr;(n/log2 n), even for randomized algorithms against oblivious adversary.We also show that various means of relaxing the constraints of the on-line model do not reduce these lower bounds. The features include presenting the input in blocks of log2 n vertices, recoloring any fraction of the vertices, presorting vertices according to degree, and disclosing the adversary's previous coloring.